Semimajor axis

The semimajor axis is half the longest diameter of an ellipse. It sets the ellipse’s characteristic size and, for an orbit, its scale.

Ellipse: A plane curve whose points have a constant sum of distances from two foci. The semimajor axis is defined from an ellipse’s longest diameter.
Kepler's laws of planetary motion: Three rules describing how planets orbit the Sun, including the relation between orbital period and orbit size. Kepler’s third law links a body's orbital period to its semimajor axis.
Orbital eccentricity: A dimensionless measure of an orbit's deviation from a circle. Eccentricity and semimajor axis together determine an elliptical orbit’s periapsis and apoapsis.
Circle: The set of points in a plane at a fixed distance from a center. A circle has equal semiaxes, so its semimajor axis is simply its radius.
Major axis: The longest diameter of an ellipse, passing through both foci and its center. The semimajor axis is half the major axis.
Kepler's third law: A relation stating that an orbiting body's squared period is proportional to the cube of its orbit's semimajor axis. It makes semimajor axis measurable from an orbital period when the central mass is known.
Periapsis: The point in an orbit where the orbiting body is closest to its primary. Its distance is the semimajor axis multiplied by one minus orbital eccentricity.
Semi-latus rectum: Half the length of a conic section's chord through a focus and perpendicular to its axis of symmetry. Unlike semimajor axis, it directly governs an orbit’s radial equation and angular momentum.
Semiminor axis: Half the shortest diameter of an ellipse, perpendicular to its semimajor axis. Together, the two semiaxes determine an ellipse’s shape and area.
Vis-viva equation: An orbital equation relating a body's speed, distance from the focus, and semimajor axis. The equation shows how semimajor axis sets orbital speed at a given distance.

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