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Semi-major axis

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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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