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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.
>
>
> "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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