LONG-TERM ALMANAC FOR SUN, MOON, AND POLARIS V1.08

*Copyright © 2001–2004 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 (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 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 (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. **Warning:**

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.