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    Re: Celestial predictions. was:[NAV-L] Old style lunar
    From: Frank Reed CT
    Date: 2004 Dec 12, 19:24 EST
    George H, you wrote:
    "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?"
    How long is your trip? If I were planning to spend two months cruising without touching an Internet-enabled port, I would simply print out the pages. If I were advising another coder how to do it from scratch, I would first request a consulting fee. If there's sufficient demand, I'll produce a commercial version of my own software (but I'm skeptical that such demand exists).
    "In practical terms, there's no requirement for position accuracy to be to
    an arc-second."
    I chose arcsecond accuracy simply because that's one step BETTER than that required by any navigational calculation. Since the Nautical Almanac lists positions to the nearest tenth of a minute, positional data accurate to the nearest arcsecond will match the published tables except approximately one in six times (when the rounding might shift the last digit in the wrong direction). You will find that almost everyone who is doing these sorts of calculations is aiming for arcsecond or better accuracy. Umland, Reis, Wepster... they're all trying for that level of accuracy, though not always with success.
    "Meeus' algorithms do all that's necessary to obtain on-board
    positions to quite sufficient accuracy for any maritime application, lunar
    distances included."
    I agree that the algorithmic approach is fine for standard line of position navigation under the assumption that we're not going to worry about errors smaller than 1 minute of arc. But I really do not think it's true that the algorthms published by Meeus are sufficient for lunar distance calculations. Meeus himself says that the Moon's longitude will be in error by as much as 10 seconds of arc. If you don't mind errors in your predicted lunars as large as 0.2 minutes of arc, then yes, you could use those Meeus algorithms. No problem. But why?? Unless you're dealing with a very old calculating device, you only need a megabyte to store a long-term almanac that can be much more accurate (42,000 bytes per year for the Sun, Moon, and 4 navigational planets at arcsecond accuracy). 
    George scoffs:
    "Frank is always quick to scoff, with words like "absurd"."

    No, Frank isn't always quick to scoff. Sometimes Frank is rather slow to scoff. At least that's what Frank thinks.
    And George writes:
    "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"? "
    It all depends on your goal. Shooting lunars is a hobby for those people who experiment with them today. If keyboarding coefficients out of a book by Meeus is ALSO one of your hobbies, then of course, do whatever makes you happy.
    And George scoffs:
    "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."
    I'm sure you meant to say 'Frank should come off it', right? And of course, no, I was not proposing that. The point is simply that the problem has been completely calculated. Why do you have such profound antipathy for a database?!
    "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'."
    How have you determined that?
    "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"
    Indeed it is. And for devices with very small amounts of memory, the algorithmic approach still has some value. But these days even cell phones come with lots of built-in memory. When memory is expensive and calculating time is unimportant, it's appropriate to write code based on long algorithms. When memory is cheap and calculating time is relevant, it's better to pre-calculate everything and look up the results in a database.
    "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."
    You should double-check the chapter on the Moon's position in that book. The code is only slightly improved over the earlier publication. And the accuracy of the planet positions are not necessarily as good as you think. Read the section on p.220 of AA.
    And wrote:
    "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
    Why? Seriously. What difference does it make what's going on inside the software?
    Frank R
    [ ] Mystic, Connecticut
    [X] Chicago, Illinois
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