Copyright © 2001−2020 Henning Umland

y m d h m s s
 Date:        Time (UT1):         ΔT:           

  GHA SHA Dec SD HP Equation of Time
Moon   Phase 
  GAST GMST Eq. of Equinoxes Δψ Δε Mean Obl. of Ecl.
  JD JDE Lunar Dist. of Sun Weekday True Obl. of Ecl.

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 GHAAries refer to the true equinox of date.

Accuracy (approximate values):
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"


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