Astrophysics (Index)About

mean anomaly

(angle describing an object's position within an elliptical orbit)

The mean anomaly of an object in an elliptical (Keplerian) orbit is a measure (specifically, an angle) describing its position along the path of the orbit. It is measured from the position of the periapsis, the point in the orbit where the object is nearest its host. The angle is determined as follows: it is the angular distance around a circle corresponding to the percentage time of the orbital period. For example, if the orbit takes 100 days and 25 days have passed since the periapsis, the mean anomaly is 90° or π/2 radians. It has the advantage of very straight-forward calculation given the time of the periapsis and the period of the orbit. The angle is taken to grow through the orbit, i.e., start at 0° and grow until it reaches 360°. (It also corresponds to the percentage of area within the shape of the orbit swept out, a consequence of Kepler's laws.)

Two other indicators used for positions within an elliptical orbit are the true anomaly and the eccentric anomaly.

The true anomaly is the angle with the host as vertex, from a line to the periapsis to a line to the orbiting body. It is also taken as always growing and positive, throughout the orbit, resetting to zero as the periapsis is reached again.

The eccentric anomaly seems more complex: given circle centered on the center of the ellipse, with a radius identical to the ellipse's semi-major axis, and an object following that circle such that its distance from the center in the direction of the semi-major axis is identical to that of the orbiting body, then the eccentric anomaly is the angle at the center, between a line to the (imaginary) object on the circle and a line to the periapsis. (In other words, if the ellipse and circle are centered on the origin of a rectangular coordinate system, and the ellipse's semi-major axis is taken as the x-axis, the imaginary object is circling such that its x coordinate always matches that of the orbiting object.) The eccentric anomaly is also taken to grow through the orbital period.

The relation between the eccentric anomaly and the mean anomaly is:

M = E - e sin E

Further reading:

Referenced by pages:
orbital element