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George wrote:
"It's certainly the case, as Frank has frequently pointed out, that when the 
lunar distance is near 90�, it's very insensitive to the details of the 
correction."

To elaborate on this, there are several things at work: 
First, there's the simple practical point which I mentioned a few days ago. 
Navigators seem to have preferred shooting Sun-Moon lunars, and that's most 
convenient from an observational perspective when the Moon is close to 90 
degrees elongation. 

Second, there are shortcuts in some clearing methods that can be applied when 
the distance is close to 90. When using one of the series methods, the 
quadratic correction is proportional to cot(LD) so it can be ignored near 90 
degrees (except in some methods, like Bowditch's principal method, where the 
quadratic correction is rendered always positive by adding a constant at an 
earlier step). This is not a significant savings in work since the quadratic 
correction was usually just a simple table lookup.

Third, as I discovered a few years ago and have mentioned many times since, 
the clearing of lunar distances has a remarkable, and as I have said 
"seemingly miraculous", freedom from errors in the Moon's altitude when the 
distance is close to 90 degrees. If the observed lunar distance is between 85 
and 95 degrees (and the objects aren't too low in the sky), the observed 
altitude of the Moon can be wrong by a degree or more and it won't make any 
difference. This makes the whole observation and calculation much more 
convenient since it means a quick observed altitude for the Moon is 
sufficient.

Fourth, and almost certainly not relevant historically, it's possible to clear 
lunars when the distance is close to 90 degrees (and over a rather broad 
range around that) without solving any spherical triangles at all. Any 
observation can be reduced to the geometrically "degenerate" case of 
vertically aligned bodies when the measured lunar distance is around 90 
degrees. That makes clearing lunars in many common practical cases a 
relatively trivial project. Too bad they didn't know this two hundred years 
ago!

-FER




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