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George H, you wrote:
"The Sun's contribution to correcting the lunar, mainly the effect of
refraction, is small, especially when the Sun is high. The Moon's
contribution, mainly its parallax, is much greater. and more dependent on
its altitude. Perhaps, then, a precise value for Sun altitude isn't really
needed, and it can be estimated instead. I haven't quite convinced myself of
the validity of that argument, and offer it up, for what it's worth, for
someone else to knock down."

Happy to oblige. In fact, it turns out that what you've said here is
backwards. The Moon's altitude is generally LESS important than the Sun's
(at the same altitude). The allowable error in the Moon's altitude is
 err_h_moon = (6')*tan(LD)/cos(h_moon)
which permits some remarkably large errors in the Moon's altitude, while the
allowable error in the Sun's or other body's altitude is
 err_h_sun = (6')*sin(LD)/cos(h_sun).
These formulae are somewhat modified by refraction especially for altitudes
below 20 degrees, but the qualitative behavior does not change. These
allowable errors refer to errors in the clearing process of 0.1 minutes or
smaller. If we also use the Sun's altitude for local time, then any error
there would apply directly (and that's an easy one to understand; assuming
the Sun is near the prime vertical, an error of a minute of arc in the Sun's
altitude yields an error of one minute of longitude, just as in modern LOP
navigation).

 -FER



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