# 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:**George Huxtable

**Date:**1999 Sep 08, 1:41 PM

Gordon Talge provides much interesting information about calculating your own almanac. As one who has been there and done it, I have some comments to make. In my opinion, it's much more satisfying, and quite feasible, to be able to calculate your own accurate "everlasting" almanac for all the navigational bodies, rather than to be dependent on others to provide new coefficients to be entered in at regular intervals. By "everlasting", I mean no more than within my lifetime and that of other readers of this mailing list; eventually, the accuracy of any predictions will degrade. By navigational bodies, I mean Sun, Moon, Venus, Mars, Jupiter, Saturn, and the 60 (or so) named stars to be found in a nautical almanac. By "accurate", I mean keeping error within the order of 0.1 minutes of arc or so, smaller than the errors in the observational procedure. Over a many-year period, this implies taking into account precession, nutation, and also the proper-motions of some nearer stars. Almost all the necessary information has been collected together by Jean Meeus, and published by Willman-Bell. Gordon mentions Meeus' "Astronomical Algorithms", a work which has been out of print for a while, but which has reappeared as a 1988 edition. I do recommend this book for anyone interested in astronomical predictions, who has a mathematical bent. It's a considerably expanded version of his earlier "Astronomical Formulae for Calculators". I used the information in that paperback (second ed., 1982) to make my own almanac program. Meeus has provided a real service in putting all that information together. Until recently. when big NASA computers came into action, almanac data was compiled from analyses of planetary motion made nearly a century ago by Simon Newcomb, an unsung American astronomer. Even now, the parameters he worked out then remain valid today for calculating almanacs to marine-navigation accuracy. What is so staggering is that all this work was done with only human computing-power. An inspiring achievement, indeed. Meeus' "Astronomical Formulae for Calculators" was based on Newcomb's analysis (and on Brown's theory of the Moon's motion). His newer book includes the recent computer predictions and gives many more terms for the expansions, but all this extra precision is, in general, irrelevant for the needs of us navigators. The problem with predicting the future position of any body in the solar system is that they are all acted on, not just by the gravity of the Sun, but also by an attraction to every other body in the system, and as all these bodies are constantly moving, there are continually-changing perturbations to all the orbits. Sometimes there can be hundreds of such terms which have to be calculated. It all depends on the accuracy required. My navigation program, in its basic form, takes a sextant observation of a body, corrects for refraction and dip, works out the altitude and azimuth of the body from the built-in almanac, allows where necessary for semidiameter and parallax, and provides a position line in terms of the amount and direction of offset from an assumed position. The user has to to the rest. The name of the body, date and time, assumed lat. and long., and the altitude by sextant, are required. Height of eye is preset. The program to do this runs on a Casio fx-730p or a fx-795p programmable pocket calculator, now alas no longer available. The language is a crude and idiosyncratic version of Basic. The program occupies all but 1 kilobyte of the maximum-available expanded memory, which is nearly 16 kilobytes. Much of this is taken up by the many coefficients of the terms used in the astro calculations. It's all desperately slow, though, taking nearly 5 minutes to compute an observation involving the Moon, Saturn, or Jupiter (because they require so many perturbation terms). The Casio calculator does all its internal calculations with the numbers in decimal form, one digit at a time, which partly explains the slowness. Theres no conversion to binary form, as in a modern computer. Gordon refers to calculating solutions for the position of a planet as involving Cartesian (X,Y,Z) coordinates for positions in space, but that isn't necessary; everything can be done in terms of the orbit paramaters of the Earth and the planet with respect to the ecliptic (semidiameter, eccentricity, inclination, etc), calculating perturbations to obtain ecliptic latitudes and longitudes, then converting to get dec and RA. Many of us simpler souls would find this more meaningful. Meeus explains all this. Converting to Cartesian, though just as precise and mathematically meaningful, seems to be taking a step away from understandable reality. That's a personal view, anyway. However it's done, you will sometimes find that visualising all those angles in 3 dimensions will make your head hurt. George Huxtable. ------------------------------ george@huxtable.u-net.com George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. Tel, or fax, to 01865 820222 or (int.) +44 1865 820222. ------------------------------