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Re: Lunarian Puzzle
From: Jim Wyse
Date: 2024 Apr 3, 08:00 -0700

Lars,

As you've realized, a rote application of the 'standard' interpolation procedure produces two estimates of LD, both of which are incorrect!! Any LD determined using interpolation needs to be validated using something else, such as the altitude of (at least) one of the two objects involved. Azimuth values are another possibility. I was trying to 'recover' the longitude for Eclipse Island that James Cook's 1766 measurements yielded and found that the (accepted?) interpolation-based method just wasn't cutting it (after checking my calculations 'seven ways from Sunday'). It was only after I narrowed up the UT intervals that I began to realize that something further was needed. Here's what I did and it seems that you proceeded in a similar fashion:

UT LD by LoC App.Sun Alt Az

17:50:00 0° 26.3' 42° 48.2' 221.7°

18:00:00 0° 23.2' 41° 39.2' 224.6°

18:10:00 0° 21.3' 40° 26.6' 227.5°

18:20:00 0° 20.9' 39° 10.5' 230.3°

18:30:00 0° 22.1' 37° 51.5' 232.9°

18:40:00 0° 24.8' 36° 29.6' 235.5°

18:50:00 0° 28.3' 35° 05.1' 238.0°

19:00:00 0° 32.6' 33° 38.4' 240.5°

An examination of the above 'localized' lunar almanac shows that Stellarium's apparent altitude for the Sun and its azimuth fall in the UT interval 18:30:00 to 18:40:00. My interpolation in this interval yielded a longitude of 57° 33.8'W which effectively 'recovers' Cook's longitudes (57° 33.4' W at the beginning of the 1766 eclipse and 57° 36.8' W at the end. Your longitude estimate of 18^h35^m4^s(or 57.7°W) is as good as it gets. Congratulations!

It was a little disingenuous of me to post this as a 'puzzle' since I was somewhat unsure of the approach I had taken and wanted some sort of validation. Now that 'Lars Bergman' has responded, my validation concerns have completely dissipated.

Thank you Lars, your solution of the 'puzzle' is much appreciated.

Cheers,

Jim

[NOTE from FER: minor typos fixed]

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