Friday, April 8, 2016

Orbital Elements for the Year 1495

  I was able to get a good fit for Regiomontanus' positions for the Sun for the year 1495 using Legendre polynomials to "smooth" the data. The difference between the two is consistent with rounding off to the nearest minute.

Again the minimum for daily changes in the positions for the smoothed data were used to determine the position of apogee and an ellipse was then fit to the daily changes in position.

The rms deviation between the fitted ellipse and the smoothed positions of the Sun was about 1.5 minutes so the original positions may not have been solely based on observations. The orbital elements are similar to those for 1494 but with a better value for the length of the year.

I tried to do a set of elements for the year 1500 but the difference between the smoothed and original positions showed relatively large deviations near Feb 28.

Supplemental (Apr 9): The fitted elliptical orbit was chosen so as to minimize the rms deviation for the interval from 20 to 320 days after the beginning of the year to make the fit more precise. The use of an eccentric circle may have may have introduce a systematic error into the Sun's positions which in turn may have affected the eccentricity of the elliptical orbit.

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