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Re: GHA of the Moon
From: Roger W. Sinnott
Date: 2020 Oct 2, 00:49 +0000
From: Roger W. Sinnott
Date: 2020 Oct 2, 00:49 +0000
James,
The Moon's orbit around the Earth is severely perturbed by the Sun (mainly). For $5, willbell.com sells a booklet called "Low-precision Formulae for Planetary Positions" by Van Flandern and Pulkkinen.
To calculate the Moon's GHA to 1-arcminute accuracy involves these steps:
(1) Evaluate 7 preliminary arguments, each from a short polynomial in time.
(2) Use them in a 55-term trig formula for the Moon's ecliptic longitude.
(3) Use them again in a 38-term formula for the Moon's ecliptic latitude.
(4) Transform the Moon's ecliptic long and lat to right ascension (RA).
(5) Obtain the Greenwich sidereal time (GST) from a short formula.
(6) Combine the RA and GST to get the GHA.
For greater accuracy than 1 arcminute, you'll need MANY more trig terms in steps 2 and 3 above. Those can be found in other books besides Van Flandern and Pulkkinen.
Roger S.
The Moon's orbit around the Earth is severely perturbed by the Sun (mainly). For $5, willbell.com sells a booklet called "Low-precision Formulae for Planetary Positions" by Van Flandern and Pulkkinen.
To calculate the Moon's GHA to 1-arcminute accuracy involves these steps:
(1) Evaluate 7 preliminary arguments, each from a short polynomial in time.
(2) Use them in a 55-term trig formula for the Moon's ecliptic longitude.
(3) Use them again in a 38-term formula for the Moon's ecliptic latitude.
(4) Transform the Moon's ecliptic long and lat to right ascension (RA).
(5) Obtain the Greenwich sidereal time (GST) from a short formula.
(6) Combine the RA and GST to get the GHA.
For greater accuracy than 1 arcminute, you'll need MANY more trig terms in steps 2 and 3 above. Those can be found in other books besides Van Flandern and Pulkkinen.
Roger S.
