Kepler's equation

Kepler's equation, M = E − e sin E, relates mean anomaly M to eccentric anomaly E for an orbit with eccentricity e. Solving it yields a body's position along an elliptical orbit at a given time.

Mean anomaly: An angle that increases uniformly with time and measures progress through an orbit from periapsis. It supplies M, the time-based quantity that Kepler's equation maps to eccentric anomaly.
Elliptical orbit: A closed orbital path shaped as an ellipse, with the attracting central body at one focus. The equation applies to this orbit shape and uses its geometry to locate the orbiting body.
Celestial mechanics: The study of the motion of celestial bodies under gravitational forces. Kepler's equation is a standard tool for predicting positions in two-body orbital motion.
Barker's equation: A relation used to calculate position along a parabolic orbit as a function of time. It serves the parabolic case, where the elliptical form of Kepler's equation does not apply.
Eccentric anomaly: An auxiliary angle that parameterizes a body's position on an elliptical orbit through a related circle. It is the unknown angle solved from mean anomaly and eccentricity.
Periapsis: The point in an orbit at which the orbiting body is closest to its central body. Both anomalies are conventionally measured from this orbital reference point.
Orbit determination: The estimation of an object's orbit from observations of its position or motion. Predicted positions from Kepler's equation can be compared with observations to estimate orbital elements.
Hyperbolic Kepler equation: The relation between mean anomaly and hyperbolic anomaly for an unbound hyperbolic orbit. It extends the anomaly-based timing approach to hyperbolic rather than elliptical paths.
Orbital eccentricity: A dimensionless measure of how much an orbit differs from a circle. It sets the size of the sine correction between the two anomalies.
Orbital period: The time an orbiting body takes to complete one revolution around its central body. The period determines how quickly mean anomaly advances with time.

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