digplanet beta 1: Athena
Share digplanet:

Agriculture

Applied sciences

Arts

Belief

Business

Chronology

Culture

Education

Environment

Geography

Health

History

Humanities

Language

Law

Life

Mathematics

Nature

People

Politics

Science

Society

Technology

In celestial mechanics, 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 in equal intervals of time by a line joining the focus and the orbiting body (Kepler's second law).

The mean anomaly increases uniformly from 0 to 2\pi 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 M, and is given by the formula:

 M =  n \, t =  \sqrt{\frac{ G( M_\star \! + \!m ) } {a^3}} \,t

where n is the mean motion, a is the length of the orbit's semi-major axis, M_\star 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 2\pi 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) \sqrt{\frac{ G( M_\star \! + \!m ) } {a^3}} \,\delta t where \delta t represents the time difference. The other anomalies can hence be calculated.

Formulas[edit]

The mean anomaly M can be computed from the eccentric anomaly E and the eccentricity e with Kepler's Equation:

M =  E - e \cdot \sin E

To find the position of the object in an elliptic Kepler orbit at a given time t, the mean anomaly is found by multiplying the time and the mean motion, then it is used to find the eccentric anomaly by solving Kepler's equation.

It is also frequently seen:

M =  M_0 + nt,

Again n is the mean motion. However, t, in this instance, is the time since epoch, which is how much time has passed since the measurement of M0 was taken. The value M0 denotes the mean anomaly at epoch, which is the mean anomaly at the time the measurement was taken.

See also[edit]

References[edit]

  • Murray, C. D. & Dermott, S. F. 1999, Solar System Dynamics, Cambridge University Press, Cambridge.
  • Plummer, H.C., 1960, An Introductory treatise on Dynamical Astronomy, Dover Publications, New York. (Reprint of the 1918 Cambridge University Press edition.)

Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Mean_anomaly — Please support Wikipedia.
A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.

1 news items

 
Insurance News Net (press release)
Mon, 24 Mar 2014 08:46:13 -0700

The ensemble mean and ensemble mean anomaly were used as predictors for precipitation and temperature, respec- tively. The results showed that the logistic regression- based probability forecasts (using retrospective forecasts) were much more skillful ...
Loading

Oops, we seem to be having trouble contacting Twitter

Talk About Mean anomaly

You can talk about Mean anomaly with people all over the world in our discussions.

Support Wikipedia

A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia. Please add your support for Wikipedia!