Orbital elements

Orbital elements are parameters that specify an orbit’s size, shape, orientation, and the orbiting body’s position at a particular time.

Semi-major axis: Half the longest diameter of an ellipse; it sets an elliptical orbit’s characteristic size and, under gravity, its period. It specifies the orbit’s size and helps determine its orbital period.
Keplerian orbit: An idealized orbit in which two bodies move under their mutual Newtonian gravitational attraction alone. Classical orbital elements describe this ideal two-body motion directly.
Two-line element set: A standardized text format that encodes satellite orbital data for use with propagation models. It packages orbital parameters for tracking Earth satellites.
Modified equinoctial elements: A set of orbital parameters designed to avoid several singularities of classical elements, especially near circular or equatorial orbits. They provide a numerically smoother alternative where classical angles become undefined.
Eccentricity: A dimensionless measure of how much a conic section departs from circularity. It distinguishes nearly circular orbits from elongated ellipses and open trajectories.
Kepler's equation: An equation relating mean anomaly to eccentric anomaly and orbital eccentricity in an elliptical orbit. It helps convert an element describing orbital phase into a position on an ellipse.
NORAD SGP4: A model for propagating satellite orbits from two-line element sets while accounting for selected perturbations. It turns widely distributed element sets into predicted satellite positions.
Delaunay variables: Canonical action-angle variables used to describe Keplerian motion in Hamiltonian mechanics. They encode orbital motion for analytical mechanics rather than serving as the usual geometric element set.
Inclination: The angle between an orbit’s plane and a chosen reference plane. It specifies the tilt of the orbital plane relative to a reference.
State vector: A representation of an object's position and velocity at a particular time. Orbital elements can be transformed into a state vector for propagation or comparison.

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