Thursday, March 24, 2016

Orbital Elements for the Year 1672

  John Gadbury's Ephemerides of the Celestial Motions for 1672 set a new benchmark for data on the motions of the planets. The positions are given daily for noon London mean time. I was able to "smooth" the data to get positions for the Sun to seconds of arc accuracy. The round off errors indicate that the data as presented is accurate to the nearest minute.

I was able to get the period by interpolating the data to find the length of the year, T, and dividing 360° by it to get the mean motion, n. The daily changes in the positions allowed the estimation of the positions of apogee and perigee for the orbit and an eccentricity of e=0.018 gave a good fit for these changes.

Here's the executive summary. The dates are given in the "Old Style" Julian calendar which was used until about 1750 in England and its American colonies. The dates in the Gregorian calendar added 10 days so the corresponding date for the apogee in the Gregorian calendar would be Jun 28.  Apogee now occurs about Jul 3rd or 4th and perigee on about Jan 2nd or 3rd. The change is quite noticeable over this period of time.

An act of Parliament made the creation of the Nautical Almanac and Astronomical Ephemeris an annual occurrence starting in 1866. Rheticus published an ephemeris for 1551 and Regiomontanus did an ephemeris for 1494-1506. The United States' Almanac, 1843-1845 is credited to Henry Wadsworth Longfellow.

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