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# Semi-major axis

The semi-major axis is indicated by the letter 'a'

The semi-major axis of any ellipse is one-half of the axis of symmetry that passes through the foci of that ellipse.

In astrophysics, the semi-major axis of an orbit is the distance between the geometric center of the orbit and either apsis. It is a commonly reported orbital element that can determine the size and shape of an orbit.

## Calculations

The distance of the foci to the point 'C' in the Figure above is the same as the semimajor axis.

The semi-major axis, usually labeled a, is the arithmetic mean of the two apsides:

a = (Q + q)/2

For this reason the semi-major axis is often cited as a "mean orbital radius."

The semi-major axis, together with the orbital eccentricity (e), can predict the periapsis and apoapsis:

Q = a(1+e)

q = a(1-e)

See orbital eccentricity for a detailed derivation.

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