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Mean motion is used as an approximation of the actual orbital speed in making an initial calculation of the body's position in its orbit, for instance, from a set of orbital elements. This mean position is refined by Kepler's equation to produce the true position.
which is called the mean angular motion of the body, with dimensions of radians per unit time or degrees per unit time. Define τ as the time at which the body is at the pericenter. From the above definitions, a new quantity, M , the mean anomaly can be defined
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.
The procedure for calculating the heliocentric polar coordinates (r,θ) of a planet as a function of the time t since perihelion, is the following five steps: Compute the mean motion n = (2π rad)/P, where P is the period. Compute the mean anomaly M = nt, where t is the time since perihelion.
The mean anomaly changes linearly with time, scaled by the mean motion, [2] =. where μ is the standard gravitational parameter. Hence if at any instant t 0 the orbital parameters are ( e 0 , a 0 , i 0 , Ω 0 , ω 0 , M 0 ) , then the elements at time t = t 0 + δt is given by ( e 0 , a 0 , i 0 , Ω 0 , ω 0 , M 0 + n δt ) .
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