Wednesday, August 9, 2017

Found an Odd Error for a Fit of the Sun's Position

  I was preparing for the solar eclipse later this month, doing a fit of the Sun's relative position from the center of the Earth, and the fit didn't turn out as I expected. A linear least squares fit of the Sun's position for the functions indicated resulted in the following relative differences between the fit and the calculated positions.

The sinusoidal function is mainly due to the Moon's pull on the Earth but there appears to be another component present. How can one explain the displacement of mean error from zero? It turns out there are some Chebyshev polynomials present.

This polynomial series generates a displacement of the following form given in AU.

After subtracting this and the displacement due to the pull of the Moon the following error remains.

The error can be measured in micro AU (μAU). For comparison the Earth moves about the Sun at a mean rate of 2π/365.24=0.0172AU/day=12μAU/min. It probably wouldn't hurt to get accurate measurements of the start and end eclipse times.

Essentially the same error or perhaps correction is present in both MICA and HORIZONS data for the Sun's position relative to the Earth.

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