Equation of the center

Simulated view of an object in an elliptic orbit, as seen from the focus of the orbit. The view rotates with the mean anomaly, so the object appears to oscillate back and forth across this mean position with the equation of the center. The object also appears to become smaller and larger as it moves farther away and nearer because of the eccentricity of the orbit. A marker (red) shows the position of the periapsis.

In two-body, Keplerian orbital mechanics, the equation of the center is the angular difference between the actual position of a body in its elliptical orbit and the position it would occupy if its motion were uniform, in a circular orbit of the same period. It is defined as the difference true anomaly, ν, minus mean anomaly, M, and is typically expressed a function of mean anomaly, M, and orbital eccentricity, e.[1]

  1. ^ Vallado, David A. (2001). Fundamentals of Astrodynamics and Applications (second ed.). Microcosm Press, El Segundo, CA. p. 82. ISBN 1-881883-12-4.