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Mean Anomaly

In celestial mechanics, the mean anomaly is a parameter relating position and time for a body moving in a Kepler orbit. It is based on the fact that equal areas are swept at the focus in equal intervals of time.

The mean anomaly increases uniformly from 0 to radians during each orbit. However, it is not an angle. Due to Kepler's second law, the mean anomaly is proportional to the area swept by the focus-to-body line since the last periapsis.

The mean anomaly is usually denoted by the letter , and is given by the formula:

where n is the mean motion, a is the length of the orbit's semi-major axis, and m are the orbiting masses, and G is the gravitational constant.

The mean anomaly is the time since the last periapsis multiplied by the mean motion, and the mean motion is divided by the duration of a full orbit.

The mean anomaly is one of three angular parameters ("anomalies") that define a position along an orbit; the other two being the eccentric anomaly and the true anomaly. 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 time difference. The other anomalies can hence be calculated.

From Wikipedia under the GNU Free Documentation License
Thu Mar 15 18:41:37 2012


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