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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Precomputed lunar distances
From: Frank Reed
Date: 2005 Apr 16, 01:50 EDT
From: Frank Reed
Date: 2005 Apr 16, 01:50 EDT
C Roberts asked: "In postings on this list , altitudes and azimuths were required for accurate calculations of distances between bodies. How can precomputed lunar distances be done as has been done for centuries?? It would seem that almanac GHA and DEC are the only data available. This same calculation would be used for inter stellar distances for checking sextant calibrations. It has been said that the values in Bauer's book are wrong. In the lunar distance calculations this value which is used to proportion for GMT is calculated. Can precomputed values be used to avoid this ?" It's really just the same as the situation in ordinary line of position celestial navigation when we deal with a computed altitude versus an observed altitude. In fact, the best place to begin with lunars or star-to-star distances is to consider a case where the entire measurement amounts to a difference in altitude. Imagine two stars that happen to be right on the celestial equator (Dec=0d00.0') and happen to differ in SHA by exactly 30 degrees. Their separation could be tabulated in advance as 30 degrees if desired. This is a fixed value valid for any observer on Earth though even for stars it would change slowly ove r time. If you take out your sextant and measure the apparent distance between these stars, you won't get that value unless you correct for the effects of refraction (and in the case of the Moon and other nearby objects, parallax, too). If you observe these two stars from a point on the Earth's equator, you will always find them on the prime vertical (due east/due west). Let's imagine a specific case... I am on the equator and I see one of the two stars I've described above around 30 degrees high in the east and the other star at nearly 60 degrees altitude directly above it. I measure the distance between them with my sextant and I measure each star's altitude, too. I look up the measured altitudes in the star refraction table in the almanac, and I find that the lower star has been lifted by refraction by 1.7 minutes of arc, the upper by 0.6 minutes of arc. That means that the apparent distance between them will be shorter than the predicted 30 degrees by 1.1 minutes. So if my measurement was 29d 29.0 (after correcting for index error) this would imply that my measurement was off by only 0.1 minutes of arc --perfect by any practical standard. Now suppose I wait two hours. The stars climb until the higher one is at the zenith. This time the lower star is lifted by 0.6 minutes and the higher star is unaffected by refraction (it can't get any higher!), so the measured distance should be shorter than the predicted 30 by only 0.6 minutes of arc. This is the process of "clearing" a star-star distance or a lunar distance. When the stars (or Moon and other body, for a lunar) are not directly above each other, we have to calculate a geometric factor that tells us what fraction of the altitude correction acts along the arc between the objects, but that's the only additional complexity. The precomputed lunar distances in the old almanacs were compared with measured distances *after* going through this process of clearing for the effects of refraction and parallax. -FER http://www.HistoricalAtlas.com/lunars