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    Re: Moon Venus Lunar - Interpretation of results
    From: Paul Hirose
    Date: 2020 Feb 11, 22:11 -0800

    Below I examine the effect of topocentric lunar distance rate on time
    determination accuracy.
    First, generate simulated Moon and Venus "observations" at 2020-01-29
    1200 and 1800 UT1. The times were selected for their quite different
    lunar distance rates at the observer. In reality the observations would
    be impractical since the Sun is above the horizon, but that doesn't
    matter in this experiment.
    I originally computed Venus data for center of light. Then I decided it
    would be difficult for someone to verify my numbers to the last digit
    since center of light isn't widely available in software. So I
    recomputed for upper limb and far limb (the correct limbs in the
    lighting conditions of date).
    69.4 s delta T
    10°N 20°W, at sea level
    10 C, 1010 mb
    2020-01-29 12:00 UT1
    14°22.15' Moon apparent upper limb altitude
    26°23.72' Venus apparent upper limb altitude
    12°26.36' apparent distance, Moon near to Venus far
    +0.356' per minute topocentric lunar distance rate
    +0.419' per minute geocentric
    18:00 UT1
    70°47.90' Moon apparent upper limb altitude
    58°17.74' Venus apparent upper limb altitude
    13°55.18' apparent distance, Moon near to Venus far
    +0.204' per minute topocentric
    +0.426' per minute geocentric
    Add 0.2' (simulated error) to the lunar distances and solve for time
    from the known position. (I call this a "lunar time sight".) It utilizes
    the lunar distance only.
    +31 s error from 1200 time sight
    +61 s error from 1800 time sight
    The lower accuracy at 1800 is what you'd expect with the difference in
    topocentric lunar distance rate (+0.204' per minute vs. +0.356' at
    1200). This reduction in angular rate was called "parallactic
    retardation" by the late George Huxtable. It's due to the rapid change
    of parallax in altitude when the Moon is high in the sky. I think his
    first mention of the phenomenon is in the "serious effects of lunar
    parallax" section in this rather long message:
    (The discussions in that month are remarkable in quantity, quality, and
    civility. It's a little depressing. Times have changed, and not entirely
    for the better. Particularly painful was the loss of George Huxtable.)
    The above computation used the lunar distances only. Next, introduce the
    altitudes and solve for time again. In this solution mode my program
    iterates to find a time and place where all three angles are duplicated.
    Intentional errors in this test are 0.2' lunar distance, 1' altitude, 1
    hour time and 10 degrees latitude and longitude. Four iterations were
    enough to match the observed angles within 0.01'. Results:
    +31 s error at 1200
    +26 s error at 1800
    The 1200 solution is no better than before, but the reduced accuracy of
    the 1800 lunar time sight has been overcome by including altitudes in
    the solution.
    All computation was performed by my Lunar 4.4 program for Windows:

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