ASTRONOMICAL AND NAUTICAL ALMANAC FOR SUN, MOON, BRIGHTER PLANETS, 58 NAVIGATIONAL STARS, AND LUNAR DISTANCES  V1.06

 Copyright © 2021 Henning Umland & Heiner Müller-Krumbhaar

Description:

This is a computer almanac developed with special attention to the needs of navigators and amateur astronomers. It is based upon the VSOP87D Theory (P. Bretagnon, G. Francou)), the 1980 IAU Nutation Theory (P. Seidelmann) including J. Laskar's formula, the LEA406b Theory for the Moon (S. Kudryavtsev), and formulas published in Astronomical Algorithms by J. Meeus and Textbook on Spherical Astronomy by W. M. Smart. The program calculates Greenwich hour angle (GHA), right ascension (RA), and declination (Dec) for Sun, Moon, Venus, Mars, Jupiter, Saturn, and navigational stars (apparent geocentric positions).

Optionally, the program also calculates geocentric altitudes and azimuths of bodies for an assumed position (sight reduction). Corrections for parallax and atmospheric refraction are not included. Azimuths are measured clockwise (0°...360°) from the geographic north direction, as is common in marine navigation.

Furthermore, the following quantities are provided:

Geocentric semidiameter (SD) and equatorial horizontal parallax (HP) for Sun, Moon, and planets
Equation of time
Illuminated fraction of the apparent disks of Moon and planets
Phase of the Moon
Greenwich mean sidereal time (GMST)
Greenwich apparent sidereal time (GAST)
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 Sun, planets, and selected star (center−center)
Day of the week

The phases of the Moon are indicated as follows:

New
+cre = waxing crescent
FQ = first quarter
+gib = waxing gibbous
Full
–gib = waning gibbous
LQ = last quarter
–cre = waning crescent

By definition, the phase is defined by the difference between the ecliptic longitudes of Moon and Sun. It does not exactly correlate with the illuminated fraction of the Moon's disk since the plane of the Moon's orbit is inclined to the ecliptic.

GHA and RA refer to the true equinox of date.

The apparent positions of the planets refer to their respective center. A phase correction is not included.

The apparent semidiameter of Venus includes the cloud layer of the planet and may be slightly greater than values calculated with other software (referring to the solid surface). The semidiameters of Jupiter and Saturn refer to the respective equator.

For determining longitude or time by lunar distances, bodies near the ecliptic are most suitable. Those are Sun, all planets, and stars with an ecliptic latitude of less than approx. ±10°. The recommended stars are marked by an asterisk in the drop-down menu. Since the lunar distance of each body passes through a minimum during each lunar orbit, the rate of change of the lunar distance becomes zero at such an instant. Therefore, the rate of change should be checked by calculating the lunar distance of the chosen body at two instants 1 h apart. This rate of change (absolute value) should be as high as possible (roughly 0.5°/h) for best precision. If it is too small, another body should be chosen.

The almanac covers a time span of 400 years (recommended range: 1800...2200), provided the ΔT value (= TT−UT1) for the given date is known. A ΔT value accurate to 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 regularly published on the web site of the International Earth Rotation and Reference Systems Service, IERS (IERS Bulletin A, General Information). Instead of UT1−UTC, DUT1 (= UT1−UTC rounded to a precision of 0.1s) can be used.

Example:   TAI−UTC = 37s,   DUT1 = −0.2s,   ΔT = 32.184 + 37 − (−0.2) = 69.4s

ΔT tends to increase in the long term (tidal friction). Since the evolution of ΔT is also influenced by various random processes, accurate long-term predictions are not possible. 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

Results were compared with Interactive Computer Ephemeris 0.51 (US Naval Observatory), HORIZONS (NASA Jet Propulsion Laboratory), and Astronomical Almanac 5.6 (Stephen L. Moshier).

^*GHA and RA for the triple-star system Polaris seemingly have a lower precision which is only geometrically caused (small polar distance). The meridians converge at the poles, and the equatorial coordinate system has a singularity there in each case. For Polaris, the possible error Δ therefore cannot be taken directly as δ GHA but must be viewed in combination with the distance from the pole as Δ = δ GHA*cos(Dec), with cos(90°)=0. Again, for that combination our precision is ± 1 arcsecond.