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    Re: Moon Parallax, Math Trivia (was Re: venus)
    From: Frank Reed CT
    Date: 2004 Oct 20, 18:35 EDT
    Herbert P wrote:
    "I believe you are mistaken. There is no resemblance to Kepler's
    equation. The characteristic feature of the latter is that the variable
    E (eccentric anomaly) appears as a term E as well as a term sin E,
    making it impossible to express E as explicit function of the mean
    anomaly. "

    Here's the direct equation for the calculation of the true altitude from the observed altitude and the horizontal parallax:
      TA = OA - HP cos TA .
    OK? You agree, I hope, that this bears a very STRONG resemblance to Kepler's equation. Now invert it. Solve for TA. Can't be done in "closed form", right? See what I mean now?? If you solve this iteratively for TA to, say, one part in a million and then compare with the Arctan solution, you will get slightly different results. They are not inverses. They solve slightly different mathematical problems. That's the "trivia" I was getting at.

    Frank R
    [ ] Mystic, Connecticut
    [X] Chicago, Illinois
       
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