In celestial mechanics, the mean anomaly is the fraction of an elliptical orbit's period that has elapsed since the orbiting body passed periapsis, expressed as an angle which can be used in calculating the position of that body 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. Definition Define as the time required for a particular body to complete one orbit. In time , the radius vector sweeps out 2 radians, or 360°. The average rate of sweep, , is then which is called the mean angular motion of the body, with dimensions of radians per unit time or degrees per unit time. Define as the time at which the body is at the pericenter. From the above definitions, a new quantity, , the mean anomaly can be defined which gives an angular distance from the pericenter at arbitrary time . with dimensions of radians or degrees. Because the rate of increase, , is a constant average, the mean anomaly increases uniformly (linearly) from 0 to 2 radians or 0° to 360° during each orbit. It is equal to 0 when the body is at the pericenter, radians (180°) at the apocenter, and 2 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) where represents the small time difference. Mean anomaly does not measure an angle between any physical objects (except at pericenter or apocenter, or for a circular orbit). 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. Formulae The mean anomaly can be computed from the eccentric anomaly and the eccentricity with Kepler's Equation: Mean anomaly is also frequently seen as where is the mean anomaly at epoch and is the epoch, a reference time to which the orbital elements are referred, which may or may not coincide with , the time of pericenter passage. The classical method of finding the position