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Subject: Re: HO 211 and Calculator Almanacs
From: Bill Murdoch (WSMurdoch@XXX.XXX)
Date: Fri Sep 10 1999 - 21:59:57 EDT
"The neat trick" is something like this.
Planetary perturbation terms can be written as a sum of terms like:
a sin(bT+c)
where a, b, and c are constants and T is a measure of time.
Meeus's tables are like that.
These terms can be changed into terms of the form
a sin(dA1+eA2+f)
where a, d, e and f are constants, d and e are integers, and A1 and A2 are
planetary anomalies, A1 of the planet of interest and A2 of another planet.
(I have been able to factor Meesus's constants to this form. My programs use
this sort of series.)
That kind of term can be changed to one like
g sin(dA1+eA2) + h cos(dA1+eA2). Newcomb's tables look like that.
Montenbruck changes the terms further to the form
g(cos(dA1)cos(eA2)-sin(dA1)sin(eA2))+h(sin(dA1)cos(eA2)+cos(dA1)sin(eA2))
using the angle sum and difference formulas.
While that may look worse, there are limited numbers of dA1 and eA2 values in
a series of perturbation terms. The sines and cosines of these can be
calculated once and then used over and over. There are thus many fewer sin
and cos calls in a calculation. Since these calls are slow in comparison to
multiplication and addition, the calculation is faster... much faster.
Bill Murdoch
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