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    Lunar distance parallactic retardation
    From: Paul Hirose
    Date: 2020 Feb 14, 13:24 -0800

    For a second test of "parallactic retardation" in a lunar distance time
    determination, I present two simulated Sun - Moon observations on
    2020-01-30. First, the constant conditions for both observations:
    2020 Jan 30 UT date
    +1m09.4s delta T
    10°N 20°W position, at sea level
    10.0 C (50.0 F) air temperature
    1010.0 mb (29.83″ Hg) air pressure
    50.0% relative humidity
    Now the observations. Caution - the Moon altitude limb is not the same
    in both observations.
    2020-01-30 13:00 UT1
      19°38.03' unrefracted center altitude
         14.82' unrefracted semidiameter
          2.64' refraction
      19°55.49' apparent upper limb altitude
      93°37.66' azimuth
      61°05.80' unrefracted center altitude
        -16.24' unrefracted semidiameter
          0.54' refraction
      60°50.10' apparent lower limb altitude
    163°28.00' predicted azimuth
    topocentric apparent Moon to Sun angle
      63°11.32' center to center, unrefracted
          2.23' refraction
      63°09.09' center to center, refracted
        -14.79' Moon near limb refracted SD
        -16.23' Sun near limb refracted SD
      62°38.06' Moon near to Sun near limb
    +0.377' per minute (topocentric)
    +0.449' per minute (geocentric)
    2020-01-30 18:00 UT1
      80°12.69' unrefracted center altitude
        -14.98' unrefracted semidiameter
          0.17' refraction
      79°57.88' apparent lower limb altitude
    202°53.37' predicted azimuth
      18°34.79' unrefracted center altitude
        -16.24' unrefracted semidiameter
          2.88' refraction
      18°21.44' apparent lower limb altitude
    247°24.27' predicted azimuth
    topocentric apparent Moon to Sun angle
      64°36.13' center to center, unrefracted
          2.70' refraction
      64°33.43' center to center, refracted
        -14.98' Moon near limb refracted SD
        -16.20' Sun near limb refracted SD
      64°02.26' computed Moon near to Sun near limb
    +0.235' per minute time (topocentric)
    +0.449' per minute (geocentric)
    Solve for time with observed lunar distance from the known position. (I
    call this a "lunar time sight," a not fully satisfactory term since it
    could be confused with a conventional time sight with the Moon. But I
    don't know what else to call it.) Lunar distances are increased 0.5' to
    simulate observational error. Solutions:
    13:01:13 at 1300
    18:02:29 at 1800
    Solve for time with the lunar distances and altitudes. To simulate
    observational error, lunar distances are increased 0.5' and altitudes
    2'. Results:
    13:01:06 at 1300
    18:01:01 at 1800
    As in my previous lunar distance experiment with Venus, the Moon is at
    low altitude in one "observation" and high altitude in the other. At
    high altitude the lunar distance rate is much reduced (+0.235' per
    minute vs. +0.377') due to the rapid variation of horizontal parallax
    when the Moon is near the zenith. ("parallactic retardation")
    Thus, it's no surprise that the lunar time sight is most sensitive to
    observational error at high altitude. But that does not seem to be true
    for the traditional lunar where altitudes are observed too.
    I should make clear that my reduction does not follow the traditional
    scheme which reduces the observed distance to the equivalent geocentric
    angle. Instead, my program works entirely with the three angles observed
    at the topocenter (observer's position). With an iterative algorithm it
    seeks the time and place where all three angles should have occurred,
    and thereby includes (to the extent they can be computed) the effects of
    parallax, refraction, and even the oblateness of the Earth.
    In this case, with the initial time estimate in error by one hour and
    position in error by 10 degrees of latitude and longitude, the program
    needed four iterations to match all angles within 0.01'.
    Are the classic methods of the lunars era likewise able to overcome
    parallactic retardation? I don't know. In fact, I'm not sure the
    phenomenon is — IN GENERAL — harmless to the accuracy of the 3-angle lunar.

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