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Re: An exotic lunar distance puzzle
From: Frank Reed
Date: 2011 May 8, 00:06 -0700

So I did a more detailed analysis this evening. Here are my results:

Lat=39d 49'N +/-4'
UT=02:15:00 +/-1 minute
lon=88d 10'W +/-16'

Exotic as this is in terms of circumstances, in many respects it's just like a 19th century lunar. The altitudes of a few stars determine latitude and local apparent time while the position of the Moon determines GMT. GMT combined with local time yield longitude. The uncertainty in longitude is due almost entirely to the uncertainty in UT. A one minute error in GMT is, of course, equivalent to a 15' error in longitude.

Here are the star altitudes I used as measured from the photo, assuming the sharp horizon line is 18.24 degrees below the coordinate (true) horizon:
iota Ceti: -16d 23'
lambda Piscium: -16d 31.5'
theta Piscium: -15d 54'
58 Pegasi: -16d 31.8'
One nice thing about using iota Ceti is that it's almost due West and since it's altitude is small, its position is insensitive to latitude changes. That way I could set the longitude using just that star's altitude and then adjust the latitude to get the other stars' altitudes right. This is very similar to the historical case where a navigator would prefer a star near the prime vertical when getting local apparent time since it then didn't suffer from any significant error if the dead reckoning latitude was wrong.

The lunar distance I used was 46.3' from 19 Piscium to the Moon's center. A trick I used to get the Moon's position as accurately as possible in the image was to draw circles on the Moon until I found one that matched up as symmetrically as possible with the Moon's limb all the way around (especially on the dark side). Then I didn't have to worry about deciding exactly where the true limb of the Moon was in the slightly blurry image.

One more trick: the scale of the image in pixels per minute of arc varies across the frame (due to camera lens distortion and the simple geometry of projection). But since we have quite a few star pairs scattered across the image, it's possible to build up a table of scales for different parts of the image relatively easily. I found that the scale varied from about 2.34 pixels per minute of arc near the Moon to over 2.49 towards the extreme left and right sides.

More details upon request, but it's possible we've beaten this to death by now. :)

-FER

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