Sunday, April 2, 2017

Moon's Effect on the Earth's Positions & the Times of the Equinox

  I used MICA to compute the Earth's heliocentric positions for 2017 and then used Excel to fit a Keplerian orbit to the resulting data.

The angle θ is in radians. The resulting orbital elements were,

The epoch is Jan 1, 2017 00:00 UT. If you look at the difference between the two curves you get a small periodic error that fits very well to 12.50 per year which corresponds to the Draconic month.

The deviations account for most but not all of the observed variation in the time of the Spring Equinox.

The speed of the Earth was approximated by dividing the circumference of the Earth's orbit, 2π AU, by the length of the year in minutes. One needs to take the tilt of the Earth's orbit into account to estimate when the Earth will cross the celestial equator.

Edit (Apr 2): Redid the last figure. Here the horizontal line is the Celestial Equator. The sloped line is the Ecliptic along which the Sun travels. The length x is proportional to the distance of a point on the circle from the equator so it is maximum for the right triangle. The numerical results remain unchanged. This calculation would be conclusive if based on the actual angular deviations. As is, the calculation shows how a vertical deviation can affect the time of the equinox.

Supplemental (Apr 2): The times of perihelion and aphelion give a little more information about the Earth's orbit. The values obtained from least squares cubic fits of r are in good agreement with published values.

Edit (Apr 2): Found an error in the linear interpolation for the aphelion. It may have been due to back stepping a fraction of a step.

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