Ephemeris

An ephemeris is a table or dataset giving calculated positions of celestial bodies at specified times, often for a chosen coordinate system and reference frame.

Numerical integration: A family of methods for approximating solutions to differential equations through successive numerical steps. Planetary motion equations are integrated numerically to calculate positions across time.
Astronomical almanac: A yearly reference publishing astronomical data, including predicted positions and times of celestial events. Almanacs present ephemeris results in tables suited to observation and planning.
Celestial mechanics: The study of the motion of celestial bodies under gravity and other forces. Ephemerides are numerical products of models developed in celestial mechanics.
Analytical ephemeris: An ephemeris generated from explicit formulas for celestial positions rather than a tabulated numerical trajectory. Analytical formulas can be compact and fast, while numerical integrations often capture complex interactions more precisely.
Babylonian astronomy: The astronomical traditions of ancient Mesopotamia, including systematic observations and mathematical prediction of celestial phenomena. Babylonian scholars developed some of the earliest known systematic planetary prediction schemes.
N-body problem: The problem of predicting the motion of multiple bodies interacting through forces such as gravity. Gravitational interactions among solar-system bodies shape many ephemeris calculations.
Astrometry: The measurement of the positions and motions of celestial objects. Observed positions can be compared with ephemerides to refine or test predictions.
Kepler's laws of planetary motion: Three laws describing how planets orbit the Sun in ellipses, sweep equal areas, and relate orbital periods to size. They provide a foundational approximation for predicting planetary positions.
Numerical ephemeris: An ephemeris based on numerically integrated equations of motion and typically distributed as sampled data. It contrasts with formula-based ephemerides in how predicted positions are represented and computed.
Almagest: A second-century astronomical treatise by Ptolemy that presented a mathematical model of the heavens and extensive tables. Its tables made predicted celestial positions usable within the Ptolemaic system.

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