Moon's Equation of The Center
In the case of the moon, its orbit around the earth has an eccentricity of approximately 0.0549. The term in, known as the principal term of the equation of the center, has a coefficient of 22639.55", approximately 0.1098 radians, or 6.289° (degrees).
The earliest known estimates of a parameter corresponding to the Moon's equation of the center are Hipparchus' estimates, based on a theory in which the Moon's orbit followed an epicycle or eccenter carried around a circular deferent. (The parameter in the Hipparchan theory corresponding to the equation of the center was the radius of the epicycle as a proportion of the radius of the main orbital circle.) Hipparchus' estimates, based on his data as corrected by Ptolemy yield a figure close to 5° (degrees).
Most of the discrepancy between the Hipparchan estimates and the modern value of the equation of the center arises because Hipparchus' data were taken from positions of the Moon at times of eclipses. He did not recognize the perturbation now called the evection. At new and full moons the evection opposes the equation of the center, to the extent of the coefficient of the evection, 4586.45". The Hipparchus parameter for the relative size of the Moon's epicycle corresponds quite closely to the difference between the two modern coefficients, of the equation of the center, and of the evection (difference 18053.1", about 5.01°).
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