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    Lunar Formulas
    From: Dan Allen
    Date: 2001 Jul 09, 1:35 PM

    Ed Falk wrote:
    > Can anyone provide a reference to the "classic" method?
    The best modern reference I have found is the out-of-print
      "Navigation Afloat", by Alton Moody, Van Nostrand: 1980.
    which contains an entire paragraph about lunars!  So that you do not need
    to go out and buy this hard to find book, here is the paragraph and
    formulas, dutifully copied by myself just minutes ago:
    Time, and hence longitude, can be determined by taking advantage of the
    relatively rapid change of apparent position of the Moon relative to
    other astronomical bodies. The classical method is by lunar distance,
    the method used by mariners before an accurate timepiece was generally
    available during a long voyage. The sextant angle between the Moon and
    the Sun or a star near the ecliptic is observed and the measured angle
    corrected for semi-diameter and any instrument error. This angle is
    designated Do. The altitude of each body is observed simultaneously or
    adjusted to the same time. The equivalent geocentric distance, Dog, is
    then calculated by means of the equation:
                                (cos Do - sin ham sin has) cos Hom cos Hos
    cos Dog = sin Hom sin Hos + ------------------------------------------
                                               cos ham cos has
    where ha is the apparent altitude (sextant altitude correcte for dip and
    index error), Ho is the observed altitude (apparent altitude corrected
    for refraction, semi-diameter, and parallax), and susbscripts M and S
    indicate Moon and Sun or star, respectively. Next, the 'calculated'
    value of lunar distance, Dc, is determined by means of the equation:
    cos Dc = sin dm sin ds + cos dm cos ds cos(SHAm - SHAs)
    where d is declination, SHA is sidereal hour angle, and subscripts M and
    S are as before. The Dc should be calculated for a time believed to be
    earlier than the correct time. The Dog and the two values of Dc are
    compared and the correct time determined by interpolation (or
    "Navigation Afloat", by Alton Moody, Van Nostrand, New York: 1980, p.

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