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    Re: UTM to lat/lon formulas
    From: George Huxtable
    Date: 2003 Dec 14, 21:56 +0000

    In the light of the corrections that appear to have been made to my copy of
    the Seidelmann "Explanatory supplement to the Ephemiris", I asked Herbert
    Prinz if I could confidently proceed to convert between lat/long and URL,
    using those corrected instructions.
    
    He answered-
    >Yes, but only if you get rid of R(phi1) in equation 4.233-8, as I suggested.
    >Otherwise you need the formula for R(phi) for finding the meridianal
    >curvature in
    >the footpoint.
    
    But as I said,
    
    >> R appears without explanation, in eq 4.233-14, as R1 in the special case
    >> for angle phi1 as-
    >>
    >> R1 = a *  (1-Sqr(e)) / (1- Sqr(e) * Sqr(sin(phi1))) ^ (3/2),
    
    and surely, that's the curvature that's required for R1 in  4.233-8.
    
    So why couldn't I just calculate a value for R1 from that equaton, once
    phi1 has been calculated, and plug it into equation 4.233-8?
    
    In fact, I've done what Herbert suggested, and eliminated R1 from eq. 4.233-8.
    
    ====================
    
    He added-
    
    >As long as we are at it, would you please check the following items  in
    >your copy?
    >
    >On p. 400, equation 7.3-4. The correct formula is
    >
    >     sin(HP) = R_Earth  /  r_Moon
    >
    >But in my copy the second member got turned around, yielding the
    >reciprocal value.
    
    In my later copy the equation is just as you have written it above, so the
    correction has been made. In addition (which you didn't mention) the r_Moon
    term has been enclosed between two vertical bars, as in a modulus sign, for
    some reason.
    >
    >On p.401, in equation 7.3-10, the semidiamer of the Moon is given as
    >
    >     SD = arctan(R_Earth  /  r_Moon)
    
    >
    >but I believe this should be the arcsin, shouldn't it?
    
    I agree it should, but the difference is quite infinitesimal for such an
    angle, the ratio
    
    sin 0.25deg / tan 0.25 deg
    
    differing from 1 by only one part in a million. It hasn't been amended in
    Seidelmann.
    >
    >I also cannot resist drawing your attention to the index as well as to p.
    >485, where
    >one finds the term "analemmic curve". I consider this the most intriguing
    >coinage in
    >American technical literature of the 20th century. But this is another
    >story (and
    >one of my pet peeves).
    
    On that topic, you can find such a curve, taken by time-lapse photography
    of the Sun over a year, on the front cover of Jean Meeus' "Astronomical
    Tables of the Sun, Moon and planets", 2nd ed.
    
    George.
    
    ================================================================
    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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