of an object in an elliptical orbit from a set of orbital elements is to calculate the mean anomaly by this equation, and then to solve Kepler's equation for the eccentric anomaly. Define as the longitude of the pericenter, the angular distance of the pericenter from a reference direction. Define as the mean longitude, the angular distance of the body from the same reference direction, assuming it moves with uniform angular motion as with the mean anomaly. Thus mean anomaly is also Mean angular motion can also be expressed, where is a gravitational parameter which varies with the masses of the objects, and is the semi-major axis of the orbit. Mean anomaly can then be expanded, and here mean anomaly represents uniform angular motion on a circle of radius . Mean anomaly can be calculated from the eccentricity and the true anomaly by finding the eccentric anomaly and then using Kepler's equation. This gives, in radians: where atan2(y, x) is the angle from the x-axis of the ray from (0, 0) to (x, y), having the same sign as y. (Note that the arguments are often reversed in spreadsheets, for example Excel.) For parabolic and hyperbolic trajectories the mean anomaly is not defined, because they don't have a period. But in those cases, as with elliptical orbits, the area swept out by a chord between the attractor and the object following the trajectory increases linearly with time. For the hyperbolic case, there is a formula similar to the above giving the elapsed time as a function of the angle (the true anomaly in the elliptic case), as explained in the article Kepler orbit. For the parabolic case there is a different formula, the limiting case for either the elliptic or the hyperbolic case as the distance between the foci goes to infinity – see Parabolic trajectory#Baker's equation. Mean anomaly can also be expressed as a series expansion: with A similar formula gives the true anomaly directly in terms of the mean anomaly: A general formulation of the above equation can be written as the equation of the center: See also Kepler's laws of planetary motion Mean longitude Mean motion Orbital elements References External links Glossary entry anomaly, mean at the US Naval Observatory's Astronomical Almanac Online Orbits