Table of the positions of celestial bodies at regular intervals, often with supplementary information. Constructed as early as the 4th century BC, ephemerides are still essential to astronomers and navigators. Modern ephemerides are calculated, with heavy computing and careful checking, after a mathematical description of a heavenly body's observed motion has been evolved. Various national ephemerides are published regularly; the U.S. ephemeris, first published in 1852, became the best and is now published jointly with the U.K. as The Astronomical Almanac.
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The position is given to astronomers in a spherical polar coordinate system of right ascension and declination or to astrologer in longitude along the zodiacal ecliptic, and sometimes declination. Astrological positions may be given for either noon or midnight.
An astronomical ephemeris may also provide data on astronomical phenomena of interest to astrologers and astronomers such as eclipses, apparent retrogradation/planetary stations, planetary ingresses, sidereal time, positions for the Mean and True nodes of the moon, the phases of the Moon, and sometimes even the position(s) of Chiron, and other minor celestial bodies. Astrologers also use other ephemerides that include tables of imaginary celestial bodies, such as Lilith, a term they use variously for the apogee of the Moon or the second focus of the Moon's orbit. Some ephemerides also contain a monthly aspectarian, while others often include the declination of the planets as well as their longitudes, right ascensions or Cartesian coordinates.
1554 - Johannes Stadius published a well-known work known as Ephemerides novae at auctae that attempted to give accurate planetary positions. The effort was not entirely successful, and there were, for example, periodic errors in Stadius’ Mercury positions of up to ten degrees.
Typically, such ephemerides cover several centuries, past and future; the future ones can be covered because celestial mechanics is an accurate theory. Nevertheless, there are secular phenomena, factors that cannot adequately be considered by ephemerides. The biggest uncertainties on planetary positions are due to the perturbations of numerous asteroids, most of whose masses are poorly known, rendering their effect uncertain. Therefore, despite efforts to overcome these uncertainties, the JPL has to revise its published ephemerides at intervals of 20 years.
Scientific ephemerides for sky observers mostly contain the position of the mentioned celestial body in right ascension and declination, because these coordinates are the most often 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 the one of the "standard" equinoxes, typically J2000.0, B1950.0, or J1900. Star maps are almost always in 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.
GPS navigation satellites transmit electronic ephemeris data consisting of health and exact location data that GPS receivers then use (together with the signal's elapsed travel time to the receiver) to calculate their own location on Earth using trilateration.
The majority of astrologers study tropical astrology, involving planetary positions referenced to the vernal (spring) equinox position along the ecliptic (the equinox being the nexus of Earth's rotational plane and Earth's orbital plane around the Sun). They use exactly the same referential frame of the astronomers, except for a small minority of astrologers who study sidereal astrology and use a different ephemerids, based on the constellations.
Though astrology is and always has been geocentric, heliocentric astrology is an emerging field; for this purpose a standard ephemeris cannot be utilized, and because of this specialized heliocentric ephemerids must be calculated and used instead of the default geocentric ephemerides that are used in standard Western astrology to construct the astrological chart/natal chart.