Thursday, April 7, 2016

Orbital Elements for the Year 1494

  It's not clear when Regiomontanus produced his Ephemerides for 1494-1506 or the location for which it was computed. The ephemeris for 1494 was used to compute a set of orbital elements and presumably the positions of the Sun were calculated for noon which was the practice since Ptolemy's time. The ephemerides of the Sun were based on observations but comparisons of the positions for the months December and January with the fit show some distortion. As with the orbital elements for 1672 the daily changes were used to determine the time and position of the Sun's apogee.

The fit of the Sun's positions for 1494 gave the following elements.

The position of perigee is a few degrees earlier than for 1672 but occurs about the same time of year. The eccentricity, e, is also slightly larger too but still less than the value for the eccentricity in Ptolemy's time.

Regiomontanus died while working on calendar reform in Rome in 1476.

Supplemental (Apr 7): I used Legendre polynomials to fit the daily positions of the Sun and then fit a Keplerian orbit to the daily changes in fit's position for the Sun. The fit of the Legendre polynomials is worse at the beginning and end of the year. The central part of the curve is a good match to the elliptical orbit.

Supplemental (Apr 8): I was checking the length of the year 1494 in Regiomontanus' Ephemerides and noticed that there were only 365 days present where it should have been designated as bisextilis, i.e., a leap year. But February, 1494 in the Ephemerides does not have 29 days.  The year 1500 is properly designated as bisextilis and February, 1500 does have 29 days.

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