In astronomy and celestial navigation, an ephemeris 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.