LONG-TERM ALMANAC FOR SUN, MOON, AND POLARIS V1.12

*Copyright © 2001−2020 Henning Umland*

**Description:**

This computer almanac is based
upon formulas published in *Astronomical Algorithms* by Jean Meeus.
The program calculates Greenwich hour angle (GHA), sidereal hour angle
(SHA), and declination (Dec) for sun, moon, and polaris.

Further, the following quantities are provided:

Greenwich hour angle of the vernal point (Aries)

Geocentric semidiameter (SD) and equatorial horizontal parallax (HP) for sun
and moon

Equation of time

Phase of the moon (illuminated fraction of the moon's disk)

Greenwich apparent sidereal time (GAST)

Greenwich mean sidereal time (GMST)

Equation of the equinoxes (= GAST−GMST)

Nutation in longitude (Δψ)

Nutation in obliquity (Δε)

Mean obliquity of the ecliptic

True obliquity of the ecliptic (= mean obliquity + Δε)

Julian date (JD)

Julian ephemeris date (JDE)

Geocentric lunar distance of the sun (center-center)

Day of the week

The almanac can be used for many decades, provided the ΔT value (= TT−UT1)
for the given date is known. An accuracy of approx. ±1s is sufficient for most
applications. Errors in ΔT have a much greater influence on the coordinates
of the moon than on the other results. ΔT is obtained through the following
formula:

ΔT = 32.184s + (TAI−UTC) − (UT1−UTC)

Current values for TAI−UTC and UT1−UTC are published on the web site
of the *International Earth Rotation Service* (IERS Bulletin A).
DUT1 is UT1−UTC rounded to 0.1s and can be used as well.

Accurate long-term predictions for ΔT are not possible because random processes are partly involved. Here are some ΔT values of the past:

1970.0: +40.2s

1980.0: +50.5s

1990.0: +56.9s

2000.0: +63.8s

2010.0: +66.1s

2020.0: +69.4s

The program regards any blank dialog box in the time input field as zero. A
missing year, month, or day will result in an error message (program must be
restarted). The number of the year must be entered in 4-digit format.

A "(+)" behind the value for the illuminated fraction of the moon's disk
indicates a waxing moon, a "(−)" a waning moon.

SHA and GHA_{Aries} refer to the true equinox of date.

GHA, SHA, and Dec of the sun: | ±1" |

GHA and SHA of the moon: | ±10" |

Dec of the moon: | ±5" |

GHA and SHA of Polaris: | ±2" |

Dec of Polaris: | ±1" |

GHA Aries: | ±1" |

HP and SD: | ±0.1" |

Equation of Time: | ±0.1s |

GAST, GMST, and Equation of Equinoxes: | ±0.001s |

Nutation (Δψ and Δε): | ±0.001" |

Mean Obliquity of the Ecliptic: | ±0.001" |

Lunar distance of sun: | ±10" |

LICENSE

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by the Free Software
Foundation, either version 3 of the license or any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
See the GNU General Public License
(http://www.gnu.org/licenses/) for more details.

Henning Umland N 53° 20' 34'' E 9° 52' 00''

Check this web site for updated versions:
https://celnav.de