In astronomy and celestial navigation, an ephemeris (plural: ephemerides; from Latin ephemeris, "diary", from Greek: εφημερίς, ephēmeris, "diary, journal") gives the positions of naturally occurring astronomical objects as well as artificial satellites in the sky at a given time or times. Historically, positions were given as printed tables of values, given at regular intervals of date and time. Modern ephemerides are often computed electronically from mathematical models of the motion of astronomical objects and the Earth. Even though the calculation of these tables was one of the first applications of mechanical computers, printed ephemerides are still produced, as they are useful when computational devices are not available.
The astronomical position calculated from an ephemeris is given in the spherical polar coordinate system of right ascension and declination. Some of the astronomical phenomena of interest to astronomers are eclipses, apparent retrograde motion/planetary stations, planetary ingresses, sidereal time, positions for the mean and true nodes of the moon, the phases of the Moon, and the positions of minor celestial bodies such as Chiron.
Ephemerides are used in celestial navigation and astronomy. They are also used by some astrologers.
For scientific uses, a modern planetary ephemeris comprises software that generates positions of planets and often of their satellites, asteroids, or comets, at virtually any time desired by the user.
Typically, such ephemerides cover several centuries, past and future; the future ones can be covered because the field of celestial mechanics has developed several accurate theories. Nevertheless, there are secular phenomena which cannot adequately be considered by ephemerides. The greatest uncertainties in the positions of planets are caused by the perturbations of numerous asteroids, most of whose masses and orbits are poorly known, rendering their effect uncertain. Reflecting the continuing influx of new data and observations, NASA's Jet Propulsion Laboratory (JPL) has revised its published ephemerides nearly every year for the past 20 years.
Scientific ephemerides for sky observers mostly contain the positions of celestial bodies in right ascension and declination, because these coordinates are the most frequently used on star maps and telescopes. The equinox of the coordinate system must be given. It is, in nearly all cases, either the actual equinox (the equinox valid for that moment, often referred to as "of date" or "current"), or that of one of the "standard" equinoxes, typically J2000.0, B1950.0, or J1900. Star maps almost always use one of the standard equinoxes.
Scientific ephemerides often contain further useful data about the moon, planet, asteroid, or comet beyond the pure coordinates in the sky, such as elongation to the sun, brightness, distance, velocity, apparent diameter in the sky, phase angle, times of rise, transit, and set, etc. Ephemerides of the planet Saturn also sometimes contain the apparent inclination of its ring.
Celestial navigation serves as a backup to the Global Positioning System. Software is widely available to assist with this form of navigation; some of this software has a self-contained ephemeris. When software is used that does not contain an ephemeris, or if no software is used, position data for celestial objects may be obtained from the modern Nautical Almanac or Air Almanac.
An ephemeris is usually only correct for a particular location on the Earth. In many cases, the differences are too small to matter. However, for nearby asteroids or the Moon, they can be quite important.
Global Positioning System (GPS) navigation satellites transmit electronic ephemeris data consisting of health and exact location data. A GPS receiver can use the transmissions from multiple such satellites to calculate its own location using trilateration.
Other modern ephemerides recently created are the EPM (Ephemerides of Planets and the Moon), from the Russian Institute for Applied Astronomy of the Russian Academy of Sciences, and the INPOP (Intégrateur numérique planétaire de l'Observatoire de Paris) by the French IMCCE.
The Photographer's Ephemeris is a free useful software tool for photographers needing the times of twilight and the rise and set times of the sun and moon.