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    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.
    ------------------------------
    

       
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