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Paul,

       Thanks for suggesting this test. The IOTA website does provide examples that can used for checking and I used it for that purpose early on. To be clear my aim here was not to try to generate very high precision ephemerides or occultation predictions. To do that I would have fired up Skyfield and solved for the times when the apparent position of the star was the required distance from the centre of the Moon. The objective was to produce an easy to use, portable application to generate tables of local circumstances and compute longitude on demand using the information that would have been found in the Nautical Almanac in the early 20^th century.  The computations in the spreadsheet are based solely on the time of conjunction in R.A. of the Moon and star (T₀) and 3 linear Besselian Elements (q₀, p', q') also denoted (y, x', y').

A comparison of how far off the disk a star stands at a given time is really useful for comparison as its not computed by the package. The high precision values used as inputs to the

T₀ (TT): 19h 33m 52.731s

Delta T: 69.52s

q₀: -0.602975

p': 0.602172

q': 0.070193

Also

Star RA: 5.64646763 h

Star dec: 21.1511853°

GHA at T₀: 2.24009589 h

These were generated by Skyfield code and if you disagree with any of them I would be very interested in hearing about it.

The site gives 18 14 36 UT for Immersion and 19 19 20 UT for Emersion at S 12 36.5 E 013 24.2. With the methodology described above my spreadsheet gives 18 14 39.6 and 19 19 24.0. If I use my times in the “Find Longitude” tab I get the input longitude back. Using the values from the web site gives longitudes that differs by 4.3 and 1.3 NM respectively.

A few comments are in order: The immersion/emersion times are rounded to seconds on the site. A 0.5s change in the immersion time changes the longitude by 40². The times depend on the value of the ratio of the Earth to Moon radii used and the geodetic reference ellipsoid. Do you know what is being used on the site?

Regards,

Robin Stuart