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    Re: Luni-Solar Distance
    From: Paul Hirose
    Date: 2010 Oct 28, 15:17 -0700

    George Huxtable wrote:
    > And I still wonder about the use of Frank's lunar-distance calculator, at-
    > http://www.historicalatlas.com/lunars/lunars_v4.html , to solve the 
    > converse problem from that it was intended for.  I would be grateful for 
    > any step-by-step guidance on how to go about using that calculator to 
    > establish the GMT at the moment of a lunar distance observation, from an 
    > unknown longitude, without observing the altitudes. 
    > 
    > Here is the example I asked about, once again-
    > 
    > "A navigator is somewhere on the Equator, at
    > lat = 0º, and knows it from his previous observations. We know (though he
    > doesn't) that at midnight, 00:00 hrs at the start of 26 March 2005, he is
    > exactly on the Greenwich meridian, at long = 0º, at which moment he takes a
    > precise lunar distance between the Moon's near limb (it's full Moon, so
    > either limb will do) and Regulus, of 36º 48.9'.
    > However, not knowing his exact longitude, he guesses it to be 01º 00' 
    > East."
    
    If longitude is unknown, I think the solution for time is indeterminate.
    
    My lunar program confirms George's distance to Regulus, and says the 
    value is increasing .31' per minute of time. Then I moved the assumed 
    position 1° east. This decreased lunar distance by .93'. In this case, 
    one degree of longitude east has the same effect as 3 minutes of time 
    earlier.
    
    So, if we move 5 degrees east and observe 15 minutes later, the two
    effects should cancel. Let's see. After I make those changes to the
    input data, my program says the lunar distance is 36°48.81'. Close!
    Moving the observation 17 seconds later makes it perfect. That is,
    George's lunar distance is observed from 0°N 0°E at midnight, and also 
    from 0°N 5°E at 00:15:17 UTC. There are an infinite number of such time 
    / longitude pairs. Without some additional constraint, there's no way to 
    know which one is correct.
    
    -- 
    I filter out messages with attachments or HTML.
    
    
    
    

       
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