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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:

http://fer3.com/arc/m2.aspx/About-Lunars-part-4-Huxtable-mar-2002-w5940

(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:
http://sofajpl.com/lunar4_4/index.html

   

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