semiaxes

Semiaxes are the lengths from the center of a symmetric shape to its boundary along the principal axes. The term is most commonly used for ellipses and ellipsoids, but it also appears in orbital mechanics to describe the size of an elliptical orbit. The plural semiaxes is used when referring to multiple axes in one figure or system.

In a plane ellipse, the major axis is the longest diameter, and the minor axis is the shortest. The semi-major axis a is half the length of the major axis, and the semi-minor axis b is half the length of the minor axis. If the ellipse is centered at the origin and aligned with the coordinate axes, its equation is x^2/a^2 + y^2/b^2 = 1. The eccentricity e satisfies e = sqrt(1 − b^2/a^2), with a ≥ b. When a = b, the ellipse is a circle and the semiaxes are equal.

An ellipsoid has three semiaxes a, b, and c along its principal axes. The volume is V = 4/3 π a b c. Unlike volume or simple measures, the surface area of a general ellipsoid does not have a simple closed form and is typically computed numerically or approximated.

In orbital mechanics, the semi-major axis a of an elliptical orbit around a focus defines the orbit’s size. It is commonly measured in astronomical units for planets around the Sun. The orbit is circular when a = b and the orbital energy and period are closely tied to a via Kepler’s laws. Semiaxes provide a compact way to describe the dimensions and scale of conic sections and related bodies.