NavList:

Peter Hakel, you wrote:
"About an hour ago I conducted a quick exercise presetting a sextant to the Sun-Moon near-limb distance (no refraction corrections)"

Is there any reason you were doing this? Just for "fun" is a perfectly reasonable answer, but do you find you have a need to preset the sextant for lunars in such detail? And if you're including such detail in the first place, why not add in the refraction? Another perfectly reasonable answer is to remind us of your spreadsheet tools... 

Usually, when I want to set up for a lunar, I get a quick estimate of the true geocentric lunar distance from an app. Historically a lunar navigator would do this by looking at the three-hour tables in the almanac and then estimating roughly based on the current GMT (which was always known within +/-15 minutes). Then just preset to that value and look through the scope. This doesn't correct for the apparent position, which is affected by moderate refraction and the substantial parallax of the Moon, and it also doesn't correct for semi-diameters. But it will certainly get both bodies in the field of view, even in a high-power scope. The remaining step, of course, is to look at the Moon through the horizon view of the sextant. Rotate the Moon's image until its "horns" are horizontal in the field of view. At that point the Sun should pop right into the field of view. And that's it.

One can even go further without detailed calculation. Suppose you decide you want to deal with the SD's and get the Moon's parallax correction in there, too. There's no reason for this -- it's just for the entertainment value of seeing the Moon and Sun align limb-to-limb on the first try. You can get an excellent approximation just by looking at the Moon in the sky. If the horns are horizontal (not in the sextant view, but horizontal in the normal sense -- relative the observer's horizon and zenith) then the altitude corrrection HP·cos(alt) gets added directly to the true geocentric lunar distance. If the horns are vertical, then there's no impact at all on the lunar distance. In between, the effect is HP·cos(alt)·cos(alpha) where alpha is the corner angle in the Moon-Zenith-Sun triangle and can be estimated by direct observation. You can estimate this net correction within +/-0.1° or so. Adding the SD's is no problem. They both get subtracted directly from the predicted center-to-center distance to give the near limb-to-limb angle

An example:
   I estimate GMT is about 12:30. Almanac gives predicted geocentric LD as 88.40° at 12:00 and 89.80° at 15:00. So at 12:30 I estimate by simple proportions that the LD should be about 88.65°. That's a good start and really all we need for practical purposes, but let's dabble in impracticality and go a bit further... The almanac also tells me that the Moon's HP is 59.0' and the sum of the Sun and Moon SDs is 32'. I go out "on deck" (or in my backyard, more likely) and look at the Moon in the sky. It's about 35° high and tilted over so that the line between the horns makes an angle of about 45° to the vertical (so alpha, see above, is also 45°). Based on experience and some estimation tricks, I know that cos(35°) is about 0.8 and cos(45°) is about 0.71. The Moon's parallax correction is thus roughly 59·0.8·0.71 which is about 33.5'. I add that and then subtract the sum of the SDs (note that this is sign-reversed from "clearing" a lunar distance since we're working in the opposite direction: trying to estimate the apparent limb-to-limb angle). That totals up to adding 1.5'. Subtract another minute or two for refraction, and we're down to zero. It's basically a wash. And this is a typical case. It's frequently the case when the Moon is tilted "up" like this (quite common with practical lunars) that the SD's and the actual clearing correction net to about zero.

Frank Reed

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