Friday, March 25, 2011

The Uniform Circular Motion Approximation for the Declination of the Sun

The Gregorian Calendar was designed to keep the date of the Equinoxes fixed and this can be used to approximate the equinox year. With leap days there are 146097 days in every 400 years which is equivalent to an average of 365.2425 days per year. In 2009 we found a formula for converting month and day to day of year which can be used to simplify the formula for the uniform circular motion approximation of the declination of the Sun. The Spring Equinox occurs on March 20/21 which is doy 79/80. The uniform circular motion approximation is a simple sine function. (The floor function reduces a decimal number to just its integer part.)

A comparison of this approximation with that of a Keplerian orbit is shown below.

The deviation on the right side is due to a nonuniformity in the motion of the Sun along the Ecliptic. The Earth moves faster in its orbit about the Sun near perihelion on about Jan 3 than near aphelion on about Jul 4 (doy 185).

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