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    Re: Lunar trouble, need help
    From: George Huxtable
    Date: 2008 Jul 8, 15:27 +0100

    I've been looking at Chauvenet a bit further, and it looks as though he
    deals, fully, with the terms for correcting Moon parallax that depend on
    Moon azimuth; terms that I have ignored, but which, under some circumstances
    Kent Nordstrom considers worth correcting for. Indeed, he may be right.
    
    In section 94 he shows an example for correcting the Moon's true
    (geocentric) altitude and azimuth for parallax, to produce apparent altitude
    and azimuth, and in section 95, the converse (which is what's needed in for
    correcting a lunar). And to my surprise, in that example (in no way
    extreme), those corrections appear to differ by as much as 15" (in altitude)
    and 10" (in azimuth) from those for a spherical Earth. In section 95 he
    shows a different way to arrive at the same result. I haven't tried to get
    to the bottom of the reasoning involved, which is rather heavy going, but
    Kent may find it instructive, in his quest for ultimate precision.
    
    That may have interesting implications. In the normal clearing process for
    lunar distances, which uses the formula; see [5530]
    
    D = arc cos[(cos d - sin s sin m) cos S cos M /(cos s cos m) +sin S sin M]
    
    or some variant of it, the assumption is made that correction for parallax,
    as for refraction, is only in the vertical plane, and has no component that
    alters the Moon's azimuth. So when Earth oblateness affects not only the
    altitude, but also the azimuth, that assumption fails; or at least, further
    correction is called for.
    
    Chauvenet deals with that by two alternative methods for clearing lunars, in
    sections 248 and 249, which I have made no attempt to follow in any detail.
    Like everything else that he touches, it's all treated with the utmost
    rigour.
    
    It should be appreciated that although Chauvenet is to some extent
    addressing mariners (and had previously been in charge of teaching
    navigation to US Navy students) he was an astronomer, and mainly writing for
    astronomers and surveyors. He wrote in an era when many of them remained out
    of reach of the electric telegraph, needed to obtain time to a much higher
    precision than mariners did, and had available more precise instruments,
    which could be firmly planted on the ground. So much of the detailed stuff
    is over-elaborate for marine navigators, but may be just the sort of
    material that appeals to Kent Nordstrom. For me, Chauvenet comes over best
    in small doses.
    
    George.
    
    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.
    
    
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