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An ellipse's semi-major axis (a) is half the distance between the ellipse's furthest two points, or equivalently, the distance from the ellipse's center to one of its points furthest from the center. The semi-minor axis (b) is an analogous distance from the ellipse's center to one of the ellipse's points nearest the center. They are mathematically related with e, the ellipse's eccentricity:
b = a (1 - e2)0.5
The semi-major axis can be used in various orbital calculations. For example, for an orbit:
T = 2π(a3/μ)0.5
Where:
(All these equations apply to a circle as well, taking its radius as both its semi-major axis and its semi-minor axis.) The semi-major axis is useful for characterizing the size of an orbit; the term orbital radius is clearly useful for circular orbits and useful to indicate an approximation of an orbit that is not far from circular, but its meaning is vague regarding decidedly eccentric orbits.
When an orbit is viewed in the sky, only a projection of it is observed, based upon the orbital inclination, typically unknown, and often what is evident is a lower bound on the semi-major axis. Sometimes, a likely semi-major axis is cited based upon the average of possible semi-major axes, assuming a randomly positioned orbital plane positioning and some knowledge of the observational error distribution. The actual orbit can be worked out with sufficient data on the position of the host in relation to the projection, and/or on the projected orbital speed throughout the orbit.