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    Re: Lunar Distance Puzzle
    From: UNK
    Date: 2011 Aug 21, 16:59 +0000

    On 2011-08-21 15:25, George B wrote:
    > The primary contribution to the distance correction is lunar parallax,
    > and as Dave showed in a refraction-free world the problem is still
    > solvable.
    Where has Dave shown that? It actually cannot be shown.
    > Finally as to Frank's comment that the third lunar distance in the
    > problem can't contribute additional information it can only confirm
    > the previous two... With one lunar distance and one equation you have
    > to input values for two of the variables, namely the two altitudes (or
    > lat and long), in order to get GMT. With two distance measurements you
    > can input GMT and solve the two equations for lat and long, i.e. find
    > out where the LOPs intersect.
    > It is important to note that with two distance measurements if you
    > input a different GMT the LOP intersection will shift to a different
    > lat and long. So the role of the third lunar distance measurement will
    > basically be to pin down GMT to the correct value. Of course all three
    > equations contribute to finding all three unknown variables, it's not
    > like we can say one of them determines GMT etc. Adding a fourth
    > measurement would not provide any new information, but would
    > over-constrain the problem and allow one to calculate a goodness of
    > fit chisq.
    Amy, Bob and Jim have together 15 candies. Amy and Bob together have 9.
    Can you tell me how many candies each child has? Oops, you need a third
    equation. Jim has 6. Can you tell me now?

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