A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2019 Feb 21, 10:18 -0800
Fred Hebard, you wrote:
Suppose the Moon is 45
Now suppose I measure the lunar distance between the Moon and some star close to the Moon in the sky. It comes out to be some angle which, after adding in the Moon's SD, gives a center-to-center lunar distance of exactly 10°. I want to correct for (remove) the effects of refraction and Moon parallax on this distance. Since the Moon and the star are at nearly the same altitude (+/-10° at most), the refraction corrections are almost identical. Does that mean we can ignore the other body's altitude entirely? Well, no.... because the other body's altitude "tells the equations" where that other body is located relative to the Moon. If the altitude of the star is 45°, same as the Moon, the two objects are separated horizontally which implies that the parallax correction --always vertical-- has very little impact on the lunar distance. Working it out in detail, the corrected lunar distance might be 10°00.5'. On the other hand, if the altitude of the other body is 55°, implying that the star is directly above the Moon, then to correct for parallax we have to add on the whole parallax correction, about 41.7', yielding a corrected distance of 10°41.7'.
See how this goes? In order to get the parallax correction right, we need the altitudes of the Sun and Moon accurate enough so that the math can determine those "corner cosines" (the factors deciding what fraction of the altitude correction acts along the lunar arc) with sufficient resolution. That's why the altitudes matter, and that's why they can be relatively low accuracy under normal circumstances. For a modern observer, if you want good results, you would typically want to measure the lunar distance itself with a good metal sextant equipped with a fairly high-power telescope (7x or above) capable of measuring angles to the nearest tenth of a minute of arc while the altitudes could be measured with a cheaper plastic sextant giving altitudes only to the nearest several minutes of arc.