Mean motion
Encyclopedia
Mean motion, 
, 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 rate.
In the databases of satellite orbital parameters the mean motion is typically specified in revolutions per day
.
where:
Mean motion can also be expressed in radians or degrees, respectively, per unit of time; where P is the Orbital Period
.
Or,
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.
, is a measure of how fast a satelliteSatellite
In the context of spaceflight, a satellite is an object which has been placed into orbit by human endeavour. Such objects are sometimes called artificial satellites to distinguish them from natural satellites such as the Moon....
progresses around its elliptical orbit. Unless the orbit is circular
Circular orbit
A circular orbit is the orbit at a fixed distance around any point by an object rotating around a fixed axis.Below we consider a circular orbit in astrodynamics or celestial mechanics under standard assumptions...
, the mean motion is only an average value, and does not represent the instantaneous angular rate.
In the databases of satellite orbital parameters the mean motion is typically specified in revolutions per day
Day
A day is a unit of time, commonly defined as an interval equal to 24 hours. It also can mean that portion of the full day during which a location is illuminated by the light of the sun...
.
Calculation
where:
is the gravitational constantGravitational constantThe gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
,
and 
are the masses of the orbiting bodies,
is semi-major axisSemi-major axisThe major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape...
.
Related Formulae
Mean motion can also be expressed in radians or degrees, respectively, per unit of time; where P is the Orbital Period
Orbital period
The orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...
.
Or,
Where M1 and M0 are the Mean Anomalies
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....
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.