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In astronomy and celestial navigation, an ephemeris (plural: ephemerides; from Latin ephemeris ("diary"), from Greek ἐφημερίς (ephēmeris, "diary, calendar")) 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 position(s) of Chiron and other minor celestial bodies.
Ephemerides are used in celestial navigation, astronomy and astrology. Astrologers typically have different needs than astronomers, for example, the calculation of astrological aspects, and may produce ephemerides specialized to their own field.
- 2nd millennium BC — Panchanga tables based on Jyotisha in the Vedic period of Indian astronomy.
- 1st millennium BC — Ephemerides in Babylonian astronomy.
- 2nd century AD — the Almagest and the Handy Tables of Ptolemy
- 8th century AD — the Zij of Ibrāhīm al-Fazārī
- 9th century AD — the Zij of Muḥammad ibn Mūsā al-Khwārizmī
- 12th century AD — the Tables of Toledo, based largely on Arabic Zij sources of Islamic astronomy, were edited by Gerard of Cremona to form the standard European ephemeris until the Alfonsine tables.
- 13th century — the Zij-i Ilkhani, or Ilkhanic Tables, were compiled at the Maragheh observatory in Persia.
- 13th century — the Alfonsine tables were compiled in Spain to correct anomalies in the Tables of Toledo, remaining the standard European ephemeris until the Prutenic Tables almost 300 years later.
- 1408 — Chinese Ephemeris Table (copy in Pepysian Library, Cambridge, UK (refer book '1434'); Chinese tables believed known to Regiomontanus).
- 1496 — the Almanach Perpetuum of Abraão ben Samuel Zacuto (one of the first books published with a movable type and printing press in Portugal)
- 1504 — While shipwrecked on the island of Jamaica, Christopher Columbus successfully predicted a lunar eclipse for the natives, using the Ephemeris of the German astronomer Regiomontanus.
- 1551 — the Prutenic Tables of Erasmus Reinhold were published, based on Copernicus's theories.
- 1554 — Johannes Stadius published Ephemerides novae at aucta, the first major ephemeris computed according to Copernicus' heliocentric model, using parameters derived from the Prutenic Tables. Although the Copernican model provided an elegant solution to the problem of computing apparent planetary positions (it avoided the need for the equant and better explained the apparent retrograde motion of planets), it still relied on the use of epicycles, leading to some inaccuracies - for example, periodic errors in the position of Mercury of up to ten degrees.
- 1627 — the Rudolphine Tables of Johannes Kepler based on elliptical planetary motion became the new standard.
- 1679 — La Connaissance des Temps ou calendrier et éphémérides du lever & coucher du Soleil, de la Lune & des autres planètes, first published by Jean Picard.
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 to revise its published ephemerides at intervals of 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.
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 (Integration Numerique Planetaire 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.
- The Astronomical Almanac (new name)
- American Ephemeris and Nautical Almanac (old name)
- Ephemeris time
- Epoch (astronomy)
- Epoch (reference date)
- Fundamental ephemeris
- January 0 or March 0
- Jet Propulsion Laboratory Development Ephemeris
- Keplerian elements
- Nautical almanac
- Osculating orbit
- Two-line elements
- ephemeris 1992.
- "Dictionary". Merriam-Webster.
- "ephemeris". Dictionnaire Gaffiot latin-français.
- Georgij A. Krasinsky and Victor A. Brumberg, Secular Increase of Astronomical Unit from Analysis of the Major Planet Motions, and its Interpretation Celestial Mechanics and Dynamical Astronomy 90: 267–288, (2004).
- Pitjeva, Elena V. (August 2006). "The dynamical model of the planet motions and EPM ephemerides". Highlights of Astronomy 14: 470. doi:10.1017/S1743921307011453.
- "INPOP10e, a 4-D planetary ephemeris". IMCCE. Retrieved 2 May 2013.
- Astronomical algorithms taken from Astronomical Algorithms, 2nd Ed. by Jean Meeus.
- Duffett-Smith, Peter (1990). Astronomy With Your Personal Computer. Cambridge University Press. ISBN 0-521-38995-X.
- "ephemeris". American Heritage Dictionary of the English Language (3rd ed.). Boston: Houghton Mifflin. 1992.
- MacCraig, Hugh (1949). The 200 Year Ephemeris. Macoy Publishing Company.
- Meeus, Jean (1991). Astronomical Algorithms. Willmann-Bell. ISBN 0-943396-35-2.
- Michelsen, Neil F. (1990). Tables of Planetary Phenomena. ACS Publications, Inc. ISBN 0-935127-08-9.
- Michelsen, Neil F. (1982). The American Ephemeris for the 21st Century - 2001 to 2100 at Midnight. Astro Computing Services. ISBN 0-917086-50-3.
- Montenbruck, Oliver (1989). Practical Ephemeris Calculations. Springer-Verlag. ISBN 0-387-50704-3.
- Seidelmann, Kenneth (2006). Explanatory supplement to the astronomical almanac. University Science Books. ISBN 1-891389-45-9.
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