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Re: Unexpected USNO height correction precepts
From: Paul Hirose
Date: 2018 Dec 24, 15:50 -0800
From: Paul Hirose
Date: 2018 Dec 24, 15:50 -0800
Computation of topocentric position angle, Venus to Sun, with respect to
the true equator and equinox of date.
1977-03-18T00:02:16.99 UT1
+47.50s delta T
topocenter:
144.8950° -27.5833° E lon, N lat
4.6 meters above ellipsoid
Venus topocentric apparent place
19.8778° +16.3211° RA, dec (true equator & equinox)
Sun topocentric apparent place
357.5051° -1.0807° RA, dec
The Sun is 22.4° west of Venus. I will solve for position angle with a
slide rule and the Bygrave formulas. Angles rounded to .1°. In the
Bygrave formulas, negative signs are ignored.
W = arc tan(tan 1.1 / cos 22.4)
= 1.2°
X = 90 - 16.4 - 1.2
= 72.4
Z = arc tan(tan 22.4 * cos 1.2 / cos 72.4)
= 53.7
X is less than 90, so replace Z with its supplement: Z = 126.3. Because
the Sun is west of Venus, position angle = 360 - Z = 233.7 with respect
to the true pole of date.
