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    Moon observation near zenith
    From: Paul Hirose
    Date: 2019 Oct 22, 12:06 -0700

    On 2019-10-19 4:46, David Iwancio wrote:
    > To see this play out in the NA table, consider what happens when the
    altitude of the center of the moon is 90°.
    Another interesting case has the center and illuminated limb on opposite
    sides of the zenith. For example, time is 2019 October 3 0h UT1.
    Position 18°32.0' S 125°45.0' W (not far from Pitcairn Island). The Sun
    is about 30° high in the west and the Moon nearly at the zenith in the
    east. For an altitude observation my Lunar 4.4 program recommends the
    Moon upper limb, but its predicted limb altitude is peculiar:
    89°56.0' unrefracted center altitude
        16.1' unrefracted semidiameter
        -0.0' refraction
    90°12.2' apparent upper limb altitude
    Oops. That happens because the program adds unrefracted Moon
    semidiameter to unrefracted center altitude. That gives the unrefracted
    altitude of the upper limb, to which it adds refraction. But in this
    freakish case the calculation fails.
    Well, actually the altitude is correct for a backsight. Even the
    refraction is correct, though too small to see at tenth minute
    precision. A fortuitous quirk in my refraction model causes
    supplementary angles to yield identical magnitudes but opposite signs.
    Thus refraction decreases a backsight altitude, as it should.
    The apparent wrong sum in the rightmost column is actually correct. For
    display, each angle is rounded to the nearest tenth minute (or whatever
    precision you select). However, the program calculates with unrounded
    values. In this case, the minutes sum is about 12.16, which rounds up to
    The bogus upper limb recommendation is also easily explained. In
    horizontal coordinates, the position angle from Moon center to Sun
    center is 357.2° (almost exactly toward the zenith). If the angle is in
    the 90° - 0 - 270° semicircle the light is from above and the upper limb
    is appropriate according to the logic of the program.
    There isn't much value in that calculation when the Moon is so close to
    the zenith because the correct limb is very sensitive to the observer's
    position. In fact, even if the shot is theoretically possible, I don't
    know if it's practical. How do you "swing" the Moon when the zenith is
    inside its limb? But it's a moot point. By the time I figured it out,
    the Moon would be past the zenith.
    Nevertheless, let's see if Lunar 4.4 can solve for time. Intentionally
    inject a full hour error in estimated time and several degrees error in
    estimated position.
    2019 Oct 3 0100 UT1 at 15 S 130 W
    90°12.2' Mon UL
    22°30.9' Sun LL
    57°01.6' lunar distance, near to near
    The solution is Oct 02 23:59:56.8, only 3.2 seconds off. Strangely, if
    the Moon altitude observation is converted to the equivalent 89°47.8' LL
    the program fails to converge on a solution.

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