Semi-major and semi-minor axes

The semimajor axis (also semi-major axis) is one half of the major axis of an ellipse, running from the center, through a focus, and to the edge of the ellipse. The major axis is the longest line that runs through the center and both foci of an ellipse, its ends being at the widest points of the shape.

In astronomy, the semimajor axis is one of the most important characteristics of an orbit, along with its period. It can be mathematically proven that for an orbiting body, the semimajor axis represents the average distance of the body from the central gravitational source. For solar system objects, the semimajor axis is related to the period of the orbit by Kepler's Third Law (originally empirically derived),

$P^{2}=a^{3}$

where P is the period in years, and a is the semimajor axis in astronomical units. This form turns out to be a simplification of the general form, as determined by Newton:

$P^{2}={\frac {4\pi ^{2}}{G(M+m)}}a^{3}$

where G is the gravitational constant, and M is the mass of the central body, and m is the mass of the orbiting body. Typically, the centraol body's mass is so much greater than the orbiting body's, that m may be ignored. Making that assumption and using typical astronomy units results in the simpler form Kepler discovered.