§ DICTIONARY · CONCEPT
semi-major axis
Half the longest diameter of an ellipse; appears in Kepler's third law as T² ∝ a³.
§ 01
Definition
The semi-major axis is half the length of the longest chord of an ellipse. It is the natural measure of the orbit's size — a kind of average distance between the orbiting body and the central focus.
Kepler's third law relates the semi-major axis a to the orbital period T by T² ∝ a³. For bodies orbiting the same central mass, the ratio T² / a³ is a constant. Newton's law of gravity explains why: the constant is 4π² / GM, where M is the mass at the focus.