### 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

- e - eccentricity.
- E -
*eccentric anomaly* in radians.
- M -
*mean anomaly* in radians.

(*orbits,astronomy,kinematics,measure*)
**Further reading:**

http://en.wikipedia.org/wiki/Mean_anomaly

http://en.wikipedia.org/wiki/True_anomaly

http://en.wikipedia.org/wiki/Eccentric_anomaly

**Referenced by pages:**

orbital element

Index