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Subject: Re: HO 211 and Calculator Almanacs
From: George Huxtable (george@XXX.XXX)
Date: Wed Sep 08 1999 - 15:40:54 EDT
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.
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george@XXX.XXX
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel, or fax, to 01865 820222 or (int.) +44 1865 820222.
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