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Paul,

       You are correct. What I labelled as “GHA at T₀” is computed from Skyfield as R.A. – GST and is therefore sloppy labelling on my part but it was never really supposed to be seen by the user. Glad that there is agreement on the nitty gritty digits. Thank you.

        If you could confirm the TT of geocentric conjunction of the Moon and star (T₀) in R.A. then I think we could draw some concrete conclusions.

        When provided with correct input data the only approximation in the spreadsheet is in the use of linear Besselian elements for the Moon. The calculation of local circumstances and the calculation of longitude from the occultation time use separate pieces of code and different numerical algorithms but produce results that are exactly consistent.

         It would seem therefore that the linear approximation is the source of the few second differences being observed. Although including the quadratic terms in the Besselian elements goes beyond what was available in Nautical Almanacs and I originally declared I would not do it, it’s relatively straightforward and might be worth adding them in to put the whole matter to bed,

Regards,

Robin Stuart

 For reference here’s the relevant data that comes to Skyfield. It is as it appears in the original Hipparcos catalog.

magnitude              2.970000

ra_degrees            84.41118447

dec_degrees           21.14259299

parallax_mas           7.820000

ra_mas_per_year        2.390000

dec_mas_per_year     -18.040000

epoch_year          1991.250000

Although we expect the RA and dec to be different presumably the proper motions come from different surveys.

Also I queried the TYCHO catalog for the ICRS J=2000.0 position http://vizier.u-strasbg.fr/viz-bin/VizieR-3 and it seems to be slightly different to what you see.