LONG-TERM ALMANAC FOR MOON, STARS, AND LUNAR DISTANCES V1.16

*Copyright © 2003−2020 Henning Umland*

** Almanac data:**

**Description:**

This computer almanac is based upon formulas published in *Astronomical
Algorithms* by Jean Meeus and *Textbook on Spherical Astronomy* by
W. M. Smart. Primarily designed for navigational applications, the program
calculates Greenwich hour angle (GHA), siderial hour angle (SHA), and
declination (Dec) for the moon and 58 bright stars including Polaris.

Further, the geocentric semidiameter (SD) and equatorial horizontal
parallax (HP) of the moon, the phase of the moon (illuminated fraction
of the moon's disk), and the Greenwich hour angle of the vernal point
(Aries) are calculated.

In addition, the program calculates the geocentric angular distance between
the chosen star and the center of the moon (lunar distance). Lunar distances
have been used in the past to determine the approximate time. It should be
observed, however, that not every star is suitable for this method. The rate of
change of the lunar distance should be as high as possible. This can be checked
by calculating the lunar distance for a time x and a time x + 1h. Usually, stars
being near the path of the moon, i. e., in the vicinity of the ecliptic, yield
the best results.

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 significant influence on the coordinates
of the moon. The effect on the coordinates of stars, however, is negligible.

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.

**Accuracy (approximate values):**

GHA and SHA of the moon: | ±10'' |

Dec of the moon: | ±4'' |

GHA and SHA of stars: | ±0.1'' (Polaris: ±1.5'') |

Dec of all stars: | ±0.1'' |

GHA Aries: | ±0.1'' |

HP and SD: | ±0.1'' |

Lunar distances: | ±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