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Dave,

Frank is right when he says that in a universe without refraction, the 
third distance does not add any information that isn't already contained 
in the first two. Therefore you cannot leave refraction out of the game.

With 0 refraction you only get a position line that looks like the 
eclipse diagrams in the N.A. It's the exact same problem: There you have 
a slowly moving line in space that connects the centers of the eclipsed 
and eclipsing bodies. In your puzzle you have a slowly moving line 
connecting the moon and that point on the celestial sphere that is 
uniquely defined by its distances from two (!) stars. When you intersect 
that line in space with the rotating earth, you get said position line.

To obtain a unique position you need more information, which I 
understood to be the refraction hidden in the three distorted distances. 
Refraction tells us something about altitude, hence the rotation angle 
of the earth, i.e. time. So it would appear that we may deduce the 
rotation angle of the earth from the given data and find the unique 
solution by intersecting the magic line in space with the surface of the 
earth at a given time. This is how I understood your thought experiment.

In reality, however, the refraction model that we use sets a limit to 
how the measured refractions can be exploited. The function for 
refraction cannot be inverted to the degree of accuracy that is required 
here. Certainly the simple formula in the N.A. is not designed to do 
this job. That's why I responded by saying that your problem cannot be 
solved. My comment has been misconstrued as a reference to a practical 
limitation and incorrectly quoted as "the method is sensitive to 
refraction", as if refraction were detrimental to finding the exact 
solution. That's not what I said. On the contrary, refraction is 
essential to the solution of your puzzle. It depends on it, and that's 
why it's not feasible.

It is only now that I am really puzzled because not only do you not seem 
to think that you need refraction, you even found a solution in a 0 
refraction model. Would you please show the details?

Herbert

P.S.

When trying to verify your topocentric distances with MICA, I get 
discrepancies of up to 1.5" between yours and mine. It could be the 
underlying ephemeris, could be delta T. Normally, I would not care, but 
in this case it seems important. What is your geoc. and topoc. moon 
position at  +3h 27m 0.4s?




On 2011-08-16 01:31, Dave Walden wrote:
>
> The Lunar distances for a "no refraction" case:
>
>
> +28� 0' 58.3"
> +37� 5' 33.8"
> +61� 36' 0.8"
>
> My solution
>
> +3h 27m 0.4s
>
> +38� 55' 39.2"N
> +77� 12' 45.3"W
>
> Still a pretty good solution. It's the parallax, not the refraction.
>
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