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    Re: Time Sight usage
    From: Henry Halboth
    Date: 2013 Jan 14, 20:46 -0500
    To all who responded:

    The solution submitted is nothing more or less than a conventional Time Sight solution, utilizing h = corrected altitude, L = latitude of observer, and p = polar distance, to produce t = meridian angle which converted to LHA is compared to GHA to produce Longitude. The easiest way to assess accuracy is to employ the online USNO caculator, which gives the following.

    Sirius at GMT 18-17-27
    GHA = 326-56.2
    DEC = 16-38.7 S 
    Hc = 49-43.5
    Az = 123.4

    Procyon at 18-31-37
    GHA = 317-03.3
    DEC = 5-21.5  N
    Hc = 46-00.9
    Az = 087.6

    which, if plotted by intercept method would give,

    for Sirius = 0 intercept, and 

    for Procyon = 0.1' away

    Also for Kermit: please note, vessel position relative to LH determined by vertical sextant angle and true bearing. No theodolite aboard and too many mosquitoes ashore at LH posit.

    Thanks again to all who responded and regards.

    Henry    



    On Mon, Jan 14, 2013 at 6:38 PM, Robert Bernecky <bernecky---.net> wrote:

    He used
    hav t = sec L csc p cos S sin S-h
    where t is meridian angle, L is latitude of the observer, h is the observed altitude of the body, p is the polar distance. if L and d are same name, p= 90 -d. otherwise p= 90+d
    S = (h+L+p)/2

    The entries are in the order:
    h
    L (from the previous day) Log sec L
    p (computed a few lines above) Log csc p
    2S (h+L+p) Log cos S (# on next line)
    S 1/2 of above Log sin S-h (# on next line)
    S-h Sum of Logs = Log hav t

    the computation is done using log base 10 of the trigonometric functions. You can recreate these numbers by typing into the search window of google. Using Sirius, for example:
    10+log ((secant( (5+5.8/60) degrees) )=
    10+log(cosecant( (106+38.7/60) degrees))=
    and so on... being careful, because it assumes radians for the arguments..
    to find the inverse log hav of 8.93916 subtract 10 to get -1.06084. make this the exponent of 10
    10^-1.06084=0.0869280625
    the inverse haversine is
    2*asin(sqrt(0.0869280625)) in deg=

    As for the GHA of each star, it looks like he precomputed Aries for 18:17:00 Z added in the SHA, then subtracted 275º and left the remainder as the first number: 51º 49'4 Sirius, and 38º 23'4 Procyon
    notice that for the Procyon sight 14 minutes later (ignoring seconds), he adds 3º 30'6 to 275º to get 278º 30'6. I assume he got that from the increments and decrements table for Aries. This is *just a guess*

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