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    Re: Lunars by series, quadratic correction
    From: Frank Reed
    Date: 2019 May 7, 11:39 -0700

    I wrote earlier:
    "In some versions of Easy Lunars, I replaced the "divide by 2" in Q0 with a factor of 0.55 because empirically that seemed to give better results. That was always a bit fishy, and just a few weeks ago I discovered a better approach which is mathematically justified: replace the Moon correction by the difference between the Moon correction and the Sun/star correction. And since these have opposite signs, this is equivalent to the sum of the absolute values of the two altitude corrections."

    And incidentally, this new-and-improved analysis also explains why my former empirical trick worked as well as it did. Changing the factor of 0.5 to 0.55 was equivalent to adding 5% to the Moon's altitude correction (squared yields 10%). That's the same thing as using the new-and-improved methodology and assuming that the Sun/star altitude correction is about 5% of the Moon's altitude correction, which is a "not too bad" approximation when both bodies are low in the sky. So you can do one of two things:

    • Replace the 0.5 with 0.55 in the quadratic correction for a "rough" approximation,
    • Replace the Moon's altitude correcction with the sum of the absolute values of both altitude corrections for a "good" approximation.

    Either will work. But don't combine them!

    Frank Reed

       
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