Ah, let?s write it all down right now anyway

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First some technical remarks. The used equinox was 1950. The obliquity of the ecliptic then was 23,4457889. To convert from the 1950 equinox to that of 1301 the correction for precession to tropical coordinates is required. As the annual rate of precession slightly changes I calculated the average annual rate of precession in 1626. This year is halfway between 1950 and end of 1301. Result is 0?0?50.216? or 1? in 71.69 years. Over the whole period this gives a rate of precession of 9?2?. I converted the Halley positions from equatorial to ecliptic coordinates and applied the issues mentioned above.
1301 Tropical positions ecliptic, longitude and latitude
Halley Sun (source: Astrodienst Ephemeris)
September
1st 24?50?Gemini +3?36? 15?48? Virgo
11th 1?24?Cancer +9?54? 25?36? Virgo
16th 9?52?Cancer +17?54? 0?31? Libra
21st 7?24?Leo +36?35? 5?27? Libra
26th 24?19?Libra +40?48? 10?24? Libra
October
1st 23?48? Scorpio +24?47? 15?22?Libra
11th 4?58? Sagittarius + 13?13? 25?20?Libra
21st 5?52? Sagittarius +8?46? 5?22? Scorpio
31st 4? 2? Sagittarius +5?51? 15?26?Scorpio
Sun?s ingress in Scorpio, 15 October, in Sagittarius, 14 November (also conjunction with Antares).
The following positions of stars and the dates for the equinoxes solstices are from Jean Meeus? book, ?Astronomical Tables of the Sun, Moon and Planets? 2nd edition, Willmann Bell
Stars, Tropical positions 1301 ecliptic (I forgot the latitude but these hardly changed)
Castor/Alpha Gemini 10?32? Cancer
Pollux/Beta Gemini 13?36? Cancer
Southern Asellus/ Delta Cancri 28?59? Cancer
Regulus/Alpha Leonis 20?7? Leo
Spica/Alpha Viginis 14?7? Libra
Zuben El Genubi/Alpha Librae 5?21? Scorpio
Dschubba/Delta Scorpii (the middle of the three before Antares) 22?50?Scorpio
Antares/Alpha Scorpii 0? 2? Sagittarius
1301 equinox/solstice
12 March 21h59m
14 June 3h52m
15 September 11h33m
13 December 20h28m
1302
13 March 3h45m
I didn't calculate the difference in days between the Julian and the Gregorian calendar but it was about 8 ? 9 days.
Note the fast change end September. It makes it difficult to interpolate with certainty. Furthermore I sometimes get different results for the elongations (last column). ?M1? signifies the magnitude or brightness. At closest passage to the earth Halley had magnitude 1 or about the same brightness as Regulus, Spica, Castor and Pollux. Another interesting issue is the high latitude of Halley above the ecliptic. Halley therefore would have been visible several hours after sunset even when in conjunction with the Sun.
I still doubt if the calculations are exactly correct. But they should approximately be within a couple of degrees. (perhaps you would like to compare some results with your computer program Margherita). Moreover the article was written in October 1985. Halley?s perihelion passage took place in april 1986. So new data and new calculating systems could have improved the calculations. Looking a bit through the article one realizes what a tremendous work the scientists did. Actually I remember seeing Halley as a 16year old on perhaps the only clear day of the terrible cloudy and rainy December of 1985. It was just a little dot near the triangle of stars of the ?jug? of the constellation Aquarius. And I had just a little 8x30 pair of binoculars, however I?m glad I saw it, now I don?t have to wait till 2062

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