# Mean anomaly - function of gravitational parameter

## Description

In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. It is the angular distance from the pericenter which a fictitious body would have if it moved in a circular orbit, with constant speed, in the same orbital period as the actual body in its elliptical orbit.

which gives an angular distance from the pericenter at arbitrary time t, with dimensions of radians or degrees.

Because the rate of increase, n, is a constant average, the mean anomaly increases uniformly (linearly) from 0 to 2π radians or 0° to 360° during each orbit. It is equal to 0 when the body is at the pericenter, π radians (180°) at the apocenter, and 2π radians (360°) after one complete revolution.If the mean anomaly is known at any given instant, it can be calculated at any later (or prior) instant by simply adding (or subtracting) n δt where δt represents the time difference.

Mean anomaly does not measure an angle between any physical objects. It is simply a convenient uniform measure of how far around its orbit a body has progressed since pericenter. The mean anomaly is one of three angular parameters (known historically as “anomalies”) that define a position along an orbit, the other two being the eccentric anomaly and the true anomaly. Here mean anomaly represents uniform angular motion on a circle of radius a.

Related formulas## Variables

M | Mean anomaly (rad) |

μ | gravitational parameter (m^{3}/s^{2}) |

a | semi-major axis (m) |

t | Arbitrary time (s) |

τ | Time at which the body is at the pericenter (s) |