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    Celestial predictions. was:[NAV-L] Old style lunar
    From: George Huxtable
    Date: 2004 Dec 11, 20:28 +0000

    Frank started this by writing-
    >>It's no longer necessary to do this algorithmically. Just open a  virtual
    >>almanac page.
    and I asked:
    >"What about if you need those predictions when you're at  sea? I ask."
    To which Frank has responded-
    >Since we're comparing Meeus algorithms with a straight database based on  JPL
    >integrations, I assume that a computing device is permitted. The software
    >and data to do this by database for a year is approximately the same  size as
    >the software to do it algorithmically, and it is many times more  accurate for
    >the Moon's position. For longer stretches of time, the database  grows in size
    >linearly. Many people approaching this problem look at the  original JPL
    >database which is hundreds of megabytes for a century of data and  assume that
    >that's too big to be practical. But there are a variety of  straight-forward
    >techniques that can reduce the size to ten megabytes for 300  years. That's the
    >whole size (ten megs) of the database behind my online  300-year almanac and
    >lunar distance predictor. The code to access it is just a  couple of hundred
    >Believe me, I used to be quite fanatic about algorithmic approaches a la
    >Meeus, Chapront-Touze etc. Then I realized that the whole approach was absurd
    >for the vast majority of "practical" applications. The positions of the planets
    >have *already* been calculated using numerical integrations that include such
    > tiny factors as the gravitational perturbations induced by the largest
    >asteroids. The almanac exists. We don't need to re-calculate it every time we
    >want the position of the Moon.
    From George-
    That's all very well, but in practical terms, what does a mariner, given an
    on-board  laptop, do to obtain positions by such methods as Frank
    advocates, when at sea? First, take a mariner that's very computer-savvy,
    and then take another that isn't. Just how do they go about it?
    In practical terms, there's no requirement for position accuracy to be to
    an arc-second. Meeus' algorithms do all that's necessary to obtain on-board
    positions to quite sufficient accuracy for any maritime application, lunar
    distances included..
    Frank is always quick to scoff, with words like "absurd". If there's a
    computer on board, what's the problem in using it to make such calculations
    using the algorithms that Meeus provides? Where lies the "absurdity"? At
    sea, we can do without such "tiny factors as the gravitational
    perturbations induced by the largest asteroids." Is Frank REALLY prosing
    that as an argument for switching to a precomputed ephemeris? If so, how
    much difference can those perturbations make? Come off it, Frank.
    My own Basic programs run on a programmable pocket calculator, with a
    memory of only 16 kilobytes all told, into which is fitted the programs,
    stored astronomical data, and the harmonic terms of the perturbations. It
    works with a cut-down set of harmonic terms, as given by Meeus in his
    earlier paperback "Astronomical formulae for calculators". My program can
    calculate positions of the four planets, 60 stars, Sun and Moon, over ?400
    years. Results come mostly within 0.1 arc-min of Almanac predictions,
    occasionally 0.2'. The worst-cases seem to be in predictions for Saturn,
    which I have discovered on occasion to differ by 0.5' from the almanac, and
    no doubt bigger discrepancies than that exist here and there. I haven't
    made any systematic search. Nevertheless, it's quite good enough for
    "ordinary" astro-navigation, though certainly not for lunars.
    In his later hardback, "Astronomical Algorithms" (1998), Meeus quadruples
    the number of such perturbation terms; far too much detail for me to pack
    into my pocket calculator (though with double the memory, I could). This
    takes the magnitude of the smallest terms down by a factor of 100 or so,
    increasing the accuracy of the predictions by a similar factor. That would
    allow predictions that were more than sufficiently accurate for lunars.
    If I were brave enough to take a laptop aboard my little boat (which I'm
    not) and could guarantee sufficient Amps (which I can't), then I would
    implement the Meeus algorithmic software  with his full set of
    If anyone could offer appropriate software for installing and interpolating
    a pre-computed database of all those bodies, as Frank is advocating, I
    would certainly weigh it up seriously against the Meeus alternative; and
    perhaps implement both.
    In the case of my programmable calculator, it works in decimal arithmetic,
    one decimal digit, serially, at a time. So, unsurprisingly, it's
    desperately slow, taking around 4 minutes to obtain a position for Jupiter,
    Saturn, or the Moon (the worst cases). With any modern computer,
    calculating time would be negligibly short.
    Finally, I should add that implementing the Meeus algorithms on any sort of
    computer is a serious task, that needs considerable pondering time. But
    what I will guarantee is that for anyone that's done it, he will understand
    a lot more about the motions of celestial bodies than he did before he
    contact George Huxtable by email at george---.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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