Semi-major and semi-minor axes

In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter. The semi-major axis is one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. Essentially, it is the radius of an orbit at the orbit's two most distant points. For the special case of a circle, the semi-major axis is the radius. One can think of the semi-major axis as an ellipse's long radius.

The length of the semi-major axis ${\displaystyle a}$ of an ellipse is related to the semi-minor axis's length ${\displaystyle b}$ through the eccentricity ${\displaystyle e}$ and the semi-latus rectum ${\displaystyle \ell }$, as follows:

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