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    Re: Lunar trouble, need help
    From: George Huxtable
    Date: 2008 Jun 26, 17:33 +0100

    On 20 June, in [5530] I analysed Jeremy's recent lunar distance, in some
    detail, explaining how it could be calculated out, in the general case, and
    arriving at numerical answers.
    In [5588], Frank Reed has considered the matter as a special case, with
    opposite azimuths, and shown how several approximations and simplifications
    are then valid in those special circumstances, but makes no reference to
    that previous work.
    I can confirm  that the agreement with my own analysis is indeed as good as
    he claims, within the errors that would be expected from taking almanac
    tabulations which are given only to the nearest tenth of an arc-minute.
    Indeed, that observation was rather a "special", in two respects, not just
    one. The azimuths were opposite, AND also the lunar distance was very nearly
    90 degrees.(well, over 85, anyway...)
    Thare are several points that arise from Frank's posting.
    1. A similar simplification occurs when the Moon and other-body azimuths are
    the same, just as when they are opposite.
    2. How can an observer be sure that the geometry is such as allow him to
    make those simple approximations? How much leeway does he have? Can Frank
    provide simple rules-of-thumb? If the effort involved in answering that
    question is comparable with the effort involved in doing the full
    calculation, one might as well choose the latter.
    3. If a learner is taught that "this is how lunars are worked out", from
    such a simplified and unusual example, then he will find himself at a loss
    when in reality he gets confronted by one that calls for spherical trig, not
    just adding and subtracting.
    4. Frank's final step was to compare the cleared distance with one computed
    from a known GMT. But that hides the real purpose of lunars, which were
    taken in order to discover unknown GMT; not as for testing prowess in using
    a sextant. The final step should be in establishing the GMT; and this can
    then raise interesting questions of iteration if altitudes are computed
    rather than measured, because an initial estimate of GMT will be asked for.
    5. I find it hard to reconcile the effect of the Moon parallax / refraction
    on this observation, stated as being 27.2', with Frank's statement, in
    "PS: And a reminder: don't fuss over the exact interpolated altitude of the
    Moon. When the lunar distance is close to 90 degrees, the altitude of the
    Moon can be way off and it will not affect the calculation significantly."
    (a point that Frank has made in previous postings).
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Navigation List archive: www.fer3.com/arc
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