Ephemeris

A tabulated set of computed positions for celestial objects over time, used in astronomy, navigation and spaceflight to predict locations of planets, moons, comets and satellites.

Author: Leandro Alegsa Creation date: November 13, 2022 Last updated: May 28, 2026

An ephemeris is a systematic table or dataset that gives the predicted positions and motions of a celestial body as a function of time. Historically produced for the Sun, Moon and planets, modern ephemerides cover natural bodies (planets, moons, comets, asteroids) and artificial satellites. They are essential tools for observers, navigators and spacecraft mission planners because they translate orbital models into coordinates at specified epochs.

Characteristics and formats

Ephemerides specify coordinates in a chosen reference frame and time scale, such as right ascension/declination or ecliptic longitude/latitude, and times given in UTC, TT or other scales. They may be presented as printed tables, machine-readable files or binary kernels for use in software. Production methods range from closed-form series expansions to high-precision numerical integration of the equations of motion that include gravitational and non-gravitational effects.

History and development

The practice of creating ephemerides goes back to antiquity with star catalogs and planetary tables; medieval and early-modern almanacs refined these predictions for navigation and calendar use. Advances in celestial mechanics in the 18th–20th centuries, and later digital computing, transformed ephemerides into highly accurate numerical products such as planetary and lunar series used by observatories and agencies worldwide.

Uses and examples

Navigation: traditional celestial navigation relies on the positions of the Sun, Moon and stars as given in an almanac or ephemeris.
Astronomy and observation: observers use ephemerides to point telescopes and to predict events like occultations and eclipses.
Space missions: spacecraft trajectory design and tracking require precise ephemerides of planets and target bodies.
Small bodies: ephemerides for bodies such as comet and asteroid help determine close approaches and impact probabilities.

Notable distinctions

Ephemeris products differ in intended accuracy and coverage: public almanacs provide convenient approximate positions, while research ephemerides incorporate more detailed physics for high precision. The term "ephemeris" may also refer to software libraries or files (for example, mission-specific kernels) that supply interpolated positions to client programs.

Because ephemerides are model dependent, users must note the reference frame, epoch and time standard used. For many applications, combining observed astrometry with updated orbital fits improves ephemerides for small or newly discovered objects.

For ephemerides published in 1783 (Berlin, 1780)

Applications

In printed form, ephemerides are available as astronomical yearbooks or, for seafaring, as nautical yearbooks. Among the earliest astronomical prints are the Ephemerides astronomicae of Regiomontanus, published in 1474, which Christopher Columbus used for navigation on his voyages of discovery.

Ephemerides for observational astronomy either use the full circle of 360 degrees along the ecliptic or give the position in equatorial coordinates. The calculation of ephemerides is one of the achievements of astronomical phenomenology and is now part of many astronomical computer programs or interactively available on the Internet.

For a satellite, the ephemeris data describes the apparent orbit in mathematical form. In the Global Positioning System (GPS) and other GNSS systems, this orbit data is part of the signal emitted by each satellite, which is then the basis for calculating the receiver position.

To estimate the probability of a possible collision of two bodies in the solar system, it is necessary to know the positions of the bodies and the temporal evolution of their orbital elements precisely. Therefore, ephemeris catalogues for asteroids are created in order to be able to determine their orbital data more precisely, which are usually only inadequately known. Special attention is paid to Earth orbital crossers, whose impacts on Earth could become a threat.

Astrological ephemerides give the ecliptical longitude of the celestial positions as degrees of the zodiacal signs. The indication of the ecliptic latitude is not common in all astrological ephemerides.

The calculation of the aspects of actual sunrise and sunset and the day arc of the sun is of particular importance for the calculation of the effectiveness of solar systems as well as in architecture for an estimation of the incidence of the sun; this is usually implemented in CAD software as a light module. Also of interest for landscape photography is the time and position of sunrise and sunset at a chosen location.

Ephemeris Calculator

The ephemeris calculation as a field of activity of astronomical phenomenology is carried out on the basis of the actually observed positions of the celestial bodies and the theory of gravitation. For future values, the expected orbital perturbations are taken into account. For this purpose, computational models such as planetary theory are set up to make the perturbation theory more precise.

Important historical tables for the ephemeris calculation were the Alfonsine tables about 1252, the Prutenian tables 1551 and the Rudolfinian tables 1627.

Author

Creation date: November 13, 2022

Last updated: May 28, 2026