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    Re: Errors in Cotter's "History of Nautical Astronomy, once more; GMT from Moon's altitude
    From: Jan Kalivoda
    Date: 2003 Apr 5, 16:56 +0200

    I have seen two articles about finding GMT from Moon's altitudes (not using 
    the term "line of position") in German nautical periodicals from the 
    beginning of the 20th century. The "lunarians" then felt that the surge went 
    against and strove to simplify the use of the Moon for longitude measurements 
    somehow so as not to be overwhelmed (vainly). This method was never seriously 
    used at sea, as I know, only the authors of these articles tried it 
    successfully.
    
    
    The principle was as follows:
    
    - Take the altitude of a star and of the Moon
    
    - Compute star's local hour angle (from its altitude and declination and the 
    geographical latitude of observer)
    
    - Compute Moon's local hour angle (dtto; Moon' declination could be taken for 
    the approximate GMT without a fatal error or the calculation could be 
    repeated after the first value of GMT had been obtained)
    
    - Find the local sidereal time from star's local hour angle and its rectascension
    
    - Find Moon's rectascension from its local hour angle and local sidereal time
    
    - Find GMT from Moon's rectascension (interpolating backwards in the Almanac)
    
    
    Very pretty in theory, isn't it? Of course, the incertainty of refraction and 
    dip enter heavily into the result, although they can neutralize each other in 
    very favourable conditions (star's hour angle, computed from its altitude,  
    is subtracted during the procedure, Moon's HA added!) . To decrease the 
    errors (I don't quote the precise error equation, which was known), it was 
    necessary:
    
    
    - be in a lower latitude, otherwise this factor could completely destroy the result
    
    - both bodies used should stay near the prime vertical (the hour angle can 
    then be computed most reliably); this tends to the next condition:
    
    - both bodies should stay in a near azimuth, so that their irregularities of 
    refraction and dip are the same
    
    - both bodies should stay in a near altitude, for the same reason
    
    
    It was a bit difficult to find such sky position, one would guess. Hence an 
    author proposed to use two stars in the same azimuth with the Moon near the 
    prime vertical, one above her, another below, and to take the average of two 
    GMT's found. Eh, ...
    
    Another author frankly says that this prodedure is useful only when a sailor 
    is in a desperate situation with the damaged chronometer in hands and without 
    any experience of lunar distances.
    
    After several years, radio time signals changed the field totally.
    
    
    Jan Kalivoda
    
    
    

       
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