# Mean motion

In orbital mechanics, mean motion (represented by $n\,\!$) 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 databases of satellite orbital parameters the mean motion is typically measured in number of revolutions per day.

## Calculation

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

For satellite orbital parameters:

$n = d\sqrt{\frac{ G( M \! + \!m ) }{4\pi^2 a^3}}\,\!$

where:

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

## Related Formulae

The mean motion has a unit of radian or degrees per unit time

$n = \frac{2\pi}{P}$

The mean motion for satellite orbital parameters is a ratio and thus have no units

$n = \frac{d}{P}$

where d is the amount of time in a day and 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 is referred to as the mean anomaly at epoch, and t the time since epoch.