Copyright © 2001–2004 Henning Umland

y m d h m s s
 Date:        Time (UT1):         Delta T:           
  GHA SHA Dec SD HP Equation of Time
Moon   Phase 
  GAST GMST Eq. of Equinoxes d psi d eps 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 (d psi)
Nutation in obliquity (d epsilon)
Mean obliquity of the ecliptic
True obliquity of the ecliptic (= mean obliquity + d epsilon)
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 Delta T value (= TT–UT1) for the given date is known. An accuracy of approx. ±1s is sufficient for most applications. Errors in Delta T have a much greater influence on the coordinates of the moon than on the other results. Delta T is obtained through the following formula:

Delta T = 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 Delta T are not possible. Here are some Delta T values of the past:

1970.0:  +40.2s
1975.0:  +45.5s
1980.0:  +50.5s
1985.0:  +54.3s
1990.0:  +56.9s
1995.0:  +60.8s
2000.0:  +63.8s

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 (d psi and d epsilon): ±0.001"
Mean Obliquity of the Ecliptic: ±0.001"
Lunar distance of sun: ±10"

This program is freeware and may be copied and distributed in unmodified form and on a non-profit basis. For your private use, feel free to modifiy the source code according to your requirements. Any commercial distribution requires the author's permission.

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

Check this web site for updated versions: http://www.celnav.de/index.htm

Warranty disclaimer:
Results obtained with this program have been cross-checked with Multiyear Interactive Computer Almanac 1.5 by USNO. However, the program is still experimental and may contain errors leading to unexpected results in rare cases. Use at your own risk.

Editing and modifying the JavaScript code may lead to unpredictable results. Users who are not familiar with JavaScript and calculations of ephemerides are strongly advised to leave the code unchanged.