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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.

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