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    Re: Haversine- how to derive it?
    From: Hanno Ix
    Date: 2015 May 17, 09:45 -0700

    John, Ed, Samuel,

    as I outlined the virtues of the haversine to Frank yesterday,

    hav (x) is

    (i) always positive,
    (ii) no matter the sign of the angles x
    (iii) never goes to infinity                   which I forgot to mention.

    Contrast this to sin(x), cos(x), tan(x) etc. and their logarithms!

    However, using the haversine G. Rudzinski and I can show you another,
    very easy calculation of Hc. Only one table, 2 pages, is used and only one
    multiplication is needed. There are no complicated sign rules
    and special cases - it will work for all permutations of  L, d and LHA.

    Given: L, d, LHA, find Hc. Execute these 6 elementary steps:

    1. calculate                 n = hav ( L - d )
    2. calculate                 p = hav (L + d )
    3. calculate                 q = p + n

    4. calculate                 n + ( 1 - q ) * hav ( LHA ); this yields hav ( ZD )
    5. find in table             ZD  by looking up the table backwards

    6. Finally                    Hc = 90 deg  - ZD 

    As can you see the steps are basic arithmetic - executable by hand in minutes.

    We discussed all this on the list under the topic Longhand Sight Reduction.
    For the azimuth we suggest using the azimuth table I published there, too.



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