Mean motion

Mean motion, $n\,\!$, is a measure of how fast a satellite progresses around its elliptical orbit. Unless the orbit is circular, the mean motion is only an average value, and does not represent the instantaneous angular velocity.

In the databases of satellite orbital parameters the mean motion is typically specified in revolutions per day.

Calculation

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

where:

• $G\!$ is the gravitational constant,
• $M\!$ and $m\!$ are the masses of the orbiting bodies,
• $a\!$ is semi-major axis.

Related Formulae

$n = \frac{2\pi }{P} = \frac{360^\circ}{P}$

Mean motion can also be expressed in radians or degrees, respectively, per unit of time; where P is the Orbital Period.

Or,

$n = \frac{M_1 - M_0}{t}$

Where M₁ and M₀ are the Mean Anomalies at particular points in time, and t is the time elapsed between the two. M₀ also frequently denotes the Mean Anomaly at Epoch and t the time since epoch.

See also

• Kepler orbit
• Mean anomaly
• Elliptic coordinates