Mean Anomaly

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Equation / Last modified by MichaelBartmess on 2017/03/29 03:51
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This vCalc equation computes the mean anomaly based on the period of the orbit.  The mean anomaly for an Earth Satellite is the angle at the Earth's centre, measured from the perigee in the direction of the satellite's motion, and assumes the satellite would be at an angle away from perigee as if the satellite were moving at a constant angular speed, i.e `M = (2*pi*t)/T` (radians), where T is the orbital period and M is the Mean Motion.

The definition of mean anomaly essentially maps a constant angular velocity onto an elliptical orbit as if a circular orbit were superimposed over the actual elliptical orbit.

In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. It is the angular distance from the pericenter, also known as the perigee point in the elliptical orbit.

The Math

`"Mean_Anomaly" = M_0 + M (t - t_0)`, where

  • `M` = Mean Motion,
  • `M_0 = "Mean_Anomaly"` at epoch
  • `t` = time after epoch
  • `t_0` = epoch time

Mean Motion, `M`,defines the angular rate of an orbit and is expressed as number of revolutions or orbits per unit time.  The unit of revolution may be expressed as a revolution, 360 degrees, or 2`pi` radians. 

Period can be expressed in any units of time but more typically is in minutes, hours or days.  We use Julian or Modified Julian Days in this equation to have a constant reference over long periods of time.

Note: the two line element set used to represent an orbital trajectory of an Earth orbiting object represent mean motion in units of `"revs"/"day"`.

Orbit Classifications by Mean Motion or Period

In many Earth orbital analysis systems, classification of orbits are defined by Near Earth Orbits (NEOs -- sometimes called Low Earth Orbits or LEOs) , Medium Earth Orbits (MEOs), Geosynchronous orbits (GEOs), or Deep Space Orbits.  These classes of orbits have arbitrary boundaries defined by their orbital period or mean motion.  Often for instance a NEO is defined as any orbit with a period less than 225 minutes (a mean motion of 6.4 revs/day).

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