# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: HO 211 and Calculator Almanacs**

**From:**Bill Murdoch

**Date:**1999 Sep 10, 8:00 PM

"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