AA+ v2.53

Welcome to AA+, a collection of freeware C++ classes which provide an implementation of the algorithms as presented in the book "Astronomical Algorithms" (2nd Edition) by Jean Meeus.

Example areas covered include the positions of the planets, comets, minor planets and the moon, calculation of times of Rising, Setting and Transit, calculation of times of Equinoxes and Solstices plus calculation of the positions of the moons of Jupiter and Saturn as well as many other algorithms presented in the book.

Features

• Simple C++ interface using static functions and class instances as return values where appropriate.
• All code compiles cleanly at the highest warning level of 4 in Visual Studio. The code also is /permissive- and /analyze clean.
• A simple test app has been provided to test and verify all the functions of the library based on examples as provided in the book.

Usage

• To get started using the code you really should have a copy of the book if you want to thoroughly understand the algorithms and be able to use the different classes and methods in conjunction with each other. For further details please see the References
• To use the classes in your code simple include AA*.cpp in your project and #include AA*.h in which ever of your modules needs to make calls to the classes.
• You can optionally pare back the modules which you do not want to include until you arrive at a minimum set for your requirements.
• To see the classes in action, have a look at the code in the main function in the module "aatest.cpp".
• The download includes a VC 2022 project and has been tested on VC 2022 on Windows 10 and GCC on Ubuntu.

Copyright

• You are allowed to include the source code in any product (commercial, shareware, freeware or otherwise) when your product is released in binary form.
• You are allowed to modify the source code in any way you want except you cannot modify the copyright details at the top of each module.
• If you want to distribute source code with your application, then you are only allowed to distribute versions released by the author. This is to maintain a single distribution point for the source code.

History

v2.53 (7 October 2023)

• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 05 October 2023 and predicted values to 12 October 2024 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

v2.52 (12 July 2023)

• Updated AAParallax.cpp to use a more accurate value of the Solar Parallax constant of 8.794148" instead of 8.794". This newer value was adopted in 1977 by the IAU. Thanks to "Pavel" for reporting this issue.
• Fixed another bug in the calculation of the return value in the CAAPhysicalMoon::AltitudeOfSun method. Thanks to "Pavel" for reporting this issue.

v2.51 (11 July 2023)

• Updated CAADiameters::GeocentricMoonSemidiameter method to use the more rigorous formula on page 390 as presented in Meeus's book. Also updated the "k" constant used in this method from 0.272481 to the more modern value of k = 0.2725076. Please see section "1.9 Mean Lunar Radius" of https://umbra.nascom.nasa.gov/eclipse/20060329/text/chapter_1.html for the reason why the new value was adopted in 1982. Thanks to "Pavel" for reporting this issue.
• Fixed a bug in CAAPhysicalMoon::AltitudeOfSun method. Thanks to "Pavel" for reporting this issue.
• Improved the k value in the CAADiameters::ApparentSaturnPolarSemidiameterA method. Thanks to "Pavel" for reporting this issue.
• Improved the k value in the CAADiameters::ApparentSaturnPolarSemidiameterB method. Thanks to "Pavel" for reporting this issue.
• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 06 July 2023 and predicted values to 13 July 2024 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

v2.50 (16 April 2023)

• Renamed CAAELP2000::MeanLongitudeOfPerilhelionOfEarthMoonBarycentre to CAAELP2000::MeanLongitudeOfPerihelionOfEarthMoonBarycentre.
• Fixed a bug in CAAPrecession::AdjustPositionUsingMotionInSpace in the calculation of the DeltaX, DeltaY & DeltaZ variables. This issue was introduced in July 2022 when C++ uniform initialization for all variable declarations was introduced. Thanks to "Pavel" for reporting this issue.
• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 13 April 2023 and predicted values to 20 April 2024 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

v2.49 (29 January 2023)

• Updated copyright details.
• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 26 January 2023 and predicted values to 3 February 2024 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.
• Renamed CAANearParabolic::CalculateTrueAnnomalyAndRadius to CAANearParabolic::CalculateTrueAnomalyAndRadius.

v2.48 (23 December 2022)

• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 22 December 2022 and predicted values to 30 December 2023 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

2.47 (13 November 2022)

• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 10 November 2022 and predicted values to 18 November 2023 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

v2.46 (1 October 2022)

• Updated the CAAElliptical::Calculate method which takes a Object parameter to return the following additional values: TrueGeocentricRectangularEcliptical, TrueHeliocentricEclipticalLongitude, TrueHeliocentricEclipticalLatitude, TrueHeliocentricDistance, TrueGeocentricEclipticalLongitude, TrueGeocentricEclipticalLatitude, TrueGeocentricDistance, TrueLightTime, TrueGeocentricRA & TrueGeocentricDeclination.
• Renamed CAAEllipticalPlanetaryDetails::ApparentGeocentricLongitude to ApparentGeocentricEclipticalLongitude.
• Renamed CAAEllipticalPlanetaryDetails::ApparentGeocentricLatitude to ApparentGeocentricEclipticalLatitude.
• Fixed an issue in CAAElliptical::Calculate method which takes a Object parameter when the Object parameter is the Sun and the code is attempting to calculate the apparent position of the Sun.
• Added support to CAAPlanetaryPhenomena2::Calculate for MinimumDistance and MaximumDistance event types. The demo application has been updated to show the closest approach of Jupiter on 7th October 1963 UT at 3.952 AU, the closest approach of 26th September 2022 UTC at 3.952 AU and the closest approach of 6th October 2129 UT at 3.948 AU.
• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 29 September 2022 and predicted values to 7 October 2023 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

v2.45 (28 August 2022)

• Fixed an issue in CAAElliptical::MinorPlanetMagnitude where brackets were missing. Thanks to "Pavel" for reporting this issue.
• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 25 August 2022 and predicted values to 2 September 2023 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

v2.44 (14 July 2022)

• Updated all the code in AAAberration.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAAngularSeparation.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AABinaryStar.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AACoordinateTransformation.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AADiameters.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AADynamicalTime.cpp to use C++ uniform initialization for all variable declarations.
• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 07 July 2022 and predicted values to 15 July 2023 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.
• Updated all the code in AAEarth.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAEaster.h to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAEclipses.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAEclipticalElements.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAElliptical.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAELP2000.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAELPMPP02.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAEquationOfTime.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAEquinosesAndSolstices.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAEquinosesAndSolstices2.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAFK5.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAGalileanMoons.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAGlobe.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAIlluminatedFraction.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAInterpolate.cpp to use C++ uniform initialization for all variable declarations.
• Updated various functions in the CAAInterpolate class to allow the epsilon value used to terminate iteration loops to be specified.
• Updated all the code in AAJewishCalendar.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAJupiter.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAKepler.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAMars.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAMercury.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAMoon.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAMoonIlluminatedFraction.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAMoonMaxDeclinations.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAMoonMaxDeclinations2.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAMoonNodes.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAMoonNodes2.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAMoonPerigeeApogee.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAMoonPerigeeApogee2.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAMoonPhases.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAMoonPhases2.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAMoslemCalendar.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AANearParabolic.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AANeptune.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AANodes.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AANutation.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAParabolic.cpp to use C++ uniform initialization for all variable declarations.
• Updated methods in the CAAParabolic class to allow the epsilon value used to terminate iteration loops to be specified.
• Updated all the code in AAParallactic.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAParallax.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAPhysicalJupiter.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAPhysicalMars.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAPhysicalMoon.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAPhysicalSun.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAPlanetaryPhenomena.cpp to use C++ uniform initialization for all variable declarations.
• Fixed a transcription error in the lookup tables AAPlanetaryPhenomena.cpp used to calculate the Station 1 values for Mars.
• Updated all the code in AAPlanetaryPhenomena2.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAPlanetPerihelionAphelion.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAPlanetPerihelionAphelion2.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAPluto.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAPrecession.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AARefraction.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AARiseTransitSet.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AARiseTransitSet2.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AASaturn.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AASaturnMoons.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAUranus.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AASaturnRings.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AASidereal.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAStellarMagnitudes.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AASun.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AATest.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAVenus.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAVSOP87.cpp to use C++ uniform initialization for all variable declarations.
• Updated all the code in AAVSOP2013.cpp to use C++ uniform initialization for all variable declarations.

v2.43 (27 March 2022)

• Fixed an issue in CAADate::DayOfWeek for dates which are close to or prior to the julian day epoch. Thanks to "znight" for reporting this issue.
• Updated all the code in the CAADate class to use C++ uniform initialization for all variable declarations.

v2.42 (20 March 2022)

• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 17 March 2022 and predicted values to 25 March 2023 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all and long term predicted values to 1 January 2032 from https://cddis.nasa.gov/archive/products/iers/deltat.preds.

v2.41 (24 January 2022)

• Updated copyright details.
• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 20 January 2022 and predicted values to 28 January 2023 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

v2.40 (22 December 2021)

• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 16 December 2021 and predicted values to 24 December 2022 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

v2.39 (22 November 2021)

• Reworked the CAABinaryStar::Calculate method to use the method as detailed in chapter 7 in the book "Observing and Measuring Visual Double Stars". This helps fix issues detected with the algorithms as presented in Chapter 57 of Meeus's book. These issues were detected when developing a program to provide a simple animation of a sample binary star system. The observed bug was causing the orbits to not be calculated as projected ellipses when the inclination value (i) approached 90 degrees.
• Updated CAABinaryStarDetails class to include rectangular coordinates as well as the existing polar coordinates.
• Made some minor optimizations to the CAAKepler::Calculate method.

v2.38 (6 November 2021)

• Fix a minor layout problem in the g_MoonCoefficients3 lookup table in AAMoon.cpp. Thanks to Jud McCranie for reporting this issue.
• Fixed a bug in CAAPhysicalMoon::CalculateOpticalLibration where the value of the variable "W" was being calculated incorrectly. Thanks to Don Cross for reporting this issue.
• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 4 November 2021 and predicted values to 12 November 2022 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

v2.37 (24 October 2021)

• Updated various classes to use C++ 11 in-class member initialization.
• Renamed CAAPlanetaryPhenomena::PlanetaryObject type to Planet.
• Renamed CAAPlanetaryPhenomena::EventType type to Type.
• Renamed CAAElliptical::EllipticalObject type to Object.
• Renamed CAADate::DAY_OF_WEEK type to DOW.
• Made CAAEaster::Calculate constexpr.
• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 21 October 2021 and predicted values to 29 October 2022 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.
• AA+ now includes complete support for the VSOP2013 theory (ftp.imcce.fr/pub/ephem/planets/vsop2013/). This theory provides for calculation of the heliocentric elliptical orbital elements and the heliocentric ecliptical and equatorial position and velocity of Mercury, Venus, the Earth-Moon Barycenter, Mars, Jupiter, Saturn, Uranus, Neptune and the dwarf planet Pluto for the equinox and ecliptic of J2000.0.

v2.36 (12 September 2021)

• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 9 September 2021 and predicted values to 17 September 2022 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.
• Removed the Height parameter from the CAARiseTransitSet2::Calculate & CalculateMoon methods. Instead now if you want to calculate times of rise or set at different altitudes you should send in an adjusted h0 parameter. For example you could use the following formulae to adjust for the Sun: double H0 = -0.8333 - CAACoordinateTransformation::RadiansToDegrees(acos(6371008 / (6371008 + Height)))
  where Height is the altitude above sea-level in meters. Thanks to Stephen F. Booth for reporting this issue.

v2.35 (21 August 2021)

• Reworked the algorithm to calculate the apparent semidiameter of the Moon in CAARiseTransitSet2::CalculateMoon. Tests indicate that this change only causes the rise / set times of the Moon to be a couple of seconds different compared to the old formula.

v2.34 (20 August 2021)

• Fixed a bug in CAARiseTransitSet2::CalculateMoon in the calculation of the H0 value. In the book Meeus uses the value +0.125 degrees for the Moon, but this value is not correct in the context of the CAARiseTransitSet2 class as this class already takes diurnal parallax of the Moon into account. Instead the H0 value is now calculated with a new formula which provides more accurate times of Moon Rise and Set. Thanks to Stephen F. Booth for reporting these bug.
• The CAARiseTransitSet2::CalculateMoon method now includes a new RefractionAtHorizon parameter. This value defaults to -0.5667 and corresponds to the amount of atmospheric refraction to use at the moment of Moon rise or set. Note that the actual H0 value for the Moon is not constant and is calculated from this value in this method using the apparent semidiameter of the Moon.
• Updated the CAARiseTransitSet2::CalculateMoon method to support the ELP2000 and ELPMPP02 theories in addition to the Meeus ELP2000 truncated algorithms.

v2.33 (11 August 2021)

• Fixed various bugs in CAARiseTransitSet2::AddEvents related to the calculation of various twilight events. Thanks to Stephen F. Booth for reporting these bugs.
• Changed AAPLUS_ELP2000_NO_HIGH_PRECISION preprocessor define to AAPLUS_NO_ELP2000 to be consistent with other AA+ preprocessor defines.
• Changed AAPLUS_VSOP87_NO_HIGH_PRECISION preprocessor define to AAPLUS_NO_VSOP87 to be consistent with other AA+ preprocessor defines.

v2.32 (9 August 2021)

• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 5 August 2021 and predicted values to 13 August 2022 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

v2.31 (8 July 2021)

• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 8 July 2021 and predicted values to 16 July 2022 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

v2.30 (5 June 2021)

• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 3 June 2021 and predicted values to 11 June 2022 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

v2.29 (1 May 2021)

• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 29 April 2021 and predicted values to 7 May 2022 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

v2.28 (20 April 2021)

• Added a preprocessor directive "AAPLUS_DELTAT_NO_HIGH_PRECISION" which if defined will only use the polynomial equations instead of lookup tables from IERS for calculating DeltaT in the method CAADynamicalTime::DeltaT. By defining this value you reduce the memory requirements needed for the lookup table "g_DeltaTValues" by 300 KB.

v2.27 (2 April 2021)

• Updated the g_DeltaTValues lookup table to use observed DeltaT values to 1 April 2021 and predicted values to 9 April 2022 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all.

17 March 2021

• Fixed a minor typo in AATest.cpp. Thanks to Roger House for reporting this issue.

v2.26 (12 March 2021)

• Reworked CAADynamicalTime::DeltaT to use std::upper_bound to speed up logic to find correct entry in the g_DeltaTValues lookup table.
• Reworked CAADynamicalTime::CumulativeLeapSeconds to use std::upper_bound to speed up logic to find correct entry in the g_LeapSecondCoefficients lookup table.
• Updated the g_DeltaTValues lookup table to use values from the year 1657 to 1972.50 to use data from https://cddis.nasa.gov/archive/products/iers/historic_deltat.data which provides a granularity of 0.5 of a year. Also updated the same array to use values from 2 January 1973 to 19 March 2022 from https://cddis.nasa.gov/archive/products/iers/finals2000A.all which provides a granularity of 1 day. Also updated the same array to use values from the year 2022.25 to 2027.75 from https://cddis.nasa.gov/archive/products/iers/deltat.preds which provides a granularity of 0.25 of a year. All of this was implemented using a program which machine generates the lookup table using custom code. This new lookup table now includes > 18k elements and provides 1 - 1 precision with all the data released by IERS. The machine generated code will also make it easier to update this data as new data is published by IERS going forward. Using this new lookup array we now have a discontinuity of c. 3.7 seconds in January 1657 and a discontinuity of c. 2.5 seconds in October 2027 for the CAADynamicalTime::DeltaT method. With these updates AA+ is now 29.7 Megabytes and 416 thousand lines of C++ source code.
• Implemented a CAADynamicalTime::SetUserDefinedDeltaT method which allows a user provided DeltaT function to be provided. By default the CAADynamicalTime::DeltaT function uses its own lookup tables and polynomials to calculate DeltaT, but if CAADynamicalTime::SetUserDefinedDeltaT has been called to provide a custom DeltaT function then the callback function provided to this method will be used instead. Setting the parameter to SetUserDefinedDeltaT to a nullptr will restore the default DeltaT method behavior.
• Changed the behavior of the CAAPlanetaryPhenomena::K method to now return the K value before it is rounded. This new behaviour is now consistent with all the other methods in the AA+ framework which return so called "K" values. This means that client code must round this value to an integer before calling other methods in this class with this K value.
• Changed the behavior of the CAAPlanetPerihelionAphelion::*K methods to now return the K value before it is rounded. This new behaviour is now consistent with all the other methods in the AA+ framework which return so called "K" values. This means that client code must round this value before calling other methods in this class with this K value.
• Merged the separate perihelion and aphelion methods for all the planets except Earth in CAAPlanetPerihelionAphelion into one method per planet. This new behaviour is now consistent with all the other methods in the AA+ framework which work with so called "K" values.
• Fixed a bug in CAAPlanetPerihelionAphelion::EarthAphelion where the kdash and ksquared values were not being calculated correctly.

v2.25 (7 March 2021)

• Updated the observed DeltaT values from https://datacenter.iers.org/eop.php to 1st March 2021.

v2.24 (5 February 2021)

• Updated the observed DeltaT values from https://datacenter.iers.org/eop.php to 1st February 2021.

v2.23 (10 January 2021)

• Reworked the K, H, Q and P methods in the AAVSOP87_"Planetname".cpp modules to pass false for bAngle to CVSOP87::Calculate. These values are not angular values in the true sense of the word and by passing false, the values returned are now in exact agreement with the vsop87.chk test values. Thanks to Cao Yu for reporting this issue.

v2.22 (9 January 2021)

• Updated copyright details.
• Updated the observed DeltaT values from https://datacenter.iers.org/eop.php to 1st January 2021.

v2.21 (4 December 2020)

• Updated the observed DeltaT values from https://datacenter.iers.org/eop.php to 1st December 2020.

v2.20 (23 November 2020)

• Reworked CAADynamicalTime::TT2UTC & CAADynamicalTime::UTC2TT methods to use std::array::size instead of sizeof.
• Reworked CAAELPMPP02::EclipticLatitude & CAAELPMPP02::RadiusVector methods to use std::array::size instead of sizeof.

v2.19 (22 November 2020)

• Updated the observed DeltaT values from https://datacenter.iers.org/eop.php to 1st November 2020. The IERS web site is the definitive source for these values as the USNO websites which I have previously used are offline at the moment for modernization efforts (See https://www.usno.navy.mil/ for the details). To obtain values for DeltaT to add to the g_DeltaTValues table in AADynamicalTime.cpp, the value "UT1-UTC" was taken from Bulletin A and the formula: DeltaT = AccumulatedLeapsSeconds + 32.184 - (UT1-UTC) was used. The "AccumulatedLeapsSeconds" for 2020 is currently 37 seconds. If you plot the values for DeltaT for 2020 you will see that around June 2020 the value for DeltaT has started to decrease instead of the long term increasing trend for DeltaT. If this trend continues we may see the first negative leap second occur in the next few years.

v2.18 (21 November 2020)

• Update the CMake project file for AA+ to require C++ 17 compilation. This fixes a compile issue when using CMake to build AA++ as the code requires C++ 17 compilation as of v2.13. Thanks to Kirill Dunko for reporting this issue.

v2.17 (11 June 2020)

• Addition of a new CAAPlanetaryPhenomena2 class.
• Removed support for Pluto from the CAAElliptical class since the CAAPluto class returns the coordinates in the equinox of J2000 instead of the equinox of the date which is required by this class.
• Removed support for Pluto from the CAARiseTransitSet2 class since the CAAPluto class returns the coordinates in the equinox of J2000 instead of the equinox of the date which is required by this class.

v2.16 (2 June 2020)

• Addition of a new CAAPlanetPerihelionAphelion2 class.

v2.15 (1 June 2020)

• Fixed a bug in CAAELP2000::SunMeanAnomaly where some local variables were not initialized. Thanks to "Carlos" for reporting this bug.
• Optimized the code in CAAVenus::EclipticLongitude.
• Renamed CAAELP2000::MoonMeanLongitude to CAAELP2000::MoonMeanMeanLongitude.
• Renamed CAAELP2000::MoonMeanLongitudeLunarPerigee to CAAELP2000::MeanLongitudeLunarPerigee.
• Renamed CAAELP2000::MoonMeanLongitudeLunarAscendingNode to CAAELP2000::MeanLongitudeLunarAscendingNode.
• Renamed CAAELP2000::EarthMoonBarycentreMeanLongitude to CAAELP2000::MeanHeliocentricMeanLongitudeEarthMoonBarycentre.
• Renamed CAAELP2000::EarthMoonBarycentreMeanLongitudeOfPerihelion to CAAELP2000::MeanLongitudeOfPerilhelionOfEarthMoonBarycentre

v2.14 (29 April 2020)

• Fixed a compilation issue on GCC where size_t was undefined in various modules. Thanks to Bert Devlieghe for reporting this bug.

v2.13 (22 April 2020)

• Updated the observed DeltaT values from ftp://cddis.gsfc.nasa.gov/pub/products/iers/deltat.data to 1st February 2020
• Updated the code to take advantage of range based for loops and std::array. Please note that these changes means that the code will no longer compile on VC 2017 due to its limited supported for large constexpr arrays.
• Fixed more Clang-Tidy static code analysis warnings in the code.
• Made a number of the CAADate methods [[nodiscard]]. This change means that the code must be compiled using the ISO C++ 17 standard or higher.

v2.12 (1 January 2020)

• Addition of a new CAAMoonPhases2 class.
• Updated copyright details.

v2.11 (10 December 2019)

• Fixed various Clang-Tidy static code analysis warnings in the code.

v2.10 (16 November 2019)

• Addition of a new CAAMoonNodes2 class.

v2.09 (2 November 2019)

• Addition of a new CAAMoonPerigeeApogee2 class.

v2.08 (22 October 2019)

• Addition of a new CAAMoonMaxDeclinations2 class.

v2.07 (28 September 2019)

• Addition of a new CAAEquinoxesAndSolstices2 class.

v2.06 (28 September 2019)

• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st September 2019

v2.05 (8 September 2019)

• Added support for EndCivilTwilight, EndNauticalTwilight, EndAstronomicalTwilight, StartAstronomicalTwilight, StartNauticalTwilight & StartCivilTwilight event types to CAARiseTransitSet2 class.

v2.04 (18 August 2019)

• Fixed some further compiler warnings when using VC 2019 Preview v16.3.0 Preview 2.0

v2.03 (15 July 2019)

• Refactored the code in various CAARiseTransitSet2 methods and improved the interpolation code to provide better accuracy of event details.

v2.02 (13 July 2019)

• Addition of a new CAARiseTransitSet2 class which addresses issues with the existing CAARiseTransitSet class which is now considered deprecated.

v2.01 (23 June 2019)

• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st June 2019

v2.0 (8 June 2019)

• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st April 2019
• Updated the predicted DeltaT values from http://maia.usno.navy.mil/ser7/deltat.preds to October 2027
• Updated the code to clean compile on VC 2019

v1.99 (16 January 2019)

• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st January 2019

v1.98 (3 January 2019)

• Updated copyright details.
• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st October 2018

v1.97 (22 September 2018)

• Fixed a number of VC 2017 15.8 C++ core guidelines compiler warnings.
• Updated the observed DeltaT values from http://toshi.nofs.navy.mil/ser7/deltat.data to 1st April 2018

v1.96 (24 July 2018)

• Fixed a number of GCC warnings in the method CAAGalileanMoons::CalculateHelper. Thanks to Todd Carnes for reporting this issue.
• Fixed a number of GCC warnings in the methods CAAPlanetaryPhenomena::K, CAAPlanetaryPhenomena::Mean, CAAPlanetaryPhenomena::True & CAAPlanetaryPhenomena::ElongationValue. Thanks to Todd Carnes for reporting this issue.
• Fixed a GCC warning in the method CAASaturnMoons::HelperSubroutine. Thanks to Todd Carnes for reporting this issue.
• Fixed a GCC warning in the CAARiseTransitSetDetails constructor. Thanks to Todd Carnes for reporting this issue.
• Fixed a number of VC 2017 15.7 C++ core guidelines compiler warnings.
• Replaced enum with enum class throughout the code.

24 April 2018

• Updated the documentation to mention that geographical longitudes are positive west of Greenwich and negative east of Greenwich. Thanks to Spencer Roff for reporting this issue.
• Did some other minor cleanups of html tags in the documentation.
• Updated the documentation for CAAGlobe::DistanceBetweenPoints to refer to all its parameters.

v1.95 (19 April 2018)

• Updated references to CAARiseTransitSet::Calculate in the documentation. Thanks to Roger House for reporting this issue.
• Updated the sample code for CAARiseTransitSet::Calculate in the documentation which demonstrates an edge case. Thanks to Roger House for reporting this issue.

v1.94 (3 March 2018)

• Fixed some compiler warnings on LLVM 9 on XCode on Mac OS in AATest.cpp when calling PrintSunAndMoonInfo2. Thanks to Michael McLaughlin for reporting this issue.

v1.93 (2 March 2018)

• Fixed a transcription bug in the CAAPrecession::PrecessEquatorial method. The "0.017998*tcubed" term was incorrectly using "0.017988*tcubed" when calculating "sigma". Thanks to Michael McLaughlin for reporting this bug. The errors were so small that the values from the worked example of 21.b from the book ended up giving the same results. If a longer timespan was used for the example instead of the 28 years then the errors would have been easier to spot from the incorrect terms. Hopefully this is the last transcription error in this method!

v1.92 (20 January 2018)

• Updated copyright details.
• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st January 2018
• Updated the predicted DeltaT values from http://maia.usno.navy.mil/ser7/deltat.preds to Jan 2026

v1.91 (1 August 2017)

• Fixed up alignment of lookup tables in AAMercury.cpp module.
• Fixed up alignment of lookup tables in AAVenus.cpp module.
• Fixed up alignment of lookup tables in AAEarth.cpp module.
• Fixed up alignment of lookup tables in AAMars.cpp module.
• Fixed up alignment of lookup tables in AAJupiter.cpp module.
• Fixed up alignment of lookup tables in AASaturn.cpp module.
• Fixed up alignment of lookup tables in AAUranus.cpp module.
• Fixed up alignment of lookup tables in AANeptune.cpp module.
• Fixed up alignment of lookup tables in AAPluto.cpp module.
• Fixed up alignment of lookup tables in AAMoon.cpp module.
• Lookup tables in AAELPMPP02.cpp now consistently use lowercase "e" when declaring values in lookup tables.

v1.90 (30 July 2017)

• AA+ now includes complete support for the ELP/MPP02 theory (ftp://cyrano-se.obspm.fr/pub/2_lunar_solutions/2_elpmpp02/) in addition to the ELP2000-82B theory (http://cdsweb.u-strasbg.fr/cgi-bin/qcat?VI/79/) and truncated ELP2000 theory as presented in Meeus's book. This theory is the most up to date version of the ELP Lunar theory. It includes fits to the JPL Ephemerides of DE405 & DE406, LLR (Lunar Laser Ranging) as well as the Nominal model used in ELP/MPP02. The full ELP/MPP02 theory is implemented by the new AAELPMPP02.cpp/h files included in the AA+ download. This new class in AA+ to support ELP/MPP02 has been machine generated by parsing the ELP/MPP02 files with a custom C++ app to generate the new header and source modules. The results have been comprehensively spot checked against the ELP/MPP02 test values provided in the ELP/MPP02 files. The AA+ implementation is based in part on a C# implementation of the theory at https://sourceforge.net/projects/astromony/files/ as well as a C implementation in GAL (General Astrodynamics Library) by Paul Willmott at http://www.amsat-bda.org/GAL_Home.html. Similar to the ELP2000-82b theory the results are returned in the equator and equinox of J2000. Client code is free to use the CAAPrecession class to precess the coordinates to the required reference frame. Please note that if you want to compile AA+ to not pull in a dependency on the new and quite large ELP/MPP02 module, then you can define the preprocessor value "AAPLUS_NO_ELPMPP02" in your project. With this addition AA+ is now 27.7 Megabytes and 377 thousand lines of C++ source code. Testing shows the time taken to call CAAELP2000::EclipticRectangularCoordinatesJ2000 on my 3.2GHz Core i7 processor is about c. 1ms while the call to the new CAAELPMPP02::EclipticRectangularCoordinatesJ2000 method including returning the derivatives takes c. 5ms. From the ELP/MPP02 paper, the longitude and latitude is three times more accurate than ELP200-82B and the distance is eight times more accurate. For the interval +1950 to +2060, there is reported accuracy of 0.06 arc seconds in longitude, 0.003 arc seconds in latitude and 4 meters in distance.
• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st June 2017.
• Updated the predicted DeltaT values from http://maia.usno.navy.mil/ser7/deltat.preds to Jan 2026.
• Removed unnecessary SECOND_2_RAD define in AAELP2000.cpp module.
• Updated various CAAELP2000 methods to use "const" parameters.

v1.80 (15 May 2017)

• Fixed an issue in CAAPhysicalSun::Calculate where the value "eta" would sometimes not be returned in the correct quadrant. Thanks to Alexandru Garofide for reporting this issue.

v1.79 (27 April 2017)

• Revisited the fix for interpolating RA values in the CAARiseTransitSet class which was made on 28 March 2009. This new fix should resolve this issue for good. Thanks to Gudni G. Sigurdsson for reporting this bug.

23 April 2017

• Updated the documentation for CAAPrecession::AdjustPositionUsingMotionInSpace to clarify the units used. Thanks to Matthew Prowse for reporting this issue.

v1.78 (19 February 2017)

• Fixed a bug in the CAADynamicalTime::UTC2TT & CAADynamicalTime::TT2UTC methods where the code would incorrectly use BaseMJD instead of JD when determining if the date is in the valid range of UTC. Thanks to Luigi Candurro for reporting this bug.

v1.77 (18 February 2017)

• Fixed a transcription error on the DeltaT value for 1 May 2015. The correct value is 67.8012 instead of 67.8011. Thanks to Luigi Candurro for reporting this error.
• Fixed a number of transcription errors on the predicted DeltaT values from 2019.75 to 2025.75. Thanks to Luigi Candurro for reporting these errors.
• CAADynamicalTime::TT2UTC is now implemented as TT2UT1 for date ranges prior to 1 January 1961 and 500 days after the last leap second (which is currently 1 January 2017). Also CAADynamicalTime::UTC2TT is now implemented as UT12TT for date ranges prior to 1 January 1961 and 500 days after the last leap second. These changes address problems where these two methods would end up using a constant offset between UTC and TT for dates away from the current epoch. This problem was discovered while calculating rise, transit and set times for the Moon in B.C.E years. Thanks to Luigi Candurro for prompting this update.
• Reworked the CAADate::SetInGregorianCalendar method to use the AfterPapalReform method.
• Documentation now includes info on CAADate::AfterPapalReform methods. Thanks to Luigi Candurro for reporting this issue.

v1.76 (12 February 2017)

• Fixed a copy and paste bug in CAASaturnMoons::CalculateHelper in the calculation of the value mu for the eight moon (Iapetus). Thanks to Cedric Foellmi for reporting this issue.

v1.75 (11 February 2017)

• Applied a bug fix to CAAMoon::EclipticLatitude and CAAMoon::RadiusVector along the same lines as the fix to CAAMoon::EclipticLongitude on February 2009. The bug fix should in fact have been applied to the later two methods. Thanks to Jeffrey Roe for reporting this issue.

v1.74 (5 February 2017)

• Updated copyright details.
• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st January 2017
• Updated the predicted DeltaT values from http://maia.usno.navy.mil/ser7/deltat.preds to Jan 2026

v1.73 (16 October 2016)

• Improved the accuracy of CAASun::ApparentEclipticLongitude when the bHighPrecision parameter is true. The code now uses a new VariationGeometricEclipticLongitude method which provides a new higher precision method to calculate the effect of aberration. This takes into account that Earth's orbit around the Sun is not a purely unperturbed elliptical orbit. This improves the accuracy of the sample 25.a/b from the book by a couple of hundreds of arc seconds. The results now are exactly in sync with the results as reported in the book. Thanks to "Pavel" for reporting this issue.

v1.72 (7 July 2016)

• Fixed a bug in the documentation for the Alpha and Delta parameters to the CAAPrecession::PrecessEquatorial method. Thanks to "Luigi" for reporting this issue.
• Fixed a bug in the documentation for the PMAlpha parameter to the CAAPrecession::AdjustPositionUsingMotionInSpace method. Thanks to "Luigi" for reporting this issue.
• Updated the CAADynamicalTime::CumulativeLeapSeconds method as taken from http://maia.usno.navy.mil/ser7/tai-utc.dat to include the leap second which will occur on 1 January 2017.
• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st July 2016
• Updated the predicted DeltaT values from http://maia.usno.navy.mil/ser7/deltat.preds to July 2026
• Fixed a compiler warning in CAAEaster::Calculate as reported at http://stackoverflow.com/questions/2348415/objective-c-astronomy-library.

v1.71 (28 April 2016)

• Fixed a bug in the AAVSOP87 modules where an incorrect value was being passed for the "nTableSize" parameter to the CVSOP87::Calculate and CVSOP87::Calculate_Dash methods. A spot check of the VSOP87 sample values in AATest.cpp now match exactly with the published VSOP87 test values. Thanks to "Pavel" for reporting this issue.

v1.70 (10 April 2016)

• Fixed a bug in the GetSunRiseTransitSet function in the AATest.cpp module where it incorrectly used Terrestrial Time instead of UTC. The error in the rise / transit / set times was roughly the difference between TT and UTC at the time of calculation. For the examples in AATest.cpp which corresponded to October 2010, DeltaT was 67 seconds. A spot check of the AA+ code against SkyMap now shows both return the same times accurate to the minute. Thanks to "Pavel" for reporting this issue.
• Fixed a bug in the GetMoonRiseTransitSet function in the AATest.cpp module where it incorrectly used Terrestrial Time instead of UTC. The error in the rise / transit / set times was roughly the difference between TT and UTC at the time of calculation. For the examples in AATest.cpp which corresponded to October 2010, DeltaT was 67 seconds. A spot check of the AA+ code against SkyMap now shows both return the same times accurate to the minute. Thanks to "Pavel" for reporting this issue.
• Introduction of a new bool CAARiseTransitSetDetails::bTransitValid member variable. It turns out that celestial objects do not always transit in a 24 hour UTC day. Test code has been added to AATest.cpp to fully exercise all the cases for the three boolean member variables of bRiseValid, bTransitValid & bSetValid. Thanks to "Pavel" for reporting this issue.

v1.69 (28 March 2016)

• Fixed two transcription errors in CAAMoonNodes::PassageThroNode. The first error was the calculation of the D4 local variable which represented 4D in Meeus's formulae while the second error was in the -E*0.0003*sin(2D - 2M) coefficient. With these two fixes the calculated time of Example 51.a from Meeus's book is within 2 seconds of the value he reports. Thanks to Alejandro Krohn for prompting this bug fix.

v1.68 (27 March 2016)

• Updated CAAEclipses::Calculate to return a bitmask of attributes about the calculated solar eclipse in CAASolarEclipseDetails::Details. These attributes correspond to the values as discussed in Meeus's book on Pages 381 & 382. Thanks to "Pavel" for providing this nice addition.

v1.67 (20 March 2016)

• CAAPrecession::AdjustPositionUsingUniformProperMotion now ensures that the return value is in the normalized range for right ascension and declination.
• CAAPrecession::AdjustPositionUsingMotionInSpace now ensures that the return value is in the normalized range for right ascension and declination.
• CAAPrecession::PrecessEquatorial now ensures that the return value is in the normalized range for right ascension and declination.
• CAAPrecession::PrecessEquatorialFK4 now ensures that the return value is in the normalized range for right ascension and declination.
• CAAPrecession::PrecessEcliptic now ensures that the return value is in the normalized range for ecliptic longitude and latitude.
• CAAPrecession::PrecessEquatorialFK4 now adds the Equinox correction to the returned right ascension. Thanks to "Pavel" for reporting this issue.
• Optimized the code in CAAPrecession::PrecessEquatorial, CAAPrecession::PrecessEquatorialFK4 & CAAPrecession::PrecessEcliptic.
• Updated the documentation for CAAPrecession::PrecessEquatorialFK4 to be explicit on what coordinate system the parameters and return value are defined in. Thanks to "Pavel" for reporting this issue.
• Fixed a transcription error in the CAAGlobe::RhoSinThetaPrime and CAAGlobe::RhoCosThetaPrime functions. The value 6378149 was being used instead of the correct value 6378140. Thanks to "Pavel" for reporting this bug.

v1.66 (9 March 2016)

• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st February 2016
• Verified the predicted DeltaT values from http://maia.usno.navy.mil/ser7/deltat.preds are up to date
• Fixed three transcription bugs in the g_MoonPerigeeApogeeCoefficients3 table. Thanks to "Pavel" for reporting this bug. A spot check of the True Perigee parallax values from 1984 to 2026 indicate that this bug did not affect the calculated distances at least in this time range to a precision of a kilometer which is well within the claimed accuracy of 12 KM as mentioned in Meeus's book on page 361.

v1.65 (4 January 2016)

• Major cleanup and refactoring of the ELP2000-82b code. The new reimplementation should prove faster and easier to maintain going forward.
• Updated copyright details

v1.64 (31 December 2015)

• AA+ now includes complete support for the ELP2000-82B theory (http://cdsweb.u-strasbg.fr/cgi-bin/qcat?VI/79/) in addition to the truncated ELP2000 theory as presented in Meeus's book. This theory is used to calculate the position of the Moon. The full ELP2000-82b theory is implemented by the new AAELP2000.cpp/h files included in the AA+ download. This new class in AA+ to support ELP2000-82b has been machine generated by parsing the ELP2000-82b files with a custom C++ app to generate the new header and source modules. The results have been comprehensively spot checked against the ELP2000-82b test values provided in the ELP2000-82b files. The AA+ implementation is based in part on a C translation of the original Fortran source code included with ELP2000-82b as well as the Libnova open source library. As the ELP2000-82b theory returns the results in the equator and equinox of J2000 / FK5 they cannot be directly integrated into the existing CAAMoon class which returns the values in the equator and equinox of the date. Client code is free to use the CAAPrecession class to precess the coordinates to the required reference frame. Please note that if you want to compile AA+ to not pull in a dependency on the new and quite large ELP2000-82b module, then you can define the preprocessor value "AAPLUS_ELP2000_NO_HIGH_PRECISION" in your project. With this addition AA+ is now 23.6 Megabytes and 330 thousand lines of C++ source code.
• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st October 2015
• Verified the predicted DeltaT values from http://maia.usno.navy.mil/ser7/deltat.preds are up to date

v1.63 (16 September 2015)

• AA+ now includes complete support for the VSOP87 theory (ftp://cdsarc.u-strasbg.fr/pub/cats/VI/81/) in addition to the truncated VSOP87 theory as presented in Meeus's book. This theory is used throughout the AA+ codebase to calculate the positions of the planets and the Sun. The full VSOP87 theory is implemented by the new AAVSOP*.cpp/h files included in the AA+ download. For a good introduction to VSOP87, please see https://en.wikipedia.org/wiki/VSOP_%28planets%29. The classes in AA+ to support VSOP87 have been machine generated by parsing the VSOP87 files with a custom C++ app to generate the new header and source modules. The results have been comprehensively spot checked against the VSOP87 test values provided in the "vsop87.chk" file in the VSOP87 files. Each VSOP theory (VSOP87, VSOP87A, VSOP87B, VSOP87C, VSOP87D, & VSOP87E) for each of the objects (Sun, Mercury, Venus, Earth, Earth-Moon Barycenter, Mars, Jupiter, Saturn, Uranus & Neptune) are implemented in separate header and source modules so client applications can decide which modules to include. The existing AA+ codebase will now optionally call into these new modules as required. With this addition AA+ has gone from 840 Kilobytes and 16 thousand lines of C++ source code library to 20 Megabytes and 291 thousand lines of a C++ source code library. In one fell swoop I have almost doubled the amount of open source code I distribute on my web site. Please note that if you want to compile AA+ to not pull in a dependency on the new and quite large VSOP87 modules, then you can define the preprocessor value "AAPLUS_VSOP87_NO_HIGH_PRECISION" in your project. This will revert the AA+ classes to just depend on the truncated VSOP87 theory as presented in Meeus's book.
• Updated the CAACoordinateTransformation::MapTo0To360Range to use the fmod C runtime function.
• Updated the CAACoordinateTransformation::MapTo0To24Range to use the fmod C runtime function.
• Added new CAACoordinateTransformation::MapTo0To2PIRange and MapToMinus90To90Range methods.
• CAAAberration::EclipticAberration, EarthVelocity and EquatorialAberration now include a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAEarth::EclipticLongitude, EclipticLatitude, RadiusVector, EclipticLongitudeJ2000 & EclipticLatitudeJ2000 now include a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAElliptical::Calculate now includes a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAEquationOfTime::Calculate now includes a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• All the methods in CAAEquinoxesAndSolstices now include a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAGalileanMoons::Calculate now includes a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAJupiter::EclipticLongitude, EclipticLatitude & RadiusVector now include a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAMars::EclipticLongitude, EclipticLatitude & RadiusVector now include a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAMercury::EclipticLongitude, EclipticLatitude & RadiusVector now include a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAANearParabolic::Calculate now includes a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAANeptune::EclipticLongitude, EclipticLatitude & RadiusVector now include a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAParabolic::Calculate now includes a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAPhysicalJupiter::Calculate now includes a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAPhysicalMars::Calculate now includes a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAPhysicalMoon::CalculateSelenographicPositionOfSun, AltitudeOfSun, TimeOfSunrise and TimeOfSunset methods now include a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAPhysicalSun::Calculate now includes a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAASaturn::EclipticLongitude, EclipticLatitude & RadiusVector now include a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAASaturnMoons::Calculate now includes a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAASaturnRings::Calculate now includes a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• All the methods in CAASun now include a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAUranus::EclipticLongitude, EclipticLatitude & RadiusVector now include a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• CAAVenus::EclipticLongitude, EclipticLatitude & RadiusVector now include a "bool bHighPrecision" parameter which if set to true means the code uses the full VSOP87 theory rather than the truncated theory as presented in Meeus's book.
• Verfied the code compiles cleanly on Visual C++ 2015.
• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st July 2015.
• Updated the predicted DeltaT values from http://maia.usno.navy.mil/ser7/deltat.preds to 1st January 2025.

v1.62 (12 July 2015)

• Fixed a bug in CAAElliptical::Calculate when calculating values for the position of the Sun. The values returned by this method are now consistent with those returned using the methods of the CAASun class, the planetarium program SkyMap and the JPL HORIZON's web site. The errors were of the order of 4 arc seconds in declination and 1.5 seconds of Right ascension for modern times. I have also taken the opportunity to optimize the code in this method. With these changes the errors are now down to 0.5 seconds of an angle in declination and right ascension. Thanks to Marko Peric for reporting this bug.

v1.61 (5 July 2015)

• U1 (the Saturnicentric longitude of the Sun) and U2 (the Saturnicentic longitude of the Earth) are now returned in CAASaturnRings::Calculate.
• Fixed a bug in the calculation of CAASaturnRingDetails::DeltaU in the method CAASaturnRings::Calculate where for some date ranges the value would end up greater than 180 degrees. The book indicates that this value should never be more than 7 degrees. The issue was related to subtraction of two angles to obtain an absolute elongation value between the two. By definition this value should never be greater than 180 degrees. The bug occurred between the dates of June 3rd 2024 and July 28th 2024 and December 1st 2024 and February 12 2025. Thanks to Frank Vergeest for reporting this bug.
• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st April 2015.

v1.60 (29 March 2015)

• Updated copyright details.
• Updates to the html documentation to clarify the units used in some of the CAACoordinateTransaction methods. Thanks to "Forrest" for reporting these issues.
• Fixed up some variable initializations around the use of modf. Thanks to Arnaud Cueille for reporting this issue.

v1.59 (15 February 2015)

• Updated copyright details.
• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st January 2015
• Updated the predicted DeltaT values from http://maia.usno.navy.mil/ser7/deltat.preds to 1st January 2024
• Updated the CumulativeLeapSeconds table from http://maia.usno.navy.mil/ser7/tai-utc.dat to 1st July 2015

v1.58 (12 November 2014)

• Updated copyright details.
• Fixed two transcription bugs in the CAAPrecession::PrecessEquatorial method. The"0.000344*T" term was incorrectly using "0.0000344*T" when calculating "sigma" and the "0.000139*Tsquared" term was incorrectly using "0.000138*Tsquared" when calculating "zeta". Thanks to Erik Grosse for reporting this bug. The errors were so small that the values from the worked example of 21.b from the book ended up giving the same results. If a longer timespan was used for the example instead of the 28 years then the errors would have been easier to spot with the incorrect terms.
• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st October 2014.
• Updated the predicted DeltaT values from http://maia.usno.navy.mil/ser7/deltat.preds to 1st January 2024.

v1.57 (28 October 2013)

• Renamed the method CAAEquinoxesAndSolstices::SpringEquinox to NorthwardEquinox to avoid the northern hemisphere bias in the name. Thanks to Marius Gleeson for prompting this update.
• Renamed the method CAAEquinoxesAndSolstices::AutumnEquinox to SouthwardEquinox to avoid the northern hemisphere bias in the name. Thanks to Marius Gleeson for prompting this update.
• Renamed the method CAAEquinoxesAndSolstices::SummerSolstice to NorthernSolstice to avoid the northern hemisphere bias in the name. Thanks to Marius Gleeson for prompting this update.
• Renamed the method CAAEquinoxesAndSolstices::WinterSolstice to SouthernSolstice to avoid the northern hemisphere bias in the name. Thanks to Marius Gleeson for prompting this update.
• The method CAAEquinoxesAndSolstices::LengthOfSpring now takes a boolean to indicate which hemisphere the observer is located in. Previously the code assumed a northern hemisphere bias. Thanks to Marius Gleeson for prompting this update.
• The method CAAEquinoxesAndSolstices::LengthOfSummer now takes a boolean to indicate which hemisphere the observer is located in. Previously the code assumed a northern hemisphere bias. Thanks to Marius Gleeson for prompting this update.
• The method CAAEquinoxesAndSolstices::LengthOfAutumn now takes a boolean to indicate which hemisphere the observer is located in. Previously the code assumed a northern hemisphere bias. Thanks to Marius Gleeson for prompting this update.
• The method CAAEquinoxesAndSolstices::LengthOfWinter now takes a boolean to indicate which hemisphere the observer is located in. Previously the code assumed a northern hemisphere bias. Thanks to Marius Gleeson for prompting this update.
• Updated the sample app to print out a table of information related to Equinoxes and Solstices.
• Addition of a CAADynamicalTime::TT2UTC method which converts from TT to UTC.
• Addition of a CAADynamicalTime::UTC2TT method which converts from UTC to TT.
• Addition of a CAADynamicalTime::TT2TAI method which converts from TT to TAI.
• Addition of a CAADynamicalTime::TAI2TT method which converts from TAI to TT.
• Addition of a CAADynamicalTime::TT2UT1 method which converts from TT to UT1.
• Addition of a CAADynamicalTime::UT12TT method which converts from UT1 to TT.
• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st September 2013.
• Addition of a CAADynamicalTime::UT1MinusUTC method which returns UT1 - UTC.
• Fixed a number of GCC compiler warnings in AATest.cpp.

v1.56 (8 September 2013)

• Fixed a bug in the calculation of HeliocentricEclipticLongitude and HeliocentricEclipticLatitude in CAAParabolic::Calculate. Thanks to Joe Novak for reporting this problem.
• Fixed a bug in the calculation of HeliocentricEclipticLongitude and HeliocentricEclipticLatitude in CAANearParabolic::Calculate. Thanks to Joe Novak for reporting this problem.

v1.55 (4 August 2013)

• Updated copyright details
• Updated the observed DeltaT values from http://maia.usno.navy.mil/ser7/deltat.data to 1st April 2013
• Updated the predicted DeltaT values from http://maia.usno.navy.mil/ser7/deltat.preds to 1st January 2023
• Fixed a transcription error in the third coefficient used to calculate the L0 term for the ecliptic longitude of Mercury. Thanks to Isaac Clark for reporting this issue.
• Fixed a transcription error in the fifth coefficient used to calculate the L2 term for the ecliptic longitude of Mercury. Thanks to Isaac Clark for reporting this issue.
• Fixed a transcription error in the second coefficient used to calculate the L4 term for the ecliptic longitude of Mercury. Thanks to Isaac Clark for reporting this issue.
• Fixed a transcription error in the ninth coefficient used to calculate the B0 term for the ecliptic latitude of Mercury. Thanks to Isaac Clark for reporting this issue.
• Fixed a transcription error in the third coefficient used to calculate the B0 term for the ecliptic latitude of Venus. Thanks to Isaac Clark for reporting this issue. Spot tests indicate that this change only affected the ecliptic latitude in the sixth decimal place.
• Fixed a transcription error in the twenty first coefficient used to calculate the L0 term for the ecliptic longitude of Earth. Thanks to Isaac Clark for reporting this issue.
• Fixed a transcription error in the sixteenth coefficient used to calculate the L1 term for the ecliptic longitude of Earth. Thanks to Isaac Clark for reporting this issue.
• Fixed a transcription error in the second coefficient used to calculate the B2 term for the ecliptic latitude of Mars. Thanks to Isaac Clark for reporting this issue.
• Fixed a transcription error in the third coefficient used to calculate the B2 term for the ecliptic latitude of Mars. Thanks to Isaac Clark for reporting this issue.
• Fixed a transcription error in the thirty ninth coefficient used to calculate the L0 term for the ecliptic longitude of Jupiter. Thanks to Isaac Clark for reporting this issue.
• Fixed a transcription error in the sixteenth coefficient used to calculate the R1 term for the ecliptic radius vector of Jupiter. Thanks to Isaac Clark for reporting this issue.
• Fixed a transcription error in the twenty ninth coefficient used to calculate the B2 term for the ecliptic latitude of Saturn. Thanks to Isaac Clark for reporting this issue. Spot tests indicate that this change only affected the ecliptic latitude in the twelfth decimal place.
• Fixed a transcription error in the second coefficient used to calculate the B0 term for the ecliptic latitude of Neptune. Thanks to Isaac Clark for reporting this issue. Spot tests indicate that this change only affected the ecliptic latitude in the sixth decimal place.

v1.54 (27 October 2012)

• Fixed a buffer initialization bug in PrintMoonPhase function in AAAtest.cpp. This was resulting in the moon phase ASCII diagrams to not show correctly on Unix terminals.
• I now have a Ubuntu 12.10 VM setup which allows the code to be fully tested on a Unix OS going forward. I am using the Code::Blocks IDE to provide a familiar development experience for this Visual Studio veteran!
• Fixed a transcription bug in CAAElementsPlanetaryOrbit::SaturnLongitudePerihelion. The correct coefficient for multiplying by T should have been 1.9637613 instead of 1.19637613. In the worked example of 31.a from Meeus's book, he uses the date June 24 2065. With this bug now eliminated the value returned is now 94.34 degrees instead of 93.84 degrees for this date. Basically the incorrect coefficient would have returned a value too small by 0.77 degrees for every Julian century after the epoch J2000.0 = 2000 January 1.5 TD = JDE 2451545.0. Thanks to Sudhakar Gumparthi for reporting this bug.

v1.53 (13 October 2012)

• Updated the sample app to show the rise, transit and set details for the Moon and Sun at the North Pole for 31 October 2012. This shows that the Sun does not rise or set on that day and transits below the horizon at 11:43:36 UTC and the Moon also does not rise or set and transits above the horizon at 00:35:12 UTC. Thanks to Michael Iverson for prompting this check.
• Removed need for std::string class from AATest.cpp module.
• Fixed a small typo in the AARiseTransitSet.cpp history comments. Thanks to Michael Iverson for reporting this issue.
• Fixed a typo in the spelling of Coefficient throughout the AADynamicalTime.cpp module. Thanks to Michael Iverson for reporting this issue.

v1.52 (12 October 2012)

• Refactored the code in CAARiseTransitSet::Calculate.
• Added comments to the documentation for CAARiseTransitSet::Calculate on the potential for returning times outside of the UTC date requested. Thanks to Rob Phillips for reporting this issue.

v1.51 (5 May 2012)

• Updated the sample app to print out the rise transit and set times for the Moon and Sun as well as a ASCII graphic of the moon phase for the month of April 2012 for the location of Wexford, Ireland. Thanks to Roger Dahl for providing this nice addition to AA+.

v1.50 (2 May 2012)

• To further improve the accuracy of the CAADynamicalTime::DeltaT method, the code now uses a lookup table between the dates of 1 February 1973 to 1 April 2012 (for observed values) and predicted values from April 2012 till April 2015. These values are as provided by IERS Rapid Service/Prediction Center at http://maia.usno.navy.mil/ser7/deltat.data and http://maia.usno.navy.mil/ser7/deltat.preds. This lookup table will of course need to be kept up to date as IERS update this information. As currently coded there is a single discontinuity of c. one second in early April 2015. At this point http://maia.usno.navy.mil/ser7/deltat.preds indicates an error value for DeltaT of about 0.9 seconds anyway.
• A new CAADynamicalTime::CumulativeLeapSeconds has been provided. This method takes as input the Julian Day value and returns the cumulative total of Leap seconds which have been applied to this point. For more information about leap seconds please see http://en.wikipedia.org/wiki/Leap_second. Using this method you can now implement code which converts from Terrestrial Time to Coordinated Universal time as follows:
  
  double TerrestialTime = some calculation using AA+ algorithms(JD);
double DeltaT = CAADynamicalTime::DeltaT(JD);
double UniversalTime1 = TerrestialTime - DeltaT/86400.0; //The time of the event using the UT1 time scale
double TerrestialAtomicTime = TerrestialTime - (32.184/86400.0); //The time of the event using the TAI time scale
double CumulativeLeapSeconds = CAADynamicalTime::CumulativeLeapSeconds(JD);
double CoordinatedUniversalTime = (DeltaT - CumulativeLeapSeconds - 32.184)/86400.0 + UniversalTime1; //The time of the event using the UTC time scale

v1.49 (1 May 2012)

• Updated CAADynamicalTime::DeltaT to use new polynomical expressions from Espenak & Meeus 2006. References used: http://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html and http://www.staff.science.uu.nl/~gent0113/deltat/deltat_old.htm (Espenak & Meeus 2006 section). Thanks to Murphy Chesney for prompting this update.

v1.48 (18 March 2012)

• Updated copyright details.
• All global "g_*" tables are now const. Thanks to Roger Dahl for reporting this issue when compiling AA+ on ARM.

v1.47 (10 September 2011)

• Fixed a bug in the calculation of the "F" local variable which represents the Moon's argument of latitude in the CAAMoonPhases::TruePhase method. Thanks to Andrew Hammond for reporting this bug.

v1.46 (8 May 2011)

• Updated copyright details.
• Fixed a compilation issue on GCC where size_t was undefined in various methods. Thanks to Carsten A. Arnholm and Andrew Hammond for reporting this bug.
• Updated CAARiseTransitSet::Calculate method to return information for circumpolar object rather than returning bValid = false for this type of object. In the case of a circumpolar object, the object does not rise or set on the day in question but will of course transit at a specific time. This change means that you do not need to recall the method with a declination value to get the transit time. In addition if an object never rises or sets, the method will still return the transit time even though it occurs below the horizon by setting the bTransitAboveHorizon value to false. Note that this means that the "Transit" value will now always include a valid value. Also the method has been renamed to Calculate. Thanks to Andrew Hood for prompting this update
• Fixed a bug in CAAGalileanMoons::CalculateHelper where the periodic terms in longitude for the four satellites (Sigma1 to Sigma4) were not being converted to radians prior to some trigonometric calculations. Thanks to Thomas Meyer for reporting this bug.

v1.45 (26 November 2010)

• CAARefraction::RefractionFromApparent now returns a constant refraction value for all altitudes below a certain limit. Thanks to mehrzad khoddam for prompting this update.
• CAARefraction::RefractionFromTrue now returns a constant refraction value for all altitudes below a certain limit. Thanks to mehrzad khoddam for prompting this update.

v1.44 (4 July 2010)

• Fixed various compiler warnings and errors when the code is compiled using C++ Builder. Thanks to Neil Bingham for reporting these issues.
• Removed unnecessary "Longitude" parameter from method CAAParallax::Ecliptic2Topocentric.

v1.43 (3 July 2010)

• Fixed a bug in the g_MoonPerigeeApogeeCoefficients3 table. The "+0.013*cos(4D - 2F)" term was incorrectly using "+0.013*cos(4D - 20F)". The error in the lunar distance because of this coding error is of the order of 1 to 2 KM. Thanks to Thomas Meyer for reporting this bug.
• Fixed a bug in the g_MoonPerigeeApogeeCoefficients1 table. The "D+2M-0.0010" term was incorrectly using "D+2M-0.0011". Thanks to Thomas Meyer for reporting this bug.

v1.42 (21 May 2010)

• Fixed spelling mistakes in AATest.cpp for "Palomar Observatory". Thanks to Leighton Paul for reporting the fact that the change for v1.41 was still spelt incorrectly.

v1.41 (10 May 2010)

• Updated copyright details.
• Minor update to CAAPhysicalMoon::CalculateTopocentric to put a value in a variable for easier debugging
• Fixed up unused variable warnings in AATest.cpp
• Fixed spelling mistakes in AATest.cpp for "Palomor Observatory"
• The CAAEllipticalObjectDetails::AstrometricGeocenticRA value is now known as AstrometricGeocentricRA. Thanks to Scott Marley for reporting this spelling mistake
• The CAANearParabolicObjectDetails::AstrometricGeocenticRA value is now known as AstrometricGeocentricRA. Thanks to Scott Marley for reporting this spelling mistake
• Removed the unused Delta parameter from the CAANutation::NutationInDeclination method. Thanks to Thomas Meyer for reporting this issue.

v1.40 (30 December 2009)

• Updated the sample app to pull in cstdio instead of cstdio.h. Thanks to Hugo Mildenberger for suggesting this update.
• Fixed a number of GCC compiler warnings in AATest.cpp. Thanks to Hugo Mildenberger for suggesting this update.
• The CMake file "CMakeLists.txt" included in the download has been updated to work correctly on Gentoo Linux. Again thanks to Hugo Mildenberger for this update.

v1.39 (24 November 2009)

• Updated the sample app and documentation to provide better guidance on how to calculate the times of Moon rise, transit and set. Thanks to Mehmet Rauf Geden for reporting this bug.

v1.38 (3 October 2009)

• Fixed a copy and paste gremlin in the CAAEarth::EclipticLatitude method where it incorrectly used B2, B3 & B4 coefficient terms for Venus. Due to how this bug occurred, the magnitude of the error from it would increase as the date deviated from the year 2000. Thanks to Isaac Salzman for reporting this bug.

v1.37 (30 April 2009)

• Fixed a bug where the M values in CAARiseTransitSet::Calculate were not being constrained to between 0 and 1. Thanks to Matthew Yager for reporting this issue.

v1.36 (28 March 2009)

• Fixed a bug in CAARiseTransitSet::Calculate where the cyclical nature of a RA value was not taken into account during the interpolation. In fact Meeus in the book even refers to this issue as "Important remarks, 2." on page 30 of the second edition. Basically when interpolating RA, we need to be careful that the 3 values are consistent with respect to each other when any one of them wraps around from 23H 59M 59S around to 0H 0M 0S. In this case, the RA has increased by 0H 0M 1S of RA instead of decreasing by 23H 59M 59S. Thanks to Corky Corcoran and Danny Flippo for both reporting this issue.
• Fixed a bug in the calculation of the parameter "H" in CAARiseTransitSet::Calculate when calculating the local hour angle of the body for the time of transit.

v1.35 (16 March 2009)

• Fixed a bug in CAAParabolic::Calculate(double JD, const CAAParabolicObjectElements& elements) in the calculation of the heliocentric rectangular ecliptical, the heliocentric ecliptical latitude and the heliocentric ecliptical longitude coordinates. The code incorrectly used the value "omega" instead of "w" in its calculation of the value "u". Unfortunately there is no worked examples in Jean Meeus's book for these particular values, hence resulting in my coding errors. Thanks to Jay Borseth for reporting this bug.
• Fixed a bug in CAANearParabolic::Calculate(double JD, const CAANearParabolicObjectElements& elements) in the calculation of the heliocentric rectangular ecliptical, the heliocentric ecliptical latitude and the heliocentric ecliptical longitude coordinates. The code incorrectly used the value "omega" instead of "w" in its calculation of the value "u". Unfortunately there is no worked examples in Jean Meeus's book for these particular values, hence resulting in my coding errors. Thanks to Jay Borseth for reporting this bug.

v1.34 (12 February 2009)

• Fixed a seemingly copy and paste bug in CAAMoon::EclipticLongitude. The layout of the code to calculate the "ThisSigma" value was incorrect. The terms involving any value of M was being multiplied by E. This was incorrect as documented at the bottom of page 338 from the second edition of Meeus's book. The correct logic is to multiple only terms which involve +1M or -1M by E and to multiple any terms which involved 2M or -2M by E*E. With the bug fixed the worked example 47.a from the book now gives: 133.16726428105474 degrees. This is a much closer result to the value as reported in the book which is 133.167265. The previous buggy code was giving the value of 133.16726382897039 degrees for the Moons apparent Longitude. The error in this example is 0.001627 arc seconds of a degree. This error value is well within the actual reported accuracy of 10 arc seconds for the code, but you would expect this error to increase as the eccentricity of earths orbit increases. Thanks to Neoklis Kyriazis for reporting this bug.

v1.33 (7 February 2009)

• Fixed a seemingly copy and paste bug in CAAMoonPerigeeApogee::TruePerigee. The layout of the code to accumulate the "Sigma" value was incorrect. The terms involving T (e.g. +0.00019*T, -0.00013*T etc were adding these terms to the argument of the sin incorrectly. With the bug fixed the worked example 50.a from the book gives: 2447442.3543003569 JDE or 1988 October 7 at 20h:30m:11.5 seconds. The previous buggy code was giving the same value of 2447442.3543003569, but this would be the case because T was a small value in the example. You would expect the error in the calculated to be bigger as the date departs from the Epoch 2000.0. Thanks to Neoklis Kyriazis for reporting this bug.
• Optimized the layout of the MoonCoefficient1 structure in the AAMoon.cpp module by making all elements integers instead of doubles.
• Optimized the layout of the PlutoCoefficient1 structure in the AAPluto.cpp module by making all elements integers instead of doubles.
• Updated the static version of CAADate::DaysInMonth to compile cleanly using code analysis.
• Updated copyright details.

v1.32 (11 November 2008)

• Fixed a bug in CAAElliptical::Calculate(double JD, const CAAEllipticalObjectElements& elements) in the calculation of the heliocentric rectangular ecliptical, the heliocentric ecliptical latitude and the heliocentric ecliptical longitude coordinates. The code incorrectly used the value "omega" instead of "w" in its calculation of the value "u". Unfortunately there is no worked examples in Jean Meeus's book for these particular values, hence resulting in my coding errors. Thanks to Carsten A. Arnholm for reporting this bug.

v1.31 (26 July 2008)

• Changed name of CAASun::EclipticRectangularCoordinatesMeanEquinox to CAASun::EquatorialRectangularCoordinatesMeanEquinox to refer to the fact that it returns equatorial coordinates instead of ecliptic coordinates. Thanks to Frank Trautmann for reporting this issue
• Updated copyright details.
• zip file now ships with a VC 2005 solution instead of a VC 6 solution file.
• Code now compiles cleanly using Code Analysis (/analyze)

v1.30 (29 January 2007)

• The static version of the CAADate::Set method has been renamed to DateToJD to avoid any confusion with the other Set methods. Thanks to Ing. Taras Kapuszczak for reporting this issue.
• The method CAADate::InGregorianCalendar has now also been renamed to the more appropriate CAADate::AfterPapalReform.
• Reinstated the bGregorianCalendar parameter for the CAADate constructors and Set methods.
• Changed the parameter layout for the static version of CAADate::DaysInMonth
• Addition of a CAADate::InGregorianCalendar method.
• Addition of a CAADate::SetInGregorianCalendar method.
• Reworked implementation of GregorianToJulian method.
• Reworked implementation of JulianToGregorian method.

v1.29 (26 January 2007)

• After a bug report from Ing. Taras Kapuszczak that a round trip of the date 25 January 100 as specified in the Gregorian calendar to the Julian day number and then back again produces the incorrect date 26 January 100, I've spent some time looking into the 2 key Meeus Julian Day algorithms. It seems that the algorithms which converts from a Calendar date to JD works ok for propalactive dates, but the reverse algorithm which converts from a JD to a Calendar date does not. Since I made the change in behaviour to support propalactive Gregorian dates to address issues with the Moslem calendar (and since then I have discovered further unresolved bugs in the Moslem calendar algorithms and advised people to check out my DTime+ library instead), I am now reverting these changes so that the date algorithms are now as presented in Meeus's book. This means that dates after 15 October 1582 are assumed to be in the Gregorian calendar and dates before are assumed to be in the Julian calendar. This change also means that some of the CAADate class methods no longer require the now defunct "bool" parameter to specify which calendar the date represents. As part of the testing for this release verification code has been added to AATest.cpp to test all the dates from JD 0 (i.e. 1 January -4712) to a date long in the future. Hopefully with this verification code, we should have no more reported issues with the class CAADate. Again if you would prefer a much more robust and comprehensive Date time class framework, don't forget to check out the authors DTime+ library.
• Optimized CAADate constructor code
• Provided a static version of CAADate::DaysInMonth() method
• Discovered an issue in CAADate::JulianToGregorian. It seems the algorithm presented in the book to do conversion from the Julian to Gregorian calendar fails for Julian dates before the Gregorian calendar reform in 1582. I have sent an email to Jean Meeus to find out if this is a bug in my code or a deficiency in the algorithm presented. Currently the code will assert in this function if it is called for a date before the Gregorian reform.
• Changed name of CAAMoonIlluminatedFraction::IluminatedFraction to CAAMoonIlluminatedFraction::IlluminatedFraction. Thanks to Ing. Taras Kapuszczak for reporting this typo!.

v1.28 (25 January 2007)

• Fixed a minor compliance issue with GCC in the AACoordinateTransformation.h to do with the declaration of various methods. Thanks to Mathieu Peyréga for reporting this issue.

v1.27 (17 January 2007)

• Updated copyright details.
• Addition of a AAPLUS_EXT_CLASS preprocessor macro to allow the code to be more easily added to an extension DLL. Thanks to Mathieu Peyréga for suggesting this update.
• Changed name of CAASun::ApparentEclipticLongtitude to CAASun::ApparentEclipticLongitude. Thanks to Mathieu Peyréga for reporting this typo!.

v1.26 (29 November 2006)

• Fixed a bug where CAAEclipticalElements::Calculate and CAAEclipticalElements::FK4B1950ToFK5J2000 would return the incorrect value for the reduced inclination when the initial inclination value was > 90 degrees.
• Addition of a new module called CAANearParabolic. This new class provides functionality for orbits which can be best modelled as near parabolic i.e. where the eccentricity is between 0.98 and 1.02. Chapter 35 in the book includes support for calculating Near-parabolic orbits, but the code is provided in BASIC and the algorithm as presented has problems converging when the eccentricity is close to 1. Instead the algorithms used in this new module are based upon the worked examples which Paul Schlyter has provided at http://stjarnhimlen.se/comp/tutorial.html#16.

23 October 2006

• Minor update to fix some incorrect book mark links in the documentation.

v1.25 (5 June 2006)

• Fixed a bug in CAAElliptical::Calculate(double JD, EllipticalObject object) where the correction for nutation was incorrectly using the Mean obliquity of the ecliptic instead of the true value. The results from the test program now agree much more closely with the example Meeus provides which is the position of Venus on 1992 Dec. 20 at 0h Dynamical Time. I've also checked the positions against the JPL Horizons web site and the agreement is much better. Because the True obliquity of the Ecliptic is defined as the mean obliquity of the ecliptic plus the nutation in obliquity, it is relatively easy to determine the magnitude of error this was causing. From the chapter on Nutation in the book, and specifically the table which gives the cosine coefficients for nutation in obliquity you can see that the absolute worst case error would be the sum of the absolute values of all of the coefficients and would have been c. 10 arc seconds of degree, which is not a small amount!. This value would be an absolute worst case and I would expect the average error value to be much much smaller (probably much less than an arc second). Anyway the bug has now been fixed. Thanks to Patrick Wong for pointing out this rather significant bug.

18 May 2006

• Jean Meeus has confirmed that there is definitely a bug in the Moslem calendar algorithms which make up the CAAMoslemCalendar class. He is not the original author of these algorithms, so he was unable to explain why they fail for some dates. As previously mentioned please use the DTime+ classes to avoid this issue.

v1.24 (12 May 2006)

• Updated the documentation to use the same style as the web site.
• Fixed a transcription error in the third coefficient used to calculate the R0 term for the radius vector of Mercury. Thanks to John Kruso for reporting this issue.
• Fixed a transcription error in the third coefficient used to calculate the R1 term for the radius vector of Mercury. Thanks to John Kruso for reporting this issue.
• Updated copyright details.

1 May 2006

• While testing v3.01 of DTime+ I discovered some bugs in the CAAMoslemCalendar class. Specifically testing some dates by creating a Moslem date, then converting to a Julian date and then converting back to the Moslem calendar highlighted some dates which fail this roundtrip test. If you are serious about developing for the Moslem calendar, then please use the Moslem calendar support in DTime+ which uses an independent algorithm for the Moslem calendar which does not have this problem. I will report this issue to Jean Meeus and possibly have a fix for it in the next update to AA+.

v1.23 (16 November 2005)

• Fixed a transcription error in the second coefficient used to calculate the longitude of Mercury. Thanks to "Maurizio" for reporting this bug.

v1.22 (5 July 2005)

• Fix for a bug to ensure that values returned from CAAEquationOfTime::Calculate does not return discontinuities. Instead it now returns negative values when required.

v1.21 (3 June 2005)

• Minor update to "CMakeLists.txt" file to fix a case sensitivity issue. Thanks to Andrew Maclean for reporting this issue.

v1.20 (2 June 2005)

• Seems the case sensitivity issue fixed in v1.17 was not fixed because I forgot to update the files in the zip download. Thanks to Andrew Maclean for reporting this issue.
• A "CMakeLists.txt" file is now included in the download. This file is used by CMake (http://www.cmake.org/HTML/Index.html) which is a cross-platform makefile generator. This allows the AA+ code to be easily compiled on Cygwin, Linux and the usual MSVC compilers. Thanks to Andrew Maclean for this nice addition.
• Some of the functions in the class "CAACoordinateTransformation" have been made inline to improve performance.
• Made all structures used by AA+ classes. This is a minor tidy up issue more than anything. Also ensured all class members are initialized to sane defaults.

v1.19 (13 May 2005)

• Fix for CAADate::Set(double JD, bool bGregorianCalendar) not setting the m_bGregorianCalendar member variable correctly.

v1.18 (21 April 2005)

• Renamed "AAAberation.cpp" to "AAAberration.cpp" so that all source code filenames match their corresponding header files. Thanks to Jürgen Schuck for suggesting this update.

v1.17 (1 February 2005)

• Fixed a case sensitivity problem (at least on Unix systems) related to the stdafx.h/cpp files. Now filename is all lowercase. Thanks to Mika Heiskanen for reporting this problem.
• Change the ordering of items in stdafx.h so that you get a clean compile on gcc. Thanks to Mika Heiskanen for reporting this problem.
• Fixed a problem with the declaration of the variable "Index" in the function CAADynamicalTime::DeltaT. Thanks to Mika Heiskanen for reporting this problem.
• Removed usage of MFC from sample app as it is not required.
• Verfied the building of the code on GCC thro the use of Cygwin's port of GCC.

v1.16 (31 January 2005)

• Fixed a bug in CAAParabolic::Calculate where the JD value was being used incorrectly in the loop. Thanks to Mika Heiskanen for reporting this problem.
• Fixed a GCC warning in CAADynamicalTime::DeltaT. Thanks to Mika Heiskanen for reporting this problem.
• Fixed a GCC compiler error related to missing include for memset in AAEclipses.cpp. Thanks to Mika Heiskanen for reporting this problem.

v1.15 (30 January 2005)

• Replaced all usage of BOOL with bool to aid in cross compiler compatibility. This also means that all occurrences of TRUE and FALSE are replaced with true and false respectively. Thanks to Mika Heiskanen for reporting this issue.
• cmath header file is now used rather than math.h. Also it now does not use the #pragma message text based on a define which is MS C specific. Again thanks to Mika Heiskanen for reporting this issue.
• Now uses asssert instead of the MFC specific ASSERT. Again thanks to Mika Heiskanen for reporting this issue.
• Addition of a new global header file "AA+.h" which allows you to include all of the AA+ framework through one header.
• Code now use static_cast's rather than old C-style casts. Again thanks to Mika Heiskanen for reporting this issue.
• Optimized some of the code in assert's which avoid unitialized variables when build in release mode. Again thanks to Mika Heiskanen for reporting this issue.

v1.14 (21 January 2005)

• Fixed a small but important error in the function PhaseAngle(r, R, Delta). The code was producing incorrect results and raises acos DOMAIN errors and floating point exceptions when calculating phase angles for the inner planets. Thanks to MICHAEL R. MEYER for reporting this problem.

v1.13 (31 December 2004)

• Fix for CAAElliptical::MinorPlanetMagnitude where the phase angle was being incorrectly converted from Radians to Degress when it was already in degrees. Thanks to Martin Burri for reporting this problem.

v1.12 (10 November 2004)

• Fix for CAADate::Get so that it works correctly for propalactive calendar dates. The Meeus implementation automatically assumes the Gregorian Calendar came into effect on 15 October 1582 (JD: 2299161), while the CAADate implementation has a "m_bGregorianCalendar" value to decide if the date was specified in the Gregorian or Julian Calendars. This difference means in effect that CAADate fully supports propalactive versions of both calendar systems. This problem was discovered when testing the Moslem calendar code which involves a round trip between Moslem -> Julian -> Gregorian calendars.

v1.11 (15 October 2004)

• bValid variable is now correctly set in CAARiseTransitSet::Calculate if the objects does actually rise and sets.

v1.10 (17 September 2004)

• Fixed a number of warnings in the code when compiled in VC .Net 2003 with the "Force conformance in For Loop Scope" compiler option is set.

6 September 2004

• Minor update to the documentation plus a full spell check!!

v1.09 (15 June 2004)

• Fixed a typo in the calculation of SunLongDash in CAAPhysicalSun::Calculate. Thanks to Brian Orme for spotting this problem.

v1.08 (31 May 2004)

• Added a missing coefficient to g_L1JupiterCoefficients array as used by CAAJupiter::EclipticLongitude. Thanks to Brian Orme for reporting this problem.
• Added missing g_B5JupiterCoefficients[] in CAAJupiter::EclipticLatitude. Again thanks to Brian Orme for reporting this problem.
• In CAASaturn::EclipticLongitude the g_L5SaturnCoefficients[] were not included. Thanks to Brian Orme for reporting this problem.
• In CAASaturn::EclipticLatitude the g_B5SaturnCoefficients[] were not included. Thanks to Brian Orme for reporting this problem.
• In CAASaturn::RadiusVector the g_R5SaturnCoefficients[] were not included. Thanks to Brian Orme for reporting this problem.

v1.07 (24 May 2004)

• Fixed a missing break statement in CAAElliptical::Calculate. Thanks to Carsten A. Arnholm for reporting this bug.
• Also fixed an issue with the calculation of the apparent distance to the Sun.

27 April 2004

• Minor update to the documentation describing CAAElliptical::MeanMotionFromSemiMajorAxis

V1.06 (22 February 2004)

• Calculation of semi durations for eclipses in CAAEclipses is now calculated only when required

V1.05 (22 February 2004)

• Fixed a bug in the calculation of the phase type from the k value in CAAMoonPhases::TruePhase.

V1.04 (21 February 2004)

• The optical libration in longitude for the moon is now returned in the range -180 - 180 degrees

V1.03 (14 February 2004)

• Fixed a "minus zero" bug in the function CAACoordinateTransformation::DMSToDegrees. The sign of the value is now taken explicitly from the new bPositive boolean parameter. Thanks to Patrick Wallace for reporting this problem.

V1.02 (9 February 2004)

• Replaced all calls to the macro "INT" with the function CAADate::INT which is what they should have been. The only affected class for this was CAAMoslemCalendar.
• Fixed a number of level 4 warnings in the CAAStellarMagnitudes class when the code is compiled in VC.Net 2003.

V1.01 (9 February 2004)

• Updated the values used in the calculation of the a1 and a2 constants for Saturn's moon Rhea (satellite V) following an email from Jean Meeus confirming that these constants are indeed incorrect as published in the book.

V1.0 (6 February 2004)

• Initial public release.

Class Framework Reference

The framework consists of the following classes:

CAAAberration

CAAAngularSeparation

CAABinaryStar

CAACoordinateTransformation

CAADate

CAADiameters

CAADynamicalTime

CAAEarth

CAAEaster

CAAEclipses

CAAEclipticalElements

CAAElementsPlanetaryOrbit

CAAElliptical

CAAELP2000

CAAELPMPP02

CAAEquationOfTime

CAAEquinoxesAndSolstices

CAAEquinoxesAndSolstices2

CAAFK5

CAAGalileanMoons

CAAGlobe

CAAIluminatedFraction

CAAInterpolate

CAAJewishCalendar

CAAJupiter

CAAKepler

CAAMars

CAAMercury

CAAMoon

CAAMoonIlluminatedFraction

CAAMoonMaxDeclinations

CAAMoonMaxDeclinations2

CAAMoonNodes

CAAMoonNodes2

CAAMoonPerigeeApogee

CAAMoonPerigeeApogee2

CAAMoonPhases

CAAMoonPhases2

CAAMoslemCalendar

CAANearParabolic

CAANeptune

CAANodes

CAANutation

CAAParabolic

CAAParallactic

CAAParallax

CAAPhysicalJupiter

CAAPhysicalMars

CAAPhysicalMoon

CAAPhysicalSun

CAAPlanetaryPhenomena

CAAPlanetaryPhenomena2

CAAPlanetPerihelionAphelion

CAAPlanetPerihelionAphelion2

CAAPluto

CAAPrecession

CAARefraction

CAARiseTransitSet (Deprecated)

CAARiseTransitSet2

CAASaturn

CAASaturnMoons

CAASaturnRings

CAASidereal

CAAStellarMagnitudes

CAASun

CAAUranus

CAAVenus

CAAVSOP2013

CAAVSOP87_EMB

CAAVSOP87_Jupiter

CAAVSOP87_Mars

CAAVSOP87_Mercury

CAAVSOP87_Neptune

CAAVSOP87_Saturn

CAAVSOP87_Uranus

CAAVSOP87_Venus

CAAVSOP87A_Earth

CAAVSOP87A_EMB

CAAVSOP87A_Jupiter

CAAVSOP87A_Mars

CAAVSOP87A_Mercury

CAAVSOP87A_Neptune

CAAVSOP87A_Saturn

CAAVSOP87A_Uranus

CAAVSOP87A_Venus

CAAVSOP87B_Earth

CAAVSOP87B_Jupiter

CAAVSOP87B_Mars

CAAVSOP87B_Mercury

CAAVSOP87B_Neptune

CAAVSOP87B_Saturn

CAAVSOP87B_Uranus

CAAVSOP87B_Venus

CAAVSOP87C_Earth

CAAVSOP87C_Jupiter

CAAVSOP87C_Mars

CAAVSOP87C_Mercury

CAAVSOP87C_Neptune

CAAVSOP87C_Saturn

CAAVSOP87C_Uranus

CAAVSOP87C_Venus

CAAVSOP87D_Earth

CAAVSOP87D_Jupiter

CAAVSOP87D_Mars

CAAVSOP87D_Mercury

CAAVSOP87D_Neptune

CAAVSOP87D_Saturn

CAAVSOP87D_Uranus

CAAVSOP87D_Venus

CAAVSOP87E_Earth

CAAVSOP87E_Jupiter

CAAVSOP87E_Mars

CAAVSOP87E_Mercury

CAAVSOP87E_Neptune

CAAVSOP87E_Saturn

CAAVSOP87E_Sun

CAAVSOP87E_Uranus

CAAVSOP87E_Venus

CAAberration

This class provides for calculation of the effects of aberration. This refers to Chapter 23 in the book.

Functions this class provides include:

EarthVelocity

EclipticAberration

EquatorialAberration

CAAAberration::EarthVelocity

static CAA3DCoordinate EarthVelocity(double JD, bool bHighPrecision)

Return Value

3D rectangular heliocentric equatorial velocity of the Earth based on the fixed equator and equinox of FK5 for the epoch J2000.0. The units of each coordinate returned are in 10 to the power of -8 astronomical units per day.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAAberration::EclipticAberration

static CAA2DCoordinate EclipticAberration(double Lambda, double Beta, double JD, bool bHighPrecision)

Return Value

Returns the correction due to aberration. The X value will contain the ecliptic longitude correction in degrees and Y will contain the ecliptic latitude correction in degrees.

Parameters

Lambda The ecliptic longitude in degrees.

Beta The ecliptic latitude in degrees.

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAAberration::EquatorsialAberration

static CAA2DCoordinate EquatorialAberration(double Alpha, double Delta, double JD, bool bHighPrecision)

Return Value

Returns the correction due to aberration. The X value will contain the right ascension correction expressed as an hour angle and Y will contain the declination correction in degrees.

Parameters

Alpha The right ascension expressed as an hour angle.

Delta The declination in degrees.

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAAngularSeparation

This class provides the algorithms which obtain various separation distances between celestial objects. This refers to Chapter 17, 19 & 20 in the book.

Functions this class provides include:

Separation

PositionAngle

DistanceFromGreatArc

SmallestCircle

CAAAngularSeparation::Separation

static double Separation(double Alpha1, double Delta1, double Alpha2, double Delta2)

Return Value

Returns the distance between the two positions in degrees.

Parameters

Alpha1 The first right ascension expressed as an hour angle.

Delta1 The first declination in degrees

Alpha2 The second right ascension expressed as an hour angle.

Delta2 The second declination in degrees

CAAAngularSeparation::PositionAngle

static double PositionAngle(double Alpha1, double Delta1, double Alpha2, double Delta2)

Return Value

Returns the position angle of (Alpha1, Delta1) relative to (Alpha2, Delta2) in degrees.

Parameters

Alpha1 The first right ascension expressed as an hour angle.

Delta1 The first declination in degrees

Alpha2 The second right ascension expressed as an hour angle.

Delta2 The second declination in degrees

CAAAngularSeparation::DistanceFromGreatArc

static double DistanceFromGreatArc(double Alpha1, double Delta1, double Alpha2, double Delta2, double Alpha3, double Delta3)

Return Value

Returns the distance of (Alpha3, Delta3) to the great circle (Alpha1, Delta1) - (Alpha2, Delta2) in degrees.

Parameters

Alpha1 The first right ascension expressed as an hour angle.

Delta1 The first declination in degrees

Alpha2 The second right ascension expressed as an hour angle.

Delta2 The second declination in degrees

Alpha3 The third right ascension expressed as an hour angle.

Delta3 The third declination in degrees

CAAAngularSeparation::SmallestCircle

static double SmallestCircle(double Alpha1, double Delta1, double Alpha2, double Delta2, double Alpha3, double Delta3, bool& bType1)

Return Value

Returns the diameter of the smallest circle encompassing the 3 points in degrees.

Parameters

Alpha1 The first right ascension expressed as an hour angle.

Delta1 The first declination in degrees

Alpha2 The second right ascension expressed as an hour angle.

Delta2 The second declination in degrees

Alpha3 The third right ascension expressed as an hour angle.

Delta3 The third declination in degrees

bType1 Upon return will be true if the smallest circle is of type 1, otherwise false, implying smallest circle is of type 2.

CAABinaryStar

This class provides for calculation of the position of a Binary Star system. This refers to Chapter 57 in the book.

Functions this class provides include:

Calculate

ApparentEccentricity

CAABinaryStar::Calculate

static CAABinaryStarDetails Calculate(double t, double P, double T, double e, double a, double i, double omega, double w)

Return Value

A class containing

r The radius vector of the secondary star in arc seconds of a degree.

Theta The apparent position angle of the secondary star in degrees.

Rho The angular separation between the two stars in arc seconds of a degree.

x The x cartesian coordinate value of the secondary star in arc seconds of a degree.

y The y cartesian coordinate value of the secondary star in arc seconds of a degree.

Parameters

t The time given in years and decimals to perform the calculation for.

P The period of revolution expressed in mean solar years.

T The time of periastron passage given in years and decimals.

e Eccentricity of the true orbit.

a The semi major axis expressed in seconds of a degree.

i The inclination of the plane of the true orbit in degrees to the plane at right angles to the line of sight.

omega The position angle of the ascending node in degrees.

w The longitude of the periastron in degrees.

CAABinaryStar::ApparentEccentricty

static double ApparentEccentricity(double e, double i, double w)

Return Value

The apparent eccentricity of the binary star orbit

Parameters

e Eccentricity of the true orbit.

i The inclination of the plane of the true orbit in degrees to the plane at right angles to the line of sight.

w The longitude of the periastron in degrees.

CAACoordinateTransformation

This class provides for the transformations of the coordinates as well as helper angle methods. This refers to Chapter 13 and parts of Chapter 1 in the book.

Functions this class provides include:

Equatorial2Ecliptic

Ecliptic2Equatorial

Equatorial2Horizontal

Horizontal2Equatorial

Equatorial2Galactic

Galactic2Equatorial

PI

DegreesToRadians

RadiansToDegrees

RadiansToHours

HoursToRadians

HoursToDegrees

DegreesToHours

DMSToDegrees

MapTo0To360Range

MapTo0To24Range

MapTo0To2PIRange

MapToMinus90To90Range

CAACoordinateTransformation::Equatorial2Ecliptic

static CAA2DCoordinate Equatorial2Ecliptic(double Alpha, double Delta, double Epsilon)

Return Value

Returns the converted ecliptic coordinates in a CAA2DCoordinate class. The x value in the class corresponds to the ecliptic longitude in degrees and the y value corresponds to the ecliptic latitude in degrees.

Parameters

Alpha The right ascension expressed as decimal hours.

Delta The declination in degrees.

Epsilon The obliquity of the ecliptic in degrees.

Remarks

The transformation of coordinates from Equatorial to Ecliptic. This refers to algorithm 13.1 and 13.2 on page 93.

CAACoordinateTransformation::Ecliptic2Equatorial

static CAA2DCoordinate Ecliptic2Equatorial(double Lambda, double Beta, double Epsilon)

Return Value

Returns the converted equatorial coordinates in a CAA2DCoordinate class. The x value in the class corresponds to the right ascension in decimal hours and the y value corresponds to the declination in degrees.

Parameters

Lambda The ecliptic longitude in degrees.

Beta The ecliptic latitude in degrees.

Epsilon the obliquity of the ecliptic in degrees.

Remarks

The transformation of coordinates from Ecliptic to Equatorial. This refers to algorithm 13.3 and 13.4 on page 93.

CAACoordinateTransformation::Equatorial2Horizontal

static CAA2DCoordinate Equatorial2Horizontal(double LocalHourAngle, double Delta, double Latitude)

Return Value

Returns the converted horizontal coordinates in a CAA2DCoordinate class. The x value in the class corresponds to the azimuth in degrees west of south and the y value corresponds to the altitude in degrees.

Parameters

LocalHourAngle The local hour angle in decimal hours, measured westwards from the South. To convert a equatorial right ascension to a local hour angle you can use the formula as mentioned on page 92: Local hour angle (H) = apparent sidereal time at Greenwich (theta) - observer's longitude (L, positive west, negative east from Greenwich) - right ascension. You should of course make sure that all the values used in this formula are expressed as decimal hours before applying the formula (in particular the observer's longitude "L" value).

Delta The declination in degrees.

Latitude The standard latitude of the position in degrees.

Remarks

The transformation of coordinates from Equatorial to Horizontal. This refers to algorithm 13.5 and 13.6 on page 93.

CAACoordinateTransformation::Horizontal2Equatorial

static CAA2DCoordinate Horizontal2Equatorial(double A, double h, double Latitude)

Return Value

Returns the converted equatorial coordinates in a CAA2DCoordinate class. The x value in the class corresponds to the local hour angle in decimal hours and the y value corresponds to the declination in degrees.

Parameters

A The azimuth in degrees west of south.

h The altitude in degrees

Latitude The standard latitude of the position in degrees.

Remarks

The transformation of coordinates from Horizontal to Equatorial. This refers to the two algorithms on the top of page 94. To convert the returned local hour angle back to a right ascension in decimal hours you can use the formula as mentioned on page 92: right ascension (alpha) = apparent sidereal time at Greenwich (theta) - Local hour angle (H) - observer's longitude (L, positive west, negative east from Greenwich). You should of course make sure that all the values used in this formula are expressed as decimal hours before applying the formula (in particular the observer's longitude "L" value).

CAACoordinateTransformation::Equatorial2Galactic

static CAA2DCoordinate Equatorial2Galactic(double Alpha, double Delta)

Return Value

Returns the converted galactic coordinates in a CAA2DCoordinate class. The x value in the class corresponds to the galactic longitude in degrees and the y value corresponds to the galactic latitude in degrees.

Parameters

Alpha The right ascension in decimal hours.

Delta The declination in degrees.

Remarks

The transformation of coordinates from Equatorial to Galactic. This refers to algorithm 13.7 and 13.8 on page 94.

CAACoordinateTransformation::Galactic2Equatorial

static CAA2DCoordinate Galactic2Equatorial(double l, double b)

Return Value

Returns the converted equatorial coordinates in a CAA2DCoordinate class. The x value in the class corresponds to the right ascension in decimal hours and the y value corresponds to the declination in degrees.

Parameters

l  The galactic longitude expressed in degrees.

b The galactic latitude expressed in degrees.

Remarks

The transformation of coordinates from Galactic to Equatorial. This refers to the last two algorithms on page 94.

CAACoordinateTransformation::PI

static double PI()

Return Value

Returns the constant value of pi i.e 3.1415926...

CAACoordinateTransformation::DegreesToRadians

static double DegreesToRadians(double Degrees)

Return Value

Returns the value in radians which was converted from degrees.

Parameters

Degrees The angular value to convert measured in degrees.

CAACoordinateTransformation::RadiansToDegrees

static double RadiansToDegrees(double Radians)

Return Value

Returns the value in degrees which was converted from radians.

Parameters

Radians The angular value to convert measured in radians.

CAACoordinateTransformation::RadiansToHours

static double RadiansToHours(double Radians)

Return Value

Returns the value expressed as an hour angle which was converted from radians.

Parameters

Radians The angular value to convert measured in radians.

CAACoordinateTransformation::HoursToRadians

static double HoursToRadians(double Hours)

Return Value

Returns the value in radians which was converted from hours.

Parameters

Hours The numeric value to convert measured in hours.

CAACoordinateTransformation::HoursToDegrees

static double HoursToDegrees(double Hours)

Return Value

Returns the value in degrees which was converted from hours.

Parameters

Hours The numeric value to convert measured in hours.

CAACoordinateTransformation::DegreesToHours

static double DegreesToHours(double Degrees)

Return Value

Returns the value in hours which was converted from degrees.

Parameters

Degrees The angular value to convert measured in degrees.

CAACoordinateTransformation::DMSToDegrees

DMSToDegrees(double Degrees, double Minutes, double Seconds, bool bPositive = true)

Return Value

Returns the value in degrees which was converted from degrees, minutes and seconds.

Parameters

Degrees  The degree part of the angular value to convert.

Minutes The minute part of the angular value to convert.

Seconds The second part of the angular value to convert.

bPositive true if the input value corresponds to a non-negative value with false implying the value is positive

Remarks

To convert the angle 21° 44' 07" you would use DMSToDegrees(21, 44, 7, true).

To convert the angle -12° 47' 22" you would use DMSToDegrees(12, 47, 22, false) or DMSToDegrees(-12, -47, -22, true).

To convert the angle -0° 32' 41" you must use DMSToDegrees(0, 32, 41, false).

CAACoordinateTransformation::MapTo0To360Range

static double MapTo0To360Range(double Degrees)

Return Value

Maps an arbitrary angular value to the range 0 to 360. i.e. inputting the value -2 will return a value of 258.

Parameters

Degrees The angular value.

CAACoordinateTransformation::MapTo0To24Range

static double MapTo0To24Range(double HourAngle)

Return Value

Maps an arbitrary value to the range 0 to 24. i.e. inputting the value -2 will return a value of 22.

Parameters

HourAngle The hour angle.

CAACoordinateTransformation::MapTo0To2PIRange

static double MapTo0To2PIRange(double Angle)

Return Value

Maps an arbitrary value to the range 0 to 2*PI. i.e. inputting the value -1 will return a value of 5.2831853071795862.

Parameters

Angle The angle in radians.

CAACoordinateTransformation::MapToMinus90To90Range

static double MapToMinus90To90Range(double Degrees)

Return Value

Maps an arbitrary angular value to the range -90 to 90.

Parameters

Degrees The angular value.

CAADate

This class provides the algorithms which convert between the Gregorian and Julian calendars and the Julian Day. This refers to Chapter 7 and parts of Chapter 9 in the book.

Functions this class provides include:

CAADate

IsLeap

Julian

operator double

Day

Month

Year

Hour

Minute

Second

Set

SetInGregorianCalendar

InGregorianCalendar

Get

DayOfWeek

DayOfYear

DaysInMonth

DaysInYear

DayOfYearToDayAndMonthAndDate

JulianToGregorian

GregorianToJulian

Leap

FractionalYear

AfterPapalReform

CAADate::CAADate

CAADate()

CAADate(long Year, long Month, double Day, bool bGregorianCalendar)

CAADate(long Year, long Month, double Day, double Hour, double Minute, double Second, bool bGregorianCalendar)

CAADate(double JD, bool bGregorianCalendar)

Parameters

Year The year. (Years are counted astronomically i.e. 1 BC = Year 0)

Month The month of the year (1 for January to 12 for December).

Day The day of the month (Can include decimals).

Hour The hour (Can include decimals).

Minute The minute (Can include decimals).

Second The seconds (Can include decimals).

JD The Julian day including decimals.

bGregorianCalendar true to imply a date in the Gregorian Calendar, false means use the Julian Calendar.

Remarks

Constructs a date given a variety of parameters.

CAADate::IsLeap

static bool IsLeap(long Year, bool bGregorianCalendar)

Return Value

true if the specified year is leap otherwise false.

Parameters

Year The year. (Years are counted astronomically i.e. 1 BC = Year 0)

bGregorianCalendar true to imply a date in the Gregorian Calendar, false means use the Julian Calendar.

CAADate::Julian

double Julian() const

Return Value

Returns the underlying Julian Day including decimals.

CAADate::operator double

operator double() const

Return Value

Returns the underlying Julian Day including decimals.

CAADate::Day

long Day() const

Return Value

Returns the day of the month this date represents.

CAADate::Month

long Month() const

Return Value

Returns the month (1 - 12) this date represents.

CAADate::Year

long Year() const

Return Value

Returns the year this date represents.

CAADate::Hour

long Hour() const

Return Value

Returns the hour this date represents.

CAADate::Minute

long Minute() const

Return Value

Returns the minute this date represents.

CAADate::Second

double Second() const

Return Value

Returns the seconds this date represents.

CAADate::Set

void Set(long Year, long Month, double Day, double Hour, double Minute, double Second, bool bGregorianCalendar)

void Set(double JD, bool bGregorianCalendar)

Parameters

Year The year. (Years are counted astronomically i.e. 1 BC = Year 0)

Month The month of the year (1 for January to 12 for December).

Day The day of the month (Can include decimals).

Hour The hour (Can include decimals).

Minute The minute (Can include decimals).

Second The seconds (Can include decimals).

JD The Julian day including decimals

bGregorianCalendar true to imply a date in the Gregorian Calendar, false means use the Julian Calendar.

Remarks

Allows the date to be modified after construction.

CAADate::SetInGregorianCalendar

void SetInGregorianCalendar(bool bGregorianCalendar)

Parameters

bGregorianCalendar true to imply a date in the Gregorian Calendar, false means use the Julian Calendar.

Remarks

Allows the date's calendar type to be changed after construction.

CAADate::InGregorianCalendar

bool InGregorianCalendar() const

Return Value

Returns true if this date is in the Gregorian calendar, false means the Julian Calendar.

CAADate::Get

void Get(long& Year, long& Month, long& Day, long& Hour, long& Minute, double& Second)

Parameters

Year Upon return will contain the year. (Years are counted astronomically i.e. 1 BC = Year 0)

Month Upon return will contain the month of the year (1 for January to 12 for December).

Day Upon return will contain the day of the month.

Hour Upon return will contain the hour.

Minute Upon return will contain the minute.

Second Upon return will contain the seconds (Can include decimals).

Remarks

Allows the date parts to be retrieved.

CAADate::DayOfWeek

DAY_OF_WEEK DayofWeek() const

Return Value

Returns an enum which identifies which day of the week this date represents.

CAADate::DayOfYear

double DayofYear() const

Return Value

Returns the day of year (including decimals) this date represents.

CAADate::DaysInMonth

long DaysInMonth() const

static DaysInMonth(long Month, bool bLeap)

Return Value

Returns the total number of days in the month (28 - 31) which this date represents. The static version of the function can be used if you do not want to construct a CAADate instance to do this test.

CAADate::DaysInYear

long DaysInYear() const

Return Value

Returns the total number of days in the year (365 or 366) which this date represents.

CAADate::DayOfYearToDayAndMonth

static DayOfYearToDayAndMonth(long DayOfYear, bool bLeap, long& DayOfMonth, long& Month)

Parameters

DayOfYear The day of the year where 1st of January is 1 going up to 365 or 366 for 31st of December

bLeap true if the year being considered is a leap year, otherwise false.

DayOfMonth Upon return will contain the day of the month.

Month Upon return will contain the month.

CAADate::JulianToGregorian

static CAACalendarDate JulianToGregorian(long Year, long Month, long Day)

Return Value

A class containing

Year The year in the Gregorian Calendar. (Years are counted astronomically i.e. 1 BC = Year 0)

Month The month of the year in the Gregorian Calendar (1 for January to 12 for December).

Day The day of the month in the Gregorian Calendar.

Parameters

Year The year in the Julian Calendar to convert. (Years are counted astronomically i.e. 1 BC = Year 0)

Month The month of the year in the Julian Calendar (1 for January to 12 for December).

Day The day of the month in the Julian Calendar.

Remarks

Converts a calendrical date expressed in the Julian Calendar to the equivalent date in the Gregorian Calendar. It is assumed that the adoption of the Gregorian Calendar occurred in 1582.

CAADate::GregorianToJulian

static CAACalendarDate GregorianToJulian(long Year, long Month, long Day)

Return Value

A class containing

Year The year in the Julian Calendar. (Years are counted astronomically i.e. 1 BC = Year 0)

Month The month of the year in the Julian Calendar (1 for January to 12 for December).

Day The day of the month in the Julian Calendar.

Parameters

Year The year in the Gregorian Calendar to convert. (Years are counted astronomically i.e. 1 BC = Year 0)

Month The month of the year in the Gregorian Calendar (1 for January to 12 for December).

Day The day of the month in the Gregorian Calendar.

Remarks

Converts a calendrical date expressed in the Gregorian Calendar to the equivalent date in the Julian Calendar.

CAADate::Leap

bool Leap() const

Return Value

true if the year which this date represents is leap otherwise false.

CAADate::FractionalYear

double FractionalYear() const

Return Value

Returns the years with decimals this date represents e.g. the middle of the year 2000 would be returned as 2000.5.

CAADate::AfterPapalReform

bool AfterPapalReform(long Year, long Month, double Day)
bool AfterPapalReform(double JD)

Parameters

Year The year. (Years are counted astronomically i.e. 1 BC = Year 0)

Month The month of the year (1 for January to 12 for December).

Day The day of the month (Can include decimals).

JD The Julian day including decimals

Remarks

Returns true if the date occurs on or after the Gregorian calendar reform which occurred on 15th October 1582 (which corresponds to Julian Day 2299160.5), otherwise false. Please note that the CAADate class assumes the calendar change occured on this date. Historically of course different countries adopted the reform at different times.

CAADiameters

This class provides the algorithms for the semi diameters of the Sun, Moon, Planets and Asteroids. This refers to Chapter 55 in the book.

Functions this class provides include:

SunSemidiameterA

MercurySemidiameterA

VenusSemidiameterA

MarsSemidiameterA

JupiterEquatorialSemidiameterA

JupiterPolarSemidiameterA

SaturnEquatorialSemidiameterA

SaturnPolarSemidiameterA

ApparentSaturnPolarSemidiameterA

UranusSemidiameterA

NeptuneSemidiameterA

MercurySemidiameterB

VenusSemidiameterB

MarsSemidiameterB

JupiterEquatorialSemidiameterB

JupiterPolarSemidiameterB

SaturnEquatorialSemidiameterB

SaturnPolarSemidiameterB

ApparentSaturnPolarSemidiameterB

UranusSemidiameterB

NeptuneSemidiameterB

PlutoSemidiameterB

GeocentricMoonSemidiameter

TopocentricMoonSemidiameter

AsteroidDiameter

ApparentAsteroidDiameter

CAADiameters::SunSemidiameterA

static double SunSemidiameterA(double Delta)

Return Value

The suns semi diameter in arc seconds.

Parameters

Delta The distance to the Sun in astronomical units.

CAADiameters::MercurySemidiameterA

static double MercurySemidiameterA(double Delta)

Return Value

Mercury's semi diameter in arc seconds.

Parameters

Delta The distance to Mercury in astronomical units.

CAADiameters::VenusSemidiameterA

static double VenusSemidiameterA(double Delta)

Return Value

Venus's semi diameter in arc seconds.

Parameters

Delta The distance to Venus in astronomical units.

CAADiameters::MarsSemidiameterA

static double MarsSemidiameterA(double Delta)

Return Value

Mars's semi diameter in arc seconds.

Parameters

Delta The distance to Mars in astronomical units.

CAADiameters::JupiterEquatorialSemidiameterA

static double JupiterEquatorialSemidiameterA(double Delta)

Return Value

Jupiter's equatorial semi diameter in arc seconds.

Parameters

Delta The distance to Jupiter in astronomical units.

CAADiameters::JupiterPolarSemidiameterA

static double JupiterPolarSemidiameterA(double Delta)

Return Value

Jupiter's polar semi diameter in arc seconds.

Parameters

Delta The distance to Jupiter in astronomical units.

CAADiameters::SaturnEquatorialSemidiameterA

static double SaturnEquatorialSemidiameterA(double Delta)

Return Value

Saturn's equatorial semi diameter in arc seconds.

Parameters

Delta The distance to Saturn in astronomical units.

CAADiameters::SaturnPolarSemidiameterA

static double SaturnPolarSemidiameterA(double Delta)

Return Value

Saturn's polar semi diameter in arc seconds.

Parameters

Delta The distance to Saturn in astronomical units.

CAADiameters::ApparentSaturnPolarSemidiameterA

static double ApparentSaturnPolarSemidiameterA(double Delta, double B)

Return Value

Saturn's polar semi diameter in arc seconds.

Parameters

Delta The distance to Saturn in astronomical units.

B The Saturnicentric latitude of the Earth in degrees.

Remarks

Due to the large inclinations of Saturn, the apparent polar semi diameter can be different to the true polar semi diameter.

CAADiameters::UranusSemidiameterA

static double UranusSemidiameterA(double Delta)

Return Value

Uranus's semi diameter in arc seconds.

Parameters

Delta The distance to Uranus in astronomical units.

CAADiameters::NeptuneSemidiameterA

static double NeptuneSemidiameterA(double Delta)

Return Value

Neptune's semi diameter in arc seconds.

Parameters

Delta The distance to Neptune in astronomical units.

CAADiameters::MercurySemidiameterB

static double MercurySemidiameterB(double Delta)

Return Value

Mercury's semi diameter in arc seconds.

Parameters

Delta The distance to Mercury in astronomical units.

Remarks

Uses the updated Astronomical Almanac for 1984 size.

CAADiameters::VenusSemidiameterB

static double VenusSemidiameterB(double Delta)

Return Value

Venus's semi diameter in arc seconds.

Parameters

Delta The distance to Venus in astronomical units.

Remarks

Uses the updated Astronomical Almanac for 1984 size.

CAADiameters::MarsSemidiameterB

static double MarsSemidiameterB(double Delta)

Return Value

Mars's semi diameter in arc seconds.

Parameters

Delta The distance to Mars in astronomical units.

Remarks

Uses the updated Astronomical Almanac for 1984 size.

CAADiameters::JupiterEquatorialSemidiameterB

static double JupiterEquatorialSemidiameterB(double Delta)

Return Value

Jupiter's equatorial semi diameter in arc seconds.

Parameters

Delta The distance to Jupiter in astronomical units.

Remarks

Uses the updated Astronomical Almanac for 1984 size.

CAADiameters::JupiterPolarSemidiameterB

static double JupiterPolarSemidiameterB(double Delta)

Return Value

Jupiter's polar semi diameter in arc seconds.

Parameters

Delta The distance to Jupiter in astronomical units.

Remarks

Uses the updated Astronomical Almanac for 1984 size.

CAADiameters::SaturnEquatorialSemidiameterB

static double SaturnEquatorialSemidiameterB(double Delta)

Return Value

Saturn's equatorial semi diameter in arc seconds.

Parameters

Delta The distance to Saturn in astronomical units.

Remarks

Uses the updated Astronomical Almanac for 1984 size.

CAADiameters::SaturnPolarSemidiameterB

static double SaturnPolarSemidiameterB(double Delta)

Return Value

Saturn's polar semi diameter in arc seconds.

Parameters

Delta The distance to Saturn in astronomical units.

Remarks

Uses the updated Astronomical Almanac for 1984 size.

CAADiameters::ApparentSaturnPolarSemidiameterB

static double ApparentSaturnPolarSemidiameterB(double Delta, double B)

Return Value

Saturn's polar semi diameter in arc seconds.

Parameters

Delta The distance to Saturn in astronomical units.

B The Saturnicentric latitude of the Earth in degrees.

Remarks

Due to the large inclinations of Saturn, the apparent polar semi diameter can be different to the true polar semi diameter. Uses the updated Astronomical Almanac for 1984 size.

CAADiameters::UranusSemidiameterB

static double UranusSemidiameterB(double Delta)

Return Value

Uranus's semi diameter in arc seconds.

Parameters

Delta The distance to Uranus in astronomical units.

Remarks

Uses the updated Astronomical Almanac for 1984 size.

CAADiameters::NeptuneSemidiameterB

static double NeptuneSemidiameterB(double Delta)

Return Value

Neptune's semi diameter in arc seconds.

Parameters

Delta The distance to Neptune in astronomical units.

Remarks

Uses the updated Astronomical Almanac for 1984 size.

CAADiameters::PlutoSemidiameterB

static double PlutoSemidiameterB(double Delta)

Return Value

Pluto's semi diameter in arc seconds.

Parameters

Delta The distance to Pluto in astronomical units.

Remarks

Uses the updated Astronomical Almanac for 1984 size.

CAADiameters::GeocentricMoonSemidiameter

static double GeocentricMoonSemidiameter(double Delta)

Return Value

The Moon's semi diameter in arc seconds.

Parameters

Delta The distance to the Moon in kilometres.

CAADiameters::TopocentricMoonSemidiameter

static double TopocentricMoonSemidiameter(double DistanceDelta, double Delta, double H, double Latitude, double Height)

Return Value

The Moon's semi diameter in arc seconds.

Parameters

DistanceDelta The distance to the Moon in kilometres.

Delta The geocentric declination of the Moon in degrees.

H The geocentric hour angle of the Moon.

Latitude  The latitude of the position in degrees.

Height The observer's height above sea level in meters

CAADiameters::AsteroidDiameter

static double AsteroidDiameter(double H, double A)

Return Value

The asteroid's diameter in kilometres.

Parameters

H The absolute magnitude of the asteroid.

A The albedo of the asteroid.

CAADiameters::ApparentAsteroidDiameter

static double ApparentAsteroidDiameter(double Delta, double d)

Return Value

The asteroid's apparent diameter in arc seconds.

Parameters

Delta The distance to the asteroid in astronomical units.

d The diameter of the asteroid in kilometres.

CAADynamicalTime

This class provides for conversion between Universal Time (both UT1 and UTC) and Terrestrial Time (TT) aka Terrestrial Dynamical Time (TDT) aka Ephemeris Time (ET). This refers to Chapter 10 in the book.

Functions this class provides include:

DeltaT

CumulativeLeapSeconds

SetUserDefinedDeltaT

TT2UTC

UTC2TT

TT2TAI

TAI2TT

TT2UT1

UT12TT

UT1MinusUTC

CAADynamicalTime::DeltaT

static double DeltaT(double JD)

Return Value

The difference DeltaT which is equal to TT - UT1 in seconds of time.

Parameters

date The Julian day to calculate DeltaT for. Because DeltaT changes so slowly, the time used can be in the TT, the UTC or UT1 timeframes.

CAADynamicalTime::CumulativeLeapSeconds

static double CumulativeLeapSeconds(double JD)

Return Value

The cumulative total of Leap seconds which have been applied to this point in seconds of time.

Parameters

date The Julian day to calculate Cumulative leap seconds for. Because Leap seconds change so slowly, the time used can be in the TT, the UTC or UT1 timeframes although technically leap seconds are only relevant to the UTC timescale.

CAADynamicalTime::SetUserDefinedDeltaT

static CAADynamicalTime::DELTAT_PROC SetUserDefinedDeltaT (DELTAT_PROC pProc)

Return Value

The previous DeltaT function in use. If the CAADynamicalTime::DeltaT method was using its own lookup tables and polynomials prior to calling this method, then the return value from this method will be "nullptr".

Parameters

pProc The new function to use for calculating DeltaT through calls to the method CAADynamicalTime::DeltaT. The function signature of this parameter is "double (*) (double JD)" which is the same as the CAADynamicalTime::DeltaT function signature.

Remarks

This method allows the logic used by the CAADynamicalTime::DeltaT method to determine the DeltaT value to be changed by a user defined function. This advanced routine could prove useful where you have knowledge of the value for DeltaT for times far in the past or the future which is not included in the built-in tables provided by CAADynamicalTime class. Please note that changing the underlying function pointer by this method is not thread protected. This means that application code should provide appropriate thread protection if you are potentially calling this method from multiple threads at the same time.

CAADynamicalTime::TT2UTC

static double TT2UTC(double JD)

Return Value

The Julian day in the UTC timeframe.

Parameters

JD The Julian day in the TT timeframe to convert.

CAADynamicalTime::UTC2TT

static double TT2UTC(double JD)

Return Value

The Julian day in the TT timeframe.

Parameters

JDThe Julian day in the UTC timeframe to convert.

CAADynamicalTime::TT2TAI

static double TT2TAI(double JD)

Return Value

The Julian day in the TAI timeframe.

Parameters

JD The Julian day in the TT timeframe to convert.

CAADynamicalTime::TAI2TT

static double TAI2TT(double JD)

Return Value

The Julian day in the TT timeframe.

Parameters

JD The Julian day in the TAI timeframe to convert.

CAADynamicalTime::TT2UT1

static double TT2UT1(double JD)

Return Value

The Julian day in the UT1 timeframe.

Parameters

JD The Julian day in the TT timeframe to convert.

CAADynamicalTime::UT12TT

static double UT12TT(double JD)

Return Value

The Julian day in the TT timeframe.

Parameters

JD The Julian day in the UT1 timeframe to convert.

CAADynamicalTime::UT1MinusUTC

static double UT12TT(double JD)

Return Value

The difference between UT1 and UTC in seconds of time.

Parameters

JD The Julian day in the UT1 timeframe.

CAAEarth

This class provides for calculation of the heliocentric position of the Earth. This refers to Chapter 32 and parts of Chapter 26 and 47 in the book

Functions this class provides include:

EclipticLongitude

EclipticLatitude

RadiusVector

EclipticLongitudeJ2000

EclipticLatitudeJ2000

Eccentricity

SunMeanAnomaly

CAAEarth::EclipticLongitude

static double EclipticLongitude(double JD, bool bHighPrecision)

Return Value

the ecliptic longitude in degrees referred to the mean dynamical ecliptic and equinox of the date defined in the VSOP theory.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEarth::EclipticLatitude

static double EclipticLatitude(double JD, bool bHighPrecision)

Return Value

the ecliptic latitude in degrees referred to the mean dynamical ecliptic and equinox of the date defined in the VSOP theory.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEarth::RadiusVector

static double RadiusVector(double JD, bool bHighPrecision)

Return Value

the radius vector in astronomical units.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEarth::EclipticLongitudeJ2000

static double EclipticLongitudeJ2000(double JD, bool bHighPrecision)

Return Value

the ecliptic longitude in degrees referred to the mean dynamical ecliptic and equinox of J2000 in the VSOP theory.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEarth::EclipticLatitudeJ2000

static double EclipticLatitudeJ2000(double JD, bool bHighPrecision)

Return Value

the ecliptic latitude in degrees referred to the mean dynamical ecliptic and equinox of J2000 defined in the VSOP theory.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEarth::Eccentricity

static double Eccentricity(double JD)

Return Value

the eccentricity of Earth's orbit.

Parameters

JD The date in Dynamical time to calculate for.

CAAEarth::SunMeanAnomaly

static double SunMeanAnomaly(double JD)

Return Value

the mean anomaly of the Sun in degrees.

Parameters

JD The date in Dynamical time to calculate for.

CAAEaster

This class provides for calculation of the date of Easter in both the Julian and Gregorian calendars. This refers to Chapter 8 in the book.

Functions this class provides include:

Calculate

CAAEaster::Calculate

static CAAEasterDetails Calculate(int nYear, bool bGregorianCalendar)

Return Value

A class containing

Month The month on which Easter Sunday occurs.

Day The day of the month on which Easter Sunday occurs.

Parameters

nYear The year to perform the calculation for.

bGregorianCalendar true if the calculation is to be performed for the Gregorian calendar, false implies the Julian Calendar

CAAEclipses

This class provides for calculation of Solar and Lunar Eclipses. This refers to Chapter 54 in the book.

Functions this class provides include:

CalculateSolar

CalculateLunar

CAAEclipses::CalculateSolar

static CAASolarEclipseDetails CalculateSolar(double k)

Return Value

A struct containing the following values:

Flags A bitmask which indicates the type of solar eclipse which has occurred. See the constant values defined in CAASolarEclopseDetails for more information.

TimeOfMaximumEclipse The date in Dynamical time of maximum eclipse.

F The moons argument of Latitude in degrees at the time of the eclipse.

u The U term for the eclipse.

gamma The gamma term for the eclipse.

GreatestMagnitude The greatest magnitude of the eclipse if the eclipse is partial.

Parameters

k The same K term as returned from CAAMoonPhases::K. For a solar eclipse, this value should be a value without any decimals as a solar eclipse refers to a New Moon.

CAAEclipses::CalculateLunar

static CAALunarEclipseDetails CalculateLunar(double k)

Return Value

A struct containing the following values:

bEclipse true if a lunar eclipse occurs at this Full Moon.

TimeOfMaximumEclipse The date in Dynamical time of maximum eclipse.

F The moons argument of Latitude in degrees at the time of the eclipse.

u The U term for the eclipse.

gamma The gamma term for the eclipse.

PenumbralRadii The radii of the eclipse for the penumbra in equatorial earth radii.

UmbralRadii The radii of the eclipse for the umbra in equatorial earth radii.

PenumbralMagnitude The magnitude of the eclipse if the eclipse is penumbral.

UmbralMagnitude The magnitude of the eclipse if the eclipse is umbral.

PartialPhaseSemiDuration The semi-duration of the eclipse during the partial phase.

TotalPhaseSemiDuration The semi-duration of the eclipse during the total phase.

PartialPhasePenumbralSemiDuration The semi-duration of the partial phase in the penumbra.

Parameters

k The same K term as returned from CAAMoonPhases::K. For a lunar eclipse, this value should be decimal value incremented by 0.5 as a lunar eclipse refers to a Full Moon.

CAAEclipticalElements

This class provides the algorithms which map ecliptical elements from one equinox to another. This refers to Chapter 24 in the book.

Functions this class provides include:

Calculate

FK4B1950ToFK5J200

CAAEclipticalElements::Calculate

static CAAEclipticalElementDetails Calculate(double i0, double w0, double omega0, double JD0, double JD)

Return Value

A struct containing the following values:

i The reduced inclination in degrees.

w The reduced argument of perihelion in degrees.

omega The reduced longitude of the ascending node in degrees

Parameters

i0 The inclination in degrees to reduce.

w0 The argument of perihelion in degrees to reduce.

omega0 The longitude of the ascending node in degrees to reduce.

JD0 The initial epoch in Dynamical time to calculate for.

JD The epoch in Dynamical time to reduce the elements to.

CAAEclipticalElements::FK4B1950ToFK5J2000

static CAAEclipticalElementDetails KF4B1950ToFK5J2000(double i0, double w0, double omega0)

Return Value

A struct containing the following values:

i The reduced inclination in degrees.

w The reduced argument of perihelion in degrees.

omega The reduced longitude of the ascending node in degrees

Parameters

i0 The inclination in degrees to reduce.

w0 The argument of perihelion in degrees to reduce.

omega0 The longitude of the ascending node in degrees to reduce.

CAAElementsPlanetaryOrbit

This class provides the algorithms to calculate the elements of the planetary orbits. This refers to Chapter 31 in the book.

Functions this class provides include:

MercuryMeanLongitude

MercurySemimajorAxis

MercuryEccentricity

MercuryInclination

MercuryLongitudeAscendingNode

MercuryLongitudePerihelion

VenusMeanLongitude

VenusSemimajorAxis

VenusEccentricity

VenusInclination

VenusLongitudeAscendingNode

VenusLongitudePerihelion

EarthMeanLongitude

EarthSemimajorAxis

EarthEccentricity

EarthInclination

EarthLongitudePerihelion

MarsMeanLongitude

MarsSemimajorAxis

MarsEccentricity

MarsInclination

MarsLongitudeAscendingNode

MarsLongitudePerihelion

JupiterMeanLongitude

JupiterSemimajorAxis

JupiterEccentricity

JupiterInclination

JupiterLongitudeAscendingNode

JupiterLongitudePerihelion

SaturnMeanLongitude

SaturnSemimajorAxis

SaturnEccentricity

SaturnInclination

SaturnLongitudeAscendingNode

SaturnLongitudePerihelion

UranusMeanLongitude

UranusSemimajorAxis

UranusEccentricity

UranusInclination

UranusLongitudeAscendingNode

UranusLongitudePerihelion

NeptuneMeanLongitude

NeptuneSemimajorAxis

NeptuneEccentricity

NeptuneInclination

NeptuneLongitudeAscendingNode

NeptuneLongitudePerihelion

MercuryMeanLongitudeJ2000

MercuryInclinationJ2000

MercuryLongitudeAscendingNodeJ2000

MercuryLongitudePerihelionJ2000

VenusMeanLongitudeJ2000

VenusInclinationJ2000

VenusLongitudeAscendingNodeJ2000

VenusLongitudePerihelionJ2000

EarthMeanLongitudeJ2000

EarthInclinationJ2000

EarthLongitudeAscendingNodeJ2000

EarthLongitudePerihelionJ2000

MarsMeanLongitudeJ2000

MarsInclinationJ2000

MarsLongitudeAscendingNodeJ2000

MarsLongitudePerihelionJ2000

JupiterMeanLongitudeJ2000

JupiterInclinationJ2000

JupiterLongitudeAscendingNodeJ2000

JupiterLongitudePerihelionJ2000

SaturnMeanLongitudeJ2000

SaturnInclinationJ2000

SaturnLongitudeAscendingNodeJ2000

SaturnLongitudePerihelionJ2000

UranusMeanLongitudeJ2000

UranusInclinationJ2000

UranusLongitudeAscendingNodeJ2000

UranusLongitudePerihelionJ2000

NeptuneMeanLongitudeJ2000

NeptuneInclinationJ2000

NeptuneLongitudeAscendingNodeJ2000

NeptuneLongitudePerihelionJ2000

CAAElementsPlanetaryOrbit::MercuryMeanLongitude

static double MercuryMeanLongitude(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::MercurySemimajorAxis

static double MercurySemimajorAxis(double JD)

Return Value

the semi major axis of the planet in astronomical units.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::MercuryEccentricity

static double MercuryEccentricity(double JD)

Return Value

the eccentricity of the orbit.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MercuryInclination

static double MercuryInclination(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MercuryLongitudeAscendingNode

static double MercuryLongitudeAscendingNode(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MercuryLongitudePerihelion

static double MercuryLongitudePerihelion(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::VenusMeanLongitude

static double VenusMeanLongitude(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::VenusSemimajorAxis

static double VenusSemimajorAxis(double JD)

Return Value

the semi major axis of the planet in astronomical units.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::VenusEccentricity

static double VenusEccentricity(double JD)

Return Value

the eccentricity of the orbit.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::VenusInclination

static double VenusInclination(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::VenusLongitudeAscendingNode

static double VenusLongitudeAscendingNode(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::VenusLongitudePerihelion

static double VenusLongitudePerihelion(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::EarthMeanLongitude

static double EarthMeanLongitude(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::EarthSemimajorAxis

static double EarthSemimajorAxis(double JD)

Return Value

the semi major axis of the planet in astronomical units.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::EarthEccentricity

static double EarthEccentricity(double JD)

Return Value

the eccentricity of the orbit.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::EarthInclination

static double EarthInclination(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::EarthLongitudePerihelion

static double EarthLongitudePerihelion(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MarsMeanLongitude

static double MarsMeanLongitude(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::MarsSemimajorAxis

static double MarsSemimajorAxis(double JD)

Return Value

the semi major axis of the planet in astronomical units.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::MarsEccentricity

static double MarsEccentricity(double JD)

Return Value

the eccentricity of the orbit.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MarsInclination

static double MarsInclination(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MarsLongitudeAscendingNode

static double MarsLongitudeAscendingNode(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MarsLongitudePerihelion

static double MarsLongitudePerihelion(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::JupiterMeanLongitude

static double JupiterMeanLongitude(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::JupiterSemimajorAxis

static double JupiterSemimajorAxis(double JD)

Return Value

the semi major axis of the planet in astronomical units.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::JupiterEccentricity

static double JupiterEccentricity(double JD)

Return Value

the eccentricity of the orbit.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::JupiterInclination

static double JupiterInclination(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::JupiterLongitudeAscendingNode

static double JupiterLongitudeAscendingNode(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::JupiterLongitudePerihelion

static double JupiterLongitudePerihelion(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::SaturnMeanLongitude

static double SaturnMeanLongitude(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::SaturnSemimajorAxis

static double SaturnSemimajorAxis(double JD)

Return Value

the semi major axis of the planet in astronomical units.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::SaturnEccentricity

static double SaturnEccentricity(double JD)

Return Value

the eccentricity of the orbit.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::SaturnInclination

static double SaturnInclination(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::SaturnLongitudeAscendingNode

static double SaturnLongitudeAscendingNode(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::SaturnLongitudePerihelion

static double SaturnLongitudePerihelion(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::UranusMeanLongitude

static double UranusMeanLongitude(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::UranusSemimajorAxis

static double UranusSemimajorAxis(double JD)

Return Value

the semi major axis of the planet in astronomical units.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::UranusEccentricity

static double UranusEccentricity(double JD)

Return Value

the eccentricity of the orbit.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::UranusInclination

static double UranusInclination(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::UranusLongitudeAscendingNode

static double UranusLongitudeAscendingNode(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::UranusLongitudePerihelion

static double UranusLongitudePerihelion(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::NeptuneMeanLongitude

static double NeptuneMeanLongitude(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::NeptuneSemimajorAxis

static double NeptuneSemimajorAxis(double JD)

Return Value

the semi major axis of the planet in astronomical units.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOribit::NeptuneEccentricity

static double NeptuneEccentricity(double JD)

Return Value

the eccentricity of the orbit.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::NeptuneInclination

static double NeptuneInclination(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::NeptuneLongitudeAscendingNode

static double NeptuneLongitudeAscendingNode(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::NeptuneLongitudePerihelion

static double NeptuneLongitudePerihelion(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the ecliptic and mean equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MercuryMeanLongitudeJ2000

static double MercuryMeanLongitudeJ2000(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MercuryInclinationJ2000

static double MercuryInclinationJ2000(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MercuryLongitudeAscendingNodeJ2000

static double MercuryLongitudeAscendingNodeJ2000(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MercuryLongitudePerihelionJ2000

static double MercuryLongitudePerihelionJ2000(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::VenusMeanLongitudeJ2000

static double VenusMeanLongitudeJ2000(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::VenusInclinationJ2000

static double VenusInclinationJ2000(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::VenusLongitudeAscendingNodeJ2000

static double VenusLongitudeAscendingNodeJ2000(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::VenusLongitudePerihelionJ2000

static double VenusLongitudePerihelionJ2000(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::EarthMeanLongitudeJ2000

static double EarthMeanLongitudeJ2000(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::EarthInclinationJ2000

static double EarthInclinationJ2000(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::EarthLongitudeAscendingNodeJ2000

static doubleEarthLongitudeAscendingNodeJ2000(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::EarthLongitudePerihelionJ2000

static double EarthLongitudePerihelionJ2000(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MarsMeanLongitudeJ2000

static double MarsMeanLongitudeJ2000(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MarsInclinationJ2000

static double MarsInclinationJ2000(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MarsLongitudeAscendingNodeJ2000

static double MarsLongitudeAscendingNodeJ2000(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::MarsLongitudePerihelionJ2000

static double MarsLongitudePerihelionJ2000(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::JupiterMeanLongitudeJ2000

static double JupiterMeanLongitudeJ2000(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::JupiterInclinationJ2000

static double JupiterInclinationJ2000(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::JupiterLongitudeAscendingNodeJ2000

static double JupiterLongitudeAscendingNodeJ2000(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::JupiterLongitudePerihelionJ2000

static double JupiterLongitudePerihelionJ2000(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::SaturnMeanLongitudeJ2000

static double SaturnMeanLongitudeJ2000(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::SaturnInclinationJ2000

static double SaturnInclinationJ2000(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::SaturnLongitudeAscendingNodeJ2000

static double SaturnLongitudeAscendingNodeJ2000(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::SaturnLongitudePerihelionJ2000

static double SaturnLongitudePerihelionJ2000(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::UranusMeanLongitudeJ2000

static double UranusMeanLongitudeJ2000(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::UranusInclinationJ2000

static double UranusInclinationJ2000(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::UranusLongitudeAscendingNodeJ2000

static double UranusLongitudeAscendingNodeJ2000(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::UranusLongitudePerihelionJ2000

static double UranusLongitudePerihelionJ2000(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::NeptuneMeanLongitudeJ2000

static double NeptuneMeanLongitudeJ2000(double JD)

Return Value

the mean longitude of the planet in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::NeptuneInclinationJ2000

static double NeptuneInclinationJ2000(double JD)

Return Value

the inclination on the plane of the ecliptic in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::NeptuneLongitudeAscendingNodeJ2000

static double NeptuneLongitudeAscendingNodeJ2000(double JD)

Return Value

the longitude of the ascending node in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElementsPlanetaryOrbit::NeptuneLongitudePerihelionJ2000

static double NeptuneLongitudePerihelionJ2000(double JD)

Return Value

the longitude of the perihelion in degrees with respect to the fixed ecliptic of J2000.

Parameters

JD The date in Dynamical time to calculate for.

CAAElliptical

This class provides for calculation of the position of an object in an elliptical orbit. This refers to Chapter 33 in the book.

Functions this class provides include:

Calculate

DistanceToLightTime

SemiMajorAxisFromPerihelionDistance

MeanMotionFromSemiMajorAxis

InstantaneousVelocity

VelocityAtPerihelion

VelocityAtAphelion

LengthOfEllipse

CometMagnitude

MinorPlanetMagnitude

CAAElliptical::Calculate

static CAAEllipticalPlanetaryDetails Calculate(double JD, EllipticalObject object, bool bHighPrecision)

Return Value

A class containing

ApparentGeocentricEclipticalLongitude The apparent geocentric ecliptical longitude in degrees of the object.

ApparentGeocentricEclipticalLatitude The apparent geocentric ecliptical latitude in degrees of the object.

ApparentGeocentricDistance The apparent distance in astronomical units between the object and the Earth.

ApparentLightTime The apparent light travel time in days.

ApparentGeocentricRA The apparent right ascension of the planet as an hour angle.

ApparentGeocentricDeclination The apparent declination of the planet in degrees.

TrueGeocentricRectangularEcliptical True 3D rectangular geocentric ecliptical coordinates of the object.

TrueHeliocentricEclipticalLongitude True heliocentric ecliptical longitude in degrees of the object.

TrueHeliocentricEclipticalLatitude True heliocentric ecliptical latitude in degrees of the object.

TrueHeliocentricDistance The true distance in astronomical units between the object and the Sun.

TrueGeocentricEclipticalLongitude The true geocentric ecliptical longitude in degrees of the object.

TrueGeocentricEclipticalLatitude The true geocentric ecliptical latitude in degrees of the object

TrueGeocentricDistance The true distance in astronomical units between the object and the Earth.

TrueLightTime The true light travel time in days.

TrueGeocentricRA The true right ascension of the planet as an hour angle.

TrueGeocentricDeclination The true declination of the planet in degrees.

Parameters

JD The date in Dynamical time to calculate for.

object An enum specifying which object (Planet except Earth or the Sun) the calculation is to be carried out for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

static CAAEllipticalObjectDetails Calculate(double JD, const CAAEllipticalObjectElements& elements, bool bHighPrecision)

Return Value

A class containing

HeliocentricRectangularEquatorial 3D rectangular heliocentric equatorial coordinates of the object.

HeliocentricRectangularEcliptical 3D rectangular heliocentric ecliptical coordinates of the object.

HeliocentricEclipticLongitude The heliocentric ecliptical longitude in degrees of the object.

HeliocentricEclipticLatitude The heliocentric ecliptical latitude in degrees of the object.

TrueGeocentricRA The geocentric right ascension of the object as an hour angle (i.e. without light time correction applied).

TrueGeocentricDeclination The geocentric declination of the object in degrees (i.e. without light time correction applied).

TrueGeocentricDistance The true distance in astronomical units between the Earth and the object.

TrueGeocentricLightTime The light travel time in days from the Earth to the object.

AstrometricGeocentricRA The geocentric right ascension of the object as an hour angle (i.e. with light time correction applied)

AstrometricGeocentricDeclination The geocentric declination of the object in degrees (i.e. with light time correction applied)

AstrometricGeocentricDistance The observed distance of the object in astronomical units.

AstrometricGeocentricLightTime The observed light travel time of the object in days.

Elongation The elongation of the object to the Sun in degrees.

PhaseAngle The phase angle (the angle Sun - object - Earth) in degrees.

Parameters

JD The date in Dynamical time to calculate for.

elements A class containing the following orbital elements

a The semi major axis in astronomical units.

e The eccentricity of the orbit.

i The inclination of the plane of the orbit in degrees.

w The argument of the perihelion in degrees.

omega The longitude of the ascending node in degrees.

JDEquinox The Julian day for which equatorial coordinates should be calculated for.

T The Julian date of the time of passage in perihelion.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAElliptical::DistanceToLightTime

static double DistanceToLightTime(double Distance)

Return Value

The light travel time in days corresponding to the distance.

Parameters

Distance The distance in astronomical units to convert.

CAAElliptical::SemiMajorAxisFromPerihelionDistance

static double SemiMajorAxisFromPerihelionDistance(double q, double e)

Return Value

The semi major axis of the orbit in astronomical units.

Parameters

q The perihelion distance in astronomical units.

e The eccentricity of the orbit.

CAAElliptical::MeanMotionFromSemiMajorAxis

static double MeanMotionFromSemiMajorAxis(double a)

Return Value

The mean motion in degrees / day.

Parameters

a The semi major axis of the orbit in astronomical units.

CAAElliptical::InstantaneousVelocity

static double InstantaneousVelocity(double r, double a)

Return Value

The instantaneous velocity of the object in kilometres per second.

Parameters

r The distance of the object from the Sun in astronomical units.

a The semi major axis of the orbit in astronomical units.

CAAElliptical::VelocityAtPerihelion

static double VelocityAtPerihelion(double e, double a)

Return Value

The velocity of the object in kilometres per second at perihelion.

Parameters

e The eccentricity of the orbit.

a The semi major axis of the orbit in astronomical units.

CAAElliptical::VelocityAtAphelion

static double VelocityAtAphelion(double e, double a)

Return Value

The velocity of the object in kilometres per second at aphelion.

Parameters

e The eccentricity of the orbit.

a The semi major axis of the orbit in astronomical units.

CAAElliptical::LengthOfEllipse

static double LengthOfEllipse(double e, double a)

Return Value

The length of the eclipse in astronomical units.

Parameters

e The eccentricity of the orbit.

a The semi major axis of the orbit in astronomical units.

CAAElliptical::CometMagnitude

static double CometMagnitude(double g, double delta, double k, double r)

Return Value

The magnitude of the comet.

Parameters

g The absolute magnitude of the comet.

delta Distance of the comet to the Earth in astronomical units.

k A constant which differs from one comet to another.

r Distance of the comet from the Sun in astronomical units

Remarks

This refers to algorithm 33.13 on page 231

CAAElliptical::MinorPlanetMagnitude

static double MinorPlanetMagnitude(double H, double delta, double G, double r, double PhaseAngle)

Return Value

The magnitude of the minor planet.

Parameters

H The mean absolute visual magnitude of the minor planet.

delta Distance of the minor planet to the Earth in astronomical units.

G The so called "slope parameter" which differs from one minor planet to another.

r Distance of the minor planet from the Sun in astronomical units

PhaseAngle the Sun - body - Earth angle in degrees

Remarks

This refers to algorithm 33.14 on page 231

CAAELP2000

This class provides for calculation of the position of the Moon using the full ELP2000-82b theory. Please refer to http://cdsweb.u-strasbg.fr/cgi-bin/qcat?VI/79/for further details.

Functions this class provides include:

EclipticLongitude

EclipticLatitude

RadiusVector

EclipticRectangularCoordinates

EclipticRectangularCoordinatesJ2000

EquatorialRectangularCoordinatesFK5

CAAELP2000::EclipticLongitude

static double EclipticLongitude(double JD)

Return Value

the ecliptic longitude in degrees referred to the ecliptic and equinox of the ELP2000-82b theory.

Parameters

JD The date in Dynamical time to calculate for.

CAAELP2000::EclipticLatitude

static double EclipticLatitude(double JD)

Return Value

the ecliptic latitude in degrees referred to the ecliptic and equinox of the ELP2000-82b theory.

Parameters

JD The date in Dynamical time to calculate for.

CAAELP2000::RadiusVector

static double RadiusVector(double JD)

Return Value

the radius vector in kilometers.

Parameters

JD The date in Dynamical time to calculate for.

CAAELP2000::EclipticRectangularCoordinates

static CAA3DCoordinate EclipticRectangularCoordinates(double JD)

Return Value

A class containing the ecliptic 3D rectangular coordinates in kilometers referred to the ecliptic and equinox of the ELP2000-82b theory.

Parameters

JD The date in Dynamical time to calculate for.

CAAELP2000::EclipticRectangularCoordinatesJ2000

static CAA3DCoordinate EclipticRectangularCoordinatesJ2000(double JD)

Return Value

A class containing the ecliptic 3D rectangular coordinates in kilometers referred to the J2000 ecliptic and equinox.

Parameters

JD The date in Dynamical time to calculate for.

CAAELP2000::EquatorialRectangularCoordinatesFK5

static CAA3DCoordinate EquatorialRectangularCoordinatesFK5(double JD)

Return Value

A class containing the equatorial 3D rectangular coordinates in kilometers referred to the FK5 J2000 FK5 reference frame.

Parameters

JD The date in Dynamical time to calculate for.

CAAELPMPP02

This class provides for calculation of the position of the Moon using the full ELP\MPP02 theory. Please refer to ftp://cyrano-se.obspm.fr/pub/2_lunar_solutions/2_elpmpp02/ for further details.

Functions this class provides include:

EclipticLongitude

EclipticLatitude

RadiusVector

EclipticRectangularCoordinates

EclipticRectangularCoordinatesJ2000

CAAELPMPP02::EclipticLongitude

static double EclipticLongitude(double JD, Correction correction = LLR, double* pDerivative = nullptr)

Return Value

the ecliptic longitude in degrees referred to the ecliptic and equinox of the ELP/MPP02 theory.

Parameters

JD The date in Dynamical time to calculate for.

correction enum value which specifies what fit of the theory to use. This can be Nominal, LLR, DE405 or DE406.

pDerivative An optional output parameter which if provided will return the derivative of the ecliptic longitude in degrees per day.

CAAELPMPP02::EclipticLatitude

static double EclipticLatitude(double JD, Correction correction = LLR, double* pDerivative = nullptr)

Return Value

the ecliptic latitude in degrees referred to the ecliptic and equinox of the ELP/MPP02 theory.

Parameters

JD The date in Dynamical time to calculate for.

correction enum value which specifies what fit of the theory to use. This can be Nominal, LLR, DE405 or DE406.

pDerivative An optional output parameter which if provided will return the derivative of the ecliptic latitude in degrees per day.

CAAELPMPP02::RadiusVector

static double RadiusVector(double JD, Correction correction = LLR, double* pDerivative = nullptr)

Return Value

the radius vector in kilometers.

Parameters

JD The date in Dynamical time to calculate for.

correction enum value which specifies what fit of the theory to use. This can be Nominal, LLR, DE405 or DE406.

pDerivative An optional output parameter which if provided will return the derivative of the radius vector in kilometers per day.

CAAELPMPP02::EclipticRectangularCoordinates

static CAA3DCoordinate EclipticRectangularCoordinates(double JD, Correction correction = LLR, CAA3DCoordinate* pDerivative = nullptr)

Return Value

A class containing the ecliptic 3D rectangular coordinates in kilometers referred to the ecliptic and equinox of the ELP/MPP02 theory.

Parameters

JD The date in Dynamical time to calculate for.

correction enum value which specifies what fit of the theory to use. This can be Nominal, LLR, DE405 or DE406.

pDerivative An optional output parameter which if provided will return the derivative of the rectangular coordinates in Kilometers per day in the ecliptic and equinox of the ELP/MPP02 theory.

CAAELPMPP02::EclipticRectangularCoordinatesJ2000

static CAA3DCoordinate EclipticRectangularCoordinatesJ2000(double JD, CAA3DCoordinate* pDerivative = nullptr)

Return Value

A class containing the ecliptic 3D rectangular coordinates in kilometers referred to the J2000 ecliptic and equinox.

Parameters

JD The date in Dynamical time to calculate for.

correction enum value which specifies what fit of the theory to use. This can be Nominal, LLR, DE405 or DE406.

pDerivative An optional output parameter which if provided will return the derivative of the rectangular coordinates in kilometers per day in the J2000 ecliptic and equinox

CAAEquationOfTime

This class provides for calculation of the Equation of Time. This refers to Chapter 28 in the book.

Functions this class provides include:

Calculate

CAAEquationOfTime::Calculate

static double Calculate(double JD, bool bHighPrecision)

Return Value

the equation of time in decimal minutes.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEquinoxesAndSolstices

This class provides the algorithms to calculate the dates of the Equinoxes and Solstices. This refers to Chapter 27 in the book.

Functions this class provides include:

NorthwardEquinox

NorthernSoltice

SouthwardEquinox

SouthernSolstice

LengthOfSpring

LengthOfSummer

LengthOfAutumn

LengthOfWinter

CAAEquinoxesAndSolstices::NorthwardEquinox

static double NorthwardEquinox(long Year, bool bHighPrecision)

Return Value

The date in Dynamical time when the sun crosses the equator in a northerly direction.

Parameters

Year The year to calculate the occurrence for. Note that this method refers to "Northward Equinox" instead of "Spring Equinox" to avoid a northern hemisphere-specific bias.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEquinoxesAndSolstices::NorthernSolstice

static double NorthernSolstice(long Year, bool bHighPrecision)

Return Value

The date in Dynamical time when the sun reaches its highest relative to the celestial equator and appears directly over the Tropic of Cancer.

Parameters

Year The year to calculate the occurrence for. Note that this method refers to "Northern Solstice" instead of "Summer Solstice" to avoid a northern hemisphere-specific bias.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEquinoxesAndSolstices::SouthwardEquinox

static double SouthwardEquinox(long Year, bool bHighPrecision)

Return Value

The date in Dynamical time when the Southward Equinox occurs.

Parameters

Year The year to calculate the occurrence for. Note that this method refers to "Southward Equinox" instead of "Fall or Autumn equinox" to avoid a northern hemisphere-specific bias.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEquinoxesAndSolstices::SouthernSolstice

static double SouthernSolstice(long Year, bool bHighPrecision)

Return Value

The date in Dynamical time when the sun reaches its lowest relative to the celestial equator and appears directly over the Tropic of Capricorn.

Parameters

Year The year to calculate the occurrence for. Note that this method refers to "Southern Solstice" instead of "Winter Solstice" to avoid a northern hemisphere-specific bias.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEquinoxesAndSolstices::LengthOfSpring

static double LengthOfSpring(long Year, bool bNorthernHemisphere, bool bHighPrecision)

Return Value

The length of the astronomical Spring season in days.

Parameters

Year The year to calculate for.

bNorthernHemisphere true to indicate the observer is in the northern hemisphere, while false means the southern hemisphere.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEquinoxesAndSolstices::LengthOfSummer

static double LengthOfSummer(long Year, bool bNorthernHemisphere, bool bHighPrecision)

Return Value

The length of the astronomical Summer season in days.

Parameters

Year The year to calculate for.

bNorthernHemisphere true to indicate the observer is in the northern hemisphere, while false means the southern hemisphere.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEquinoxesAndSolstices::LengthOfAutumn

static double LengthOfAutumn(long Year, bool bNorthernHemisphere, bool bHighPrecision)

Return Value

The length of the astronomical Autumn season in days.

Parameters

Year The year to calculate for.

bNorthernHemisphere true to indicate the observer is in the northern hemisphere, while false means the southern hemisphere.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEquinoxesAndSolstices::LengthOfWinter

static double LengthOfWinter(long Year, bool bNorthernHemisphere, bool bHighPrecision)

Return Value

The length of the astronomical Winter season in days.

Parameters

Year The year to calculate for.

bNorthernHemisphere true to indicate the observer is in the northern hemisphere, while false means the southern hemisphere.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAEquinoxesAndSolstices2

This class uses interpolation to calculate the same details as those provided with the existing CAAEquinoxesAndSolstices class.

Functions this class provides include:

Calculate

CAAEquinoxesAndSolstices2::Calculate

static std::vector<CAAEquinoxesAndSolsticestDetails2> Calculate(double StartJD, double EndJD, double StepInterval = 0.007, bool bHighPrecision = false)

Return Value

A standard C++ array containing a class which itself contains:

type An enum class instance which represents the type of event found. This can be NorthwardEquinox, NorthernSolstice, SouthwardEquinox or SouthernSolstice.

JD The date in Dynamical time on which the event occurs.

Declination Valid only for NorthernSolstice or SouthernSolstice events, this will be the apparent declination of the Sun.

Parameters

StartJD The Julian Day corresponding to the Dynamical Time for the date when you want to start the calculation for.

EndJD The Julian Day corresponding to the Dynamical Time for the date when you want to end the calculation for.

StepInterval The step interval in fractions of days to do the calculation for. The default value of 0.007 corresponds to roughly 10 minutes which is a reasonable tradeoff between performance and accuracy.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAFK5

This class provides the algorithms to convert to the FK5 standard reference frame. This refers to parts of Chapter 26 and 32 in the book.

Functions this class provides include:

CorrectionInLongitude

CorrectionInLatitude

ConvertVSOPToFK5J2000

ConvertVSOPToFK5B1950

ConvertVSOPToFK5AnyEquinox

CAAFK5::CorrectionInLongitude

static double CorrectionInLongitude(double longitude, double Latitude, double JD)

Return Value

The correction in degrees to convert a VSOP heliocentric longitude to the FK5 reference frame.

Parameters

Longitude The VSOP heliocentric longitude in degrees.

Latitude The VSOP heliocentric latitude in degrees.

JD The date in Dynamical time to calculate for.

CAAFK5::CorrectionInLatitude

static double CorrectionInLatitude(double longitude, double JD)

Return Value

The

Parameters

Longitude The VSOP heliocentric longitude in degrees.

JD The date in Dynamical time to calculate for.

CAAFK5::ConvertVSOPToFK5J2000

static CAA3DCoordinate ConvertVSOPToFK5J2000(const CAA3DCoordinate& value)

Return Value

A class containing the converted equatorial FK5 J2000 reference frame coordinates.

Parameters

value The geometric rectangular ecliptical coordinates of the object (e.g. the Sun) to convert from the dynamical reference frame (VSOP) to the equatorial FK5 J2000 reference frame.

CAAFK5::ConvertVSOPToFK5B1950

static CAA3DCoordinate ConvertVSOPToFK5B1950(const CAA3DCoordinate& value)

Return Value

A class containing the converted equatorial FK5 B1950 reference frame coordinates.

Parameters

value The geometric rectangular ecliptical coordinates of the object (e.g. the Sun) to convert from the dynamical reference frame (VSOP) to the equatorial FK5 B1950 reference frame.

CAAFK5::ConvertVSOPToFK5AnyEquinox

static CAA3DCoordinate ConvertVSOPToFK5AnyEquinox(const CAA3DCoordinate& value, double JDEquinox)

Return Value

A class containing the converted equatorial FK5 reference frame coordinates.

Parameters

value The geometric rectangular ecliptical coordinates of the object (e.g. the Sun) to convert from the dynamical reference frame (VSOP) to the equatorial FK5 reference frame of JDEquinox.

JDEquinox The Julian day for which equatorial coordinates should be calculated for.

CAAGalileanMoons

This class provides for calculation of the positions of the Galilean moons of Jupiter. This refers to Chapter 44 in the book.

Functions this class provides include:

Calculate

CAAGalileanMoons::Calculate

static CAAGalileanMoonsDetails Calculate(double JD, bool bHighPrecision)

Return Value

A class which itself contains a class for each moon. This contained class itself contains

MeanLongitude The mean longitude of the moon in degrees.

TrueLongitude The true longitude of the moon in degrees.

TropicalLongitude The tropical longitude of the moon in degrees.

EquatorialLatitude The latitude in degrees of the moon with respect to Jupiter's equatorial plane.

r The radius vector of the moon in equatorial radii of Jupiter.

TrueRectangularCoordinates The true 3D rectangular coordinates of the moon.

ApparentRectangularCoordinates The apparent 3D rectangular coordinates of the moon.

bInTransit A Boolean which if true means that the moon is in front of Jupiter as viewed from the Earth otherwise false.

bInOccultation A Boolean which if true means that the moon is behind Jupiter as viewed from the Earth otherwise false.

bInEclipse A Boolean which if true means that the moon is behind Jupiter as viewed from the Sun otherwise false.

bInShadowTransit A Boolean which if true means that the moon is in front of Jupiter as viewed from the Earth otherwise false.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAGlobe

This class provides some basic algorithms related to the figure of the Earth's surface.

Functions this class provides include:

RhoSinThetaPrime

RhoCosThetaPrime

RadiusOfParallelOfLatitude

RadiusOfCurvature

DistanceBetweenPoints

CAAGlobe::RhoSinThetaPrime

static double RhoSinThetaPrime(double GeographicalLatitude, double Height)

Return Value

A numeric value of your position relative to the centre of the earth expressed in units of the equatorial radius. For more information refer to the diagram on Page 81.

Parameters

GeographicalLatitude The latitude of the position in degrees.

Height The observer's height above sea level in meters

CAAGlobe::RhoCosThetaPrime

static double RhoCosThetaPrime(double GeographicalLatitude, double Height)

Return Value

A numeric value of your position relative to the centre of the earth expressed in units of the equatorial radius. For more information refer to the diagram on Page 81.

Parameters

GeographicalLatitude The latitude of the position in degrees.

Height The observer's height above sea level in meters

CAAGlobe::RadiusOfParallelOfLatitude

static double RadiusOfParallelOfLatitude(double GeographicalLatitude)

Return Value

The radius of parallel of latitude expressed in kilometres.

Parameters

GeographicalLatitude The latitude of the position in degrees.

CAAGlobe::RadiusOfCurvature

static double RadiusOfCurvature(double GeographicalLatitude)

Return Value

The radius of curvature of latitude expressed in kilometres.

Parameters

GeographicalLatitude The latitude of the position in degrees.

CAAGlobe::DistanceBetweenPoints

static double DistanceBetweenPoints(double GeographicalLatitude1, double GeographicalLongitude1, double GeographicalLatitude2, double GeographicalLongitude2)

Return Value

The shortest distance between two known points on the surface of the Earth expressed in kilometres.

Parameters

GeographicalLatitude1 The latitude of the first point in degrees.

GeographicLongitude1 The longitude of the first point in degrees (Positive west, negative east from Greenwich).

GeographicLatitude2 The latitude of the second point in degrees.

GeographicalLongitude2 The longitude of the second point in degrees (Positive west, negative east from Greenwich).

CAAIlluminatedFraction

This class provides the algorithms to calculate a planet's phase angle, illuminated fraction and magnitude. This refers to Chapter 41 in the book.

Functions this class provides include:

PhaseAngle

PhaseAngleRectangular

IlluminatedFraction

MercuryMagnitudeAA

MercuryMagnitudeMuller

VenusMagnitudeAA

VenusMagnitudeMuller

MarsMagnitudeAA

MarsMagnitudeMuller

JupiterMagnitudeAA

JupiterMagnitudeMuller

SaturnMagnitudeAA

SaturnMagnitudeMuller

UranusMagnitudeAA

UranusMagnitudeMuller

NeptuneMagnitudeAA

NeptuneMagnitudeMuller

PlutoMagnitudeAA

CAAIlluminatedFraction::PhaseAngle

static double PhaseAngle(double r, double R, double Delta)

static double PhaseAngle(double R, double R0, double B, double L, double L0, double Delta)

Return Value

The phase angle in degrees.

Parameters (First Version)

r The planet's distance to the Sun in astronomical units.

R The distance of the Sun from the Earth in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

Parameters (Second Version)

R The planet's distance to the Sun in astronomical units.

R0 The distance of the Sun from the Earth in astronomical units.

B The planet's heliocentric latitude in degrees.

L The planet's heliocentric longitude in degrees.

L0 The heliocentric latitude of the Earth in degrees.

Delta The planet's distance from the Earth in astronomical units.

CAAIlluminatedFraction::PhaseAngleRectangular

static double PhaseAngleRectangular(double x, double y, double z, double B, double L, double Delta)

Return Value

The phase angle in degrees.

Parameters

x The geocentric rectangular ecliptical X coordinate of the object.

y The geocentric rectangular ecliptical Y coordinate of the object.

z The geocentric rectangular ecliptical Y coordinate of the object.

B The planet's heliocentric latitude in degrees.

L The planet's heliocentric longitude in degrees.

Delta The planet's distance from the Earth in astronomical units.

CAAIlluminatedFraction::IlluminatedFraction

static double IlluminatedFraction(double r, double R, double Delta)

static double IlluminatedFraction(double PhaseAngle)

Return Value

The phase angle in degrees.

r The planet's distance to the Sun in astronomical units.

R The distance of the Sun from the Earth in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

PhaseAngle The planet's phase angle in degrees.

CAAIlluminatedFraction::MercuryMagnitudeAA

static double MercuryMagnitudeAA(double r, double Delta, double i)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

i The planet's phase angle in degrees.

Remarks

Uses the formula to calculate the magnitude as provided in the Astronomical Almanac.

CAAIlluminatedFraction::MercuryMagnitudeMuller

static double MercuryMagnitudeMuller(double r, double Delta, double Delta)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

i The planet's phase angle in degrees.

Remarks

Uses the formula to calculate the magnitude as provided by G. Muller.

CAAIlluminatedFraction::VenusMagnitudeAA

static double VenusMagnitudeAA(double r, double Delta, double i)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

i The planet's phase angle in degrees.

Remarks

Uses the formula to calculate the magnitude as provided in the Astronomical Almanac.

CAAIlluminatedFraction::VenusMagnitudeMuller

static double VenusMagnitudeMuller(double r, double Delta, double Delta)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

i The planet's phase angle in degrees.

Remarks

Uses the formula to calculate the magnitude as provided by G. Muller.

CAAIlluminatedFraction::MarsMagnitudeAA

static double MarsMagnitudeAA(double r, double Delta, double i)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

i The planet's phase angle in degrees.

Remarks

Uses the formula to calculate the magnitude as provided in the Astronomical Almanac.

CAAIlluminatedFraction::MarsMagnitudeMuller

static double MarsMagnitudeMuller(double r, double Delta, double i)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

i The planet's phase angle in degrees.

Remarks

Uses the formula to calculate the magnitude as provided by G. Muller.

CAAIlluminatedFraction::JupiterMagnitudeAA

static double JupiterMagnitudeAA(double r, double Delta, double i)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

i The planet's phase angle in degrees.

Remarks

Uses the formula to calculate the magnitude as provided in the Astronomical Almanac.

CAAIlluminatedFraction::JupiterMagnitudeMuller

static double JupiterMagnitudeMuller(double r, double Delta)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

Remarks

Uses the formula to calculate the magnitude as provided by G. Muller.

CAAIlluminatedFraction::SaturnMagnitudeAA

static double SaturnMagnitudeAA(double r, double Delta, double DeltaU, double B)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

DeltaU The difference between the Saturnicentric longitudes of the Sun and the Earth, measured in the plane o the ring in degrees.

B The Saturnicentric latitude of the Earth referred to the plane of the ring in degrees

Remarks

Uses the formula to calculate the magnitude as provided in the Astronomical Almanac.

CAAIlluminatedFraction::SaturnMagnitudeMuller

static double SaturnMagnitudeMuller(double r, double Delta, double DeltaU, double B)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

DeltaU The difference between the Saturnicentric longitudes of the Sun and the Earth, measured in the plane o the ring in degrees.

B The Saturnicentric latitude of the Earth referred to the plane of the ring in degrees

Remarks

Uses the formula to calculate the magnitude as provided by G. Muller.

CAAIlluminatedFraction::UranusMagnitudeAA

static double UranusMagnitudeAA(double r, double Delta)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

Remarks

Uses the formula to calculate the magnitude as provided in the Astronomical Almanac.

CAAIlluminatedFraction::UranusMagnitudeMuller

static double UranusMagnitudeMuller(double r, double Delta)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

Remarks

Uses the formula to calculate the magnitude as provided by G. Muller.

CAAIlluminatedFraction::NeptuneMagnitudeAA

static double NeptuneMagnitudeAA(double r, double Delta)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

Remarks

Uses the formula to calculate the magnitude as provided in the Astronomical Almanac.

CAAIlluminatedFraction::NeptuneMagnitudeMuller

static double NeptuneMagnitudeMuller(double r, double Delta)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

Remarks

Uses the formula to calculate the magnitude as provided by G. Muller.

CAAIlluminatedFraction::PlutoMagnitudeAA

static double PlutoMagnitudeAA(double r, double Delta)

Return Value

The magnitude of the planet.

Parameters

r The planet's distance to the Sun in astronomical units.

Delta The planet's distance from the Earth in astronomical units.

Remarks

Uses the formula to calculate the magnitude as provided in the Astronomical Almanac.

CAAInterpolate

This class provides the algorithms for interpolation. This refers to Chapter 3 in the book.

Functions this class provides include:

Interpolate

InterpolateToHalves

LangrangeInterpolate

Extremum

Zero

Zero2

CAAInterpolate::Interpolate

static double Interpolate(double n, double Y1, double Y2, double Y3)

static double Interpolate(double n, double Y1, double Y2, double Y3, double Y4, double Y5)

Return Value

The interpolated Y value.

Parameters

n The interpolating factor.

Y1 The first Y value to interpolate from.

Y2 The second Y value to interpolate from.

Y3 The third Y value to interpolate from.

Y4 The fourth Y value to interpolate from.

Y5 The fifth Y value to interpolate from.

Remarks

Interpolates a function from 3 or 5 points.

CAAInterpolate::InterpolateToHalves

static double InterpolateToHalves(double Y1, double Y2, double Y3, double Y4)

Return Value

The interpolated Y value.

Parameters

Y1 The first Y value to interpolate from.

Y2 The second Y value to interpolate from.

Y3 The third Y value to interpolate from.

Y4 The fourth Y value to interpolate from.

Remarks

Interpolates a function to the middle location where 4 evenly spaced values are provided.

CAAInterpolate::LagrangeInterpolate

static double LagrangeInterpolate(double X, int n, const double* pX, const double* pY)

Return Value

The interpolated Y value.

Parameters

X The X value to interpolate for.

n The size of the pX and pY arrays.

pX Pointer to the array of X coordinates to interpolate from.

pY Pointer to the array of Y coordinates to interpolate from.

Remarks

Interpolates a function using Lagrange's formula where an arbitrary number of values are provided.

CAAInterpolate::Extremum

static double Extremum(double Y1, double Y2, double Y3, double& nm)

static double Extremum(double Y1, double Y2, double Y3, double Y4, double Y5, double& nm, double epsilon = 1e-12)

Return Value

The extreme Y value.

Parameters

Y1 The first Y value to interpolate from.

Y2 The second Y value to interpolate from.

Y3 The third Y value to interpolate from.

Y4 The fourth Y value to interpolate from.

Y5 The fifth Y value to interpolate from.

epsilon The value used to terminate iteration loops inside the method.

nm Upon return will contain the corresponding value of the argument X where the extremum is reached.

Remarks

Interpolates a function to determine where the function reaches an extremum.

CAAInterpolate::Zero

static double Zero(double Y1, double Y2, double Y3, double epsilon = 1e-12)

static double Zero(double Y1, double Y2, double Y3, double Y4, double Y5, double epsilon = 1e-12)

Return Value

The value of the argument X for which the function y becomes zero.

Parameters

Y1 The first Y value to interpolate from.

Y2 The second Y value to interpolate from.

Y3 The third Y value to interpolate from.

Y4 The fourth Y value to interpolate from.

Y5 The fifth Y value to interpolate from.

epsilon The value used to terminate iteration loops inside the methods.

Remarks

Finds where a function reaches zero when the function is "almost a straight line".

CAAInterpolate::Zero2

static double Zero2(double Y1, double Y2, double Y3, double epsilon = 1e-12)

static double Zero2(double Y1, double Y2, double Y3, double Y4, double Y5, double epsilon = 1e-12)

Return Value

The value of the argument X for which the function y becomes zero.

Parameters

Y1 The first Y value to interpolate from.

Y2 The second Y value to interpolate from.

Y3 The third Y value to interpolate from.

Y4 The fourth Y value to interpolate from.

Y5 The fifth Y value to interpolate from.

epsilon The value used to terminate iteration loops inside the methods.

Remarks

Finds where a function reaches zero when the curvature of the function is important.

CAAJewishCalendar

This class provides the algorithms which convert between the Gregorian, Julian and Jewish calendars. This refers to Chapter 9 in the book.

Functions this class provides include:

DateOfPesach

DaysInYear

IsLeap

CAAJewishCalendar::DateOfPesach

static CAACalendarDate DateOfPesach(long Year, bool bGregorianCalendar = false)

Return Value

A class containing

Year The year in the Jewish Calendar.

Month The month of the year in the Gregorian or Julian Calendar corresponding to when Pesach occurs.

Day The day of the month in the Gregorian or Julian Calendar corresponding to when Pesach occurs.

Parameters

Year The year in the Julian or Gregorian Calendar to calculate Jewish Easter or Pesach for. (Years are counted astronomically i.e. 1 BC = Year 0)

bGregorianCalendar true to imply a date in the Gregorian Calendar, false means use the Julian Calendar.

CAAJewishCalendar::DaysInYear

static long DaysInYear(long Year)

Return Value

The number of days in the specified Jewish Year

Parameters

Year The year in the Jewish Calendar.

CAAJewishCalendar::IsLeap

static bool IsLeap(long Year)

Return Value

true if the specified year is leap otherwise false.

Parameters

Year The year in the Jewish calendar.

CAAJupiter

This class provides for calculation of the heliocentric position of Jupiter. This refers to Chapter 32 in the book.

Functions this class provides include:

EclipticLongitude

EclipticLatitude

RadiusVector

CAAJupiter::EclipticLongitude

static double EclipticLongitude(double JD, bool bHighPrecision)

Return Value

the ecliptic longitude in degrees referred to the mean dynamical ecliptic and equinox of the date defined in the VSOP theory.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAJupiter::EclipticLatitude

static double EclipticLatitude(double JD, bool bHighPrecision)

Return Value

the ecliptic latitude in degrees referred to the mean dynamical ecliptic and equinox of the date defined in the VSOP theory.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAJupiter::RadiusVector

static double RadiusVector(double JD, bool bHighPrecision)

Return Value

the radius vector in astronomical units.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAKepler

This class provides for the solution of Kepler's equation. This refers to Chapter 30 in the book.

Functions this class provides include:

Calculate

CAAKepler::Calculate

static double Calculate(double M, double e, int nIterations = 53)

Return Value

The Eccentric anomaly in degrees (i.e. the solution to Kepler's equation).

Parameters

M The mean anomaly in degrees.

e The eccentricity of the orbit

nIterations The method uses the third method to solve the equation. This uses a binary chop to find the solution. The default value of 53 is the number of iterations required to obtain the accuracy of the standard Visual C "double".

CAAMars

This class provides for calculation of the heliocentric position of Mars. This refers to Chapter 32 in the book.

Functions this class provides include:

EclipticLongitude

EclipticLatitude

RadiusVector

CAAMars::EclipticLongitude

static double EclipticLongitude(double JD, bool bHighPrecision)

Return Value

the ecliptic longitude in degrees referred to the mean dynamical ecliptic and equinox of the date defined in the VSOP theory.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAMars::EclipticLatitude

static double EclipticLatitude(double JD, bool bHighPrecision)

Return Value

the ecliptic latitude in degrees referred to the mean dynamical ecliptic and equinox of the date defined in the VSOP theory.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAMars::RadiusVector

static double RadiusVector(double JD, bool bHighPrecision)

Return Value

the radius vector in astronomical units.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAMercury

This class provides for calculation of the heliocentric position of Mercury. This refers to Chapter 32 in the book.

Functions this class provides include:

EclipticLongitude

EclipticLatitude

RadiusVector

CAAMercury::EclipticLongitude

static double EclipticLongitude(double JD, bool bHighPrecision)

Return Value

the ecliptic longitude in degrees referred to the mean dynamical ecliptic and equinox of the date defined in the VSOP theory.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAMercury::EclipticLatitude

static double EclipticLatitude(double JD, bool bHighPrecision)

Return Value

the ecliptic latitude in degrees referred to the mean dynamical ecliptic and equinox of the date defined in the VSOP theory.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAMercury::RadiusVector

static double RadiusVector(double JD, bool bHighPrecision)

Return Value

the radius vector in astronomical units.

Parameters

JD The date in Dynamical time to calculate for.

bHighPrecision If true then use the full VSOP87 theory instead of the truncated version as provided in Meeus's book.

CAAMoon

This class provides the algorithms which obtain the position of the Moon. This refers to Chapter 47 in the book.

Functions this class provides include:

EclipticLongitude

EclipticLatitude

RadiusVector

MeanAnomaly

MeanElongation

MeanLongitude

MeanLongitudeAscendingNode

TrueLongitudeAscendingNode

MeanLongitudePergiee

ArgumentOfLatitude

RadiusVectorToHorizontalParallax

HorizontalParallaxToRadiusVector

CAAMoon::EclipticLongitude

static double EclipticLongitude(double JD)

Return Value

the ecliptic longitude in degrees referred to the mean dynamical ecliptic and equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAMoon::EclipticLatitude

static double EclipticLatitude(double JD)

Return Value

the ecliptic latitude in degrees referred to the mean dynamical ecliptic and equinox of the date.

Parameters

JD The date in Dynamical time to calculate for.

CAAMoon::RadiusVector

static double RadiusVector(double JD)

Return Value

the radius vector in kilometres.

Parameters

JD The date in Dynamical time to calculate for.

CAAMoon::MeanAnomaly

static double MeanAnomaly(double JD)

Return Value

the mean anomaly of the Moon in degrees.

Parameters

JD The date in Dynamical time to calculate for.

CAAMoon::MeanElongation

static double MeanElongation(double JD)

Return Value

the mean elongation of the Moon in degrees.

Parameters

JD The date in Dynamical time to calculate for.

CAAMoon::MeanLongitude

static double MeanLongitude(double JD)

Return Value

the mean longitude of the Moon in degrees.

Parameters

JD The date in Dynamical time to calculate for.

CAAMoon::MeanLongitudeAscendingNode

static double MeanLongitudeAscendingNode(double JD)

Return Value

the mean longitude of the ascending node of the Moon in degrees.

Parameters

JD The date in Dynamical time to calculate for.

CAAMoon::TrueLongitudeAscendingNode

static double TrueLongitudeAscendingNode(double JD)

Return Value

the true longitude of the ascending node of the lunar orbit in degrees.

Parameters

JD The date in Dynamical time to calculate for.

CAAMoon::MeanLongitudePerigee

static double MeanLongitudePerigee(double JD)

Return Value

the mean longitude of the perigee of the lunar orbit in degrees.

Parameters

JD The date in Dynamical time to calculate for.

CAAMoon::ArgumentOfLatitude

static double ArgumentOfLatitude(double JD)

Return Value

the argument of latitude (mean distance of the Moon from its ascending node) in degrees.

Parameters

JD The date in Dynamical time to calculate for.

CAAMoon::RadiusVectorToHorizontalParallax

static double RadiusVectorToHorizontalParallax(double RadiusVector)

Return Value

the parallax of the object in degrees.

Parameters

RadiusVector The distance to the object (e.g. Moon) in kilometres.

CAAMoon::HorizontalParallaxToRadiusVector

static double HorizontalParallaxToRadiusVector(double Parallax)

Return Value

RadiusVector The distance to the object in kilometres.

Parameters

the parallax of the object (e.g. Moon) in degrees.

CAAMoonIlluminatedFraction

This class provides algorithms for the Moon's elongation, phase angle and illuminated fraction. This refers to Chapter 48 in the book.

Functions this class provides include:

GeocentricElongation

PhaseAngle

IlluminatedFraction

PositionAngle

CAAMoonIlluminatedFraction::GeocentricElongation

static double GeocentricElongation(double ObjectAlpha, double ObjectDelta, double SunAlpha, double SunDelta)

Return Value

the elongation of the object from the Sun

Parameters

ObjectAlpha The geocentric right ascension of the object (e.g. the Moon) expressed as an hour angle.

ObjectDelta The geocentric declination of the object (e.g. the Moon) in degrees.

SunAlpha The geocentric right ascension of the Sun expressed as an hour angle.

SunDelta The geocentric declination of the Sun in degrees.

CAAMoonIlluminatedFraction::PhaseAngle

static double PhaseAngle(double GeocentricElongation, double EarthObjectDistance, double EarthSunDistance)

Return Value

the phase angle in degrees.

Parameters

GeocentricElongation The geocentric elongation in degrees.

EarthObjectDistance The distance in astronomical units between the Earth and the object (the Moon)

EarthSunDistance The distance in astronomical units between the Earth and the Sun

Remarks

The EarthObjectDistance and EarthSunDistance should be expressed in the same units for instance in kilometres.

CAAMoonIlluminatedFraction::IlluminatedFraction

static double IlluminatedFraction(double PhaseAngle)

Return Value

the illuminated fraction (a value form 0 to 1).

Parameters

PhaseAngle The phase angle in degrees.

CAAMoonIlluminatedFraction::PositionAngle

static double PositionAngle(double Alpha0, double Delta0, double Alpha, double Delta)

Return Value

the position angle of the midpoint of the illuminated limb of the object (the Moon) in degrees.

Parameters

Alpha0 The geocentric right ascension of the Sun expressed as an hour angle.

Delta0 The geocentric declination of the Sun in degrees.

Alpha The geocentric right ascension of the object (e.g. the Moon) expressed as an hour angle.

Delta The geocentric declination of the object (e.g. the Moon) in degrees.

CAAMoonMaxDeclinations

This class provides algorithms to calculate the times when the Moon reaches its maximum Northerly and Southerly declinations. This refers to Chapter 52 in the book.

Functions this class provides include:

K

MeanGreatestDeclination

MeanGreatestDeclinationValue

TrueGreatestDeclination

TrueGreatestDeclinationValue

CAAMoonMaxDeclinations::K

static double K(double Year)

Return Value

Returns the approximate value of K (required by the other methods of CAAMoonMaxDeclinations) for calculation of the Moon's max declination.

Parameters

Year The Year including decimals to calculate the K value for.

Remarks

Please note that the return value from this method must be rounded to an integer by client code before calling other methods in this class with this K value. Any other value of K will give meaningless values.

CAAMoonMaxDeclinations::MeanGreatestDeclination

static double MeanGreatestDeclination(double k, bool bNortherly)

Return Value

Returns the date in Dynamical time when the mean maximum declination occurs.

Parameters

k The K value to calculate the max declination for. This K value must be an integer value. Any other value of K will give meaningless values.

bNortherly true if this is a calculation for a maximum northerly declination, false implies a calculation of the a maximum southerly declination.

CAAMoonMaxDeclinations::MeanGreatestDeclinationValue

static double MeanGreatestDeclinationValue(double k)

Return Value

Returns the mean maximum declination in degrees.

Parameters

k The K value to calculate the max declination for. This K value must be an integer value. Any other value of K will give meaningless values.

CAAMoonMaxDeclinations::TrueGreatestDeclination

static double TrueGreatestDeclination(double k, bool bNortherly)

Return Value

Returns the date in Dynamical time when the true maximum declination occurs.

Parameters

k The K value to calculate the max declination for. This K value must be an integer value. Any other value of K will give meaningless values.

bNortherly true if this is a calculation for a maximum northerly declination, false implies a calculation of the a maximum southerly declination.

CAAMoonMaxDeclinations::TrueGreatestDeclinationValue

static double TrueGreatestDeclinationValue(double k)

Return Value

Returns the true maximum declination in degrees.

Parameters

k The K value to calculate the max declination for. This K value must be an integer value. Any other value of K will give meaningless values.

CAAMoonMaxDeclinations2

This class uses interpolation to calculate the same details as those provided with the existing CAAMoonMaxDeclinations class.

Functions this class provides include:

Calculate

CAAMoonMaxDeclinations2::Calculate

static std::vector<CAAMoonMaxDeclinationsDetails2> Calculate(double StartJD, double EndJD, double StepInterval = 0.007, Algorithm algorithm = Algorithm::MeeusTruncated)

Return Value

A standard C++ array containing a class which itself contains:

type An enum class instance which represents the type of event found. This can be MaxNorthernDeclination or MaxSourthernDeclination.

JD The date in Dynamical time on which the event occurs.

Declination this will be the maximum geocentric declination of the Moon at time JD.

RA this will be the Right Ascension of the Moon at time JD

Parameters

StartJD The Julian Day corresponding to the Dynamical Time for the date when you want to start the calculation for.

EndJD The Julian Day corresponding to the Dynamical Time for the date when you want to end the calculation for.

StepInterval The step interval in fractions of days to do the calculation for. The default value of 0.007 corresponds to roughly 10 minutes which is a reasonable tradeoff between performance and accuracy.

Algorithm An enum class representing the algorithm to use for the calculation. Can be MeeusTruncated which represents the truncated ELP2000 algorithm presented in the book, ELP2000 which uses the full ELP2000 algorithm, ELPMPP02Nominal which uses the ELPMPP02 Nominal fit, ELPMPP02LLR which uses the ELPMPP02 Lunar Laser Ranging fit, ELPMPP02DE405 which uses the ELPMPP02 DE405 fit and ELPMPP02DE406 which uses the ELPMPP02 DE406 fit.

CAAMoonNodes

This class provides algorithms which obtain dates when the Moon passes through its nodes. This refers to Chapter 51 in the book.

Functions this class provides include:

K

PassageThroNode

CAAMoonNodes::K

static double K(double Year)

Return Value

Returns the approximate value of K (required by the other methods of CAAMoonNodes) for calculation of the specified passage thro the node.

Parameters

Year The Year including decimals to calculate the K value for.

Remarks

Please note that the return value from this method must be rounded to an integer or an integer + 0.5 by client code before calling other methods in this class with this K value. Any other value of K will give meaningless values.

CAAMoonNodes::PassageThroNode

static double PassageThroNode(double k)

Return Value

Returns the date in Dynamical time when the specified passage thro the node occurs.

Parameters

k The K value to calculate the passage thro the node for. This K value must be an integer value or an integer value + 0.5. Any other value of K will give meaningless values.

CAAMoonNodes2

This class uses interpolation to calculate the same details as those provided with the existing CAAMoonNodes class.

Functions this class provides include:

Calculate

CAAMoonNodes2::Calculate

static std::vector<CAAMoonNodesDetails2> Calculate(double StartJD, double EndJD, double StepInterval = 0.007, Algorithm algorithm = Algorithm::MeeusTruncated)

Return Value

A standard C++ array containing a class which itself contains:

type An enum class instance which represents the type of event found. This can be Ascending or Descending.

JD The date in Dynamical time on which the event occurs.

Parameters

StartJD The Julian Day corresponding to the Dynamical Time for the date when you want to start the calculation for.

EndJD The Julian Day corresponding to the Dynamical Time for the date when you want to end the calculation for.

StepInterval The step interval in fractions of days to do the calculation for. The default value of 0.007 corresponds to roughly 10 minutes which is a reasonable tradeoff between performance and accuracy.

Algorithm An enum class representing the algorithm to use for the calculation. Can be MeeusTruncated which represents the truncated ELP2000 algorithm presented in the book, ELP2000 which uses the full ELP2000 algorithm, ELPMPP02Nominal which uses the ELPMPP02 Nominal fit, ELPMPP02LLR which uses the ELPMPP02 Lunar Laser Ranging fit, ELPMPP02DE405 which uses the ELPMPP02 DE405 fit and ELPMPP02DE406 which uses the ELPMPP02 DE406 fit.

CAAMoonPerigeeApogee

This class provides algorithms to calculate the approximate times when the distance between the Earth and the Moon is a minimum (perigee) or a maximum (apogee). This refers to Chapter 50 in the book.

Functions this class provides include:

K

MeanPerigee

MeanApogee

TruePerigee

TrueApogee

PerigeeParallax

ApogeeParallax

CAAMoonPerigeeApogee::K

static double K(double Year)

Return Value

Returns the approximate value of K (required by the other methods of CAAMoonPerigeeApogee) for calculation of the specified phase.

Parameters

Year The Year including decimals to calculate the K value for.

Remarks

Please note that the return value from this method must be rounded to an integer or an integer + 0.5 by client code before calling other methods in this class with this K value. Any other value of K will give meaningless values.

CAAMoonPerigeeApogee::MeanPerigee

static double MeanPerigee(double k)

Return Value

Returns the date in Dynamical time when the mean perigee occurs.

Parameters

k The K value to calculate the perigee for. This K value must be an integer value. Any other value of K will give meaningless values.

CAAMoonPerigeeApogee::MeanApogee

static double MeanApogee(double k)

Return Value

Returns the date in Dynamical time when the specified mean apogee occurs.

Parameters

k The K value to calculate the apogee for. This K value must be an integer value + 0.5. Any other value of K will give meaningless values.