<P> where G (\ displaystyle G) is the gravitational constant, M (\ displaystyle M) is the mass of the central body, and m (\ displaystyle m) is the mass of the orbiting body . Typically, the central body's mass is so much greater than the orbiting body's, that m (\ displaystyle m) may be ignored . Making that assumption and using typical astronomy units results in the simpler form Kepler discovered . </P> <P> The orbiting body's path around the barycentre and its path relative to its primary are both ellipses . The semi-major axis is sometimes used in astronomy as the primary - to - secondary distance when the mass ratio of the primary to the secondary is significantly large (M ≫ m (\ displaystyle M \ gg m)); thus, the orbital parameters of the planets are given in heliocentric terms . The difference between the primocentric and "absolute" orbits may best be illustrated by looking at the Earth--Moon system . The mass ratio in this case is 7001813005900000000 ♠ 81.300 59 . The Earth--Moon characteristic distance, the semi-major axis of the geocentric lunar orbit, is 384,400 km . The barycentric lunar orbit, on the other hand, has a semi-major axis of 379,700 km, the Earth's counter-orbit taking up the difference, 4,700 km . The Moon's average barycentric orbital speed is 1.010 km / s, whilst the Earth's is 0.012 km / s . The total of these speeds gives a geocentric lunar average orbital speed of 1.022 km / s; the same value may be obtained by considering just the geocentric semi-major axis value . </P> <P> It is often said that the semi-major axis is the "average" distance between the primary focus of the ellipse and the orbiting body . This is not quite accurate, because it depends on what the average is taken over . </P> <Ul> <Li> averaging the distance over the eccentric anomaly (q.v.) indeed results in the semi-major axis . </Li> <Li> averaging over the true anomaly (the true orbital angle, measured at the focus) results, oddly enough, in the semi-minor axis b = a 1 − e 2 (\ displaystyle b = a (\ sqrt (1 - e ^ (2)))). </Li> <Li> averaging over the mean anomaly (the fraction of the orbital period that has elapsed since pericentre, expressed as an angle), finally, gives the time - average a (1 + e 2 2). (\ displaystyle a \ left (1 + (\ frac (e ^ (2)) (2)) \ right). \,) </Li> </Ul>

A planet's semi major axis is related to its orbital period