LONG-TERM ALMANAC FOR MOON, STARS, AND LUNAR DISTANCES V1.13
Copyright © 2003−2008 Henning Umland
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) − DUT1
Current values for TAI−UTC and DUT1 (= UT1−UTC) are published on the web site of the IERS Rapid Service / Prediction Center (IERS Bulletin A).
Reliable long-term predictions for ΔT are not possible. Here are some ΔT values of the past:
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 GHAAries 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''|
|HP and SD:||±0.1''|
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''
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