Orbital eccentricity is the measure of the departure of an orbit from a perfect circle.
In geometry, eccentricity (e) is a concept universally applicable to conic sections.
For the general case of an ellipse having semi-major axis a and distance c from the center to either focus:
A circle is a "degenerate" ellipse. In a circle, the two foci converge at the center. Therefore
A parabola is an extreme case of an ellipse and is the first open conic section. For any parabola:
Therefore, for any closed orbit,
In astrodynamics, any given pair of apsides can predict the semi-major axis and eccentricity of any orbit. Specifically, for periapsis q and apoapsis Q:
By the same token, a and e can predict Q and q.
Subtracting the first equation from the second yields
From the above:
For , , the orbital radius, as one would expect.