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    Re: Latitude by transits of a circumpolar star both above and below the pole
    From: George Huxtable
    Date: 2007 Oct 2, 09:40 +0100

    Andres Ruiz wrote-
    
    In the book: "An Introduction to Practical Astronomy", (Elias Loomis, NY, 
    1860)
    Chapter VI contains an old method of determining the latitude of a place by 
    observations of a circumpolar star at the time of its upper and lower 
    culminations
    
    ===That sounds very like chapter 6 in "Spherical and Practical Astronomy", 
    by William Chauvenet. Would it perhaps be an early version of that work?===
    
    * It is independent of the declination of the observed star
    * It is as free as possible from the errors of refraction
    If both altitudes being measured from the north horizon:
    Latitude: B = 1/2*(H_up + H_low)
    Where H is the altitude measured by the sextant, corrected for index error, 
    dip and refraction.
    
    ===It's true that it was independent of the declination, so it was useful to 
    astronomers who wanted to precisely find their latitudes in the days when 
    declinations in star catalogues were not necessarily to be relied on. Today, 
    when star declinations are known far more precisely than any of us will ever 
    need, it's of historical interest only. I don't see how it can be in any way 
    free from refraction errors. There's a different method that did minimise 
    refraction errors, by comparing meridian altitudes of two chosen stars that 
    happened to cross the meridian at similar altitudes, one North of the 
    zenith, the other South.===
    
    This past weekend I try to use the method, and I have not been able to find 
    a star that had the two transits at the same night.
    Simulating some data, the problem from my latitude at this moment is the 
    difference between the times of the two phenomena: one by day and another at 
    night.
    
    UT H
    h m Culmination � �
    29-sep-2007 Polaris 2 20 Upper N 44 1.2
    29-sep-2007 Polaris 14 18 Lower 42 36.8
    29-sep-2007 Merak 10 39.1 Upper N 76 59
    29-sep-2007 Merak 22 37.1 Lower 9 39.8
    29-sep-2007 Alkaid 13 24.4 Upper N 84 2.9
    29-sep-2007 Alkaid 1 26.1 Lower 2 35.9
    
    Has anybody used this simple method in order to obtain the latitude, at land 
    or at sea?
    
    === Andres will not find a suitable star, except in Winter. Upper and lower 
    transits occur (nearly) 12 hours apart, so until the nights get at least 12 
    hours long, between twilights, there will be no suitable star. It wasn't a 
    problem to astronomers, with big transit telescopes, who could see stars 
    even in daylight, but Andres will have to wait a few weeks longer.
    
    George.
    
    contact George Huxtable at george---.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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