In astronomy and celestial navigation, an ephemeris (plural: ephemerides) is a book with tables that gives the trajectory of naturally occurring astronomical objects as well as artificial satellites in the sky, i.e., the position (and possibly velocity) over time. The etymology is from Latin ephemeris 'diary' and from Greek ἐφημερίς (ephemeris) 'diary, journal'.[1][2][3][4] Historically, positions were given as printed tables of values, given at regular intervals of date and time. The calculation of these tables was one of the first applications of mechanical computers. Modern ephemerides are often provided in electronic form. However, printed ephemerides are still produced, as they are useful when computational devices are not available.

The astronomical position calculated from an ephemeris is often given in the spherical polar coordinate system of right ascension and declination, together with the distance from the origin if applicable. 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 astrologers.[5]


A Latin translation of al-Khwārizmī's zīj, page from Corpus Christi College MS 283
Alfonsine tables
Page from Almanach Perpetuum
  • 1st millennium BC – Ephemerides in Babylonian astronomy.
  • 2nd century AD – the Almagest and the Handy Tables of Ptolemy
  • 8th century AD – the zīj of Ibrāhīm al-Fazārī
  • 9th century AD – the zīj of Muḥammad ibn Mūsā al-Khwārizmī
  • 12th century AD – the Tables of Toledo – based largely on Arabic zīj sources of Islamic astronomy – were edited by Gerard of Cremona to form the standard European ephemeris until the Alfonsine Tables.
  • 13th century AD – the Zīj-i Īlkhānī (Ilkhanic Tables) were compiled at the Maragheh observatory in Persia.
  • 13th century AD – 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.
  • 13th century AD - the Dresden Codex, an extant Mayan ephemeris
  • 1408 – Chinese ephemeris table (copy in Pepysian Library, Cambridge, UK (refer book '1434'); Chinese tables believed known to Regiomontanus).
  • 1474 – Regiomontanus publishes his day-to-day Ephemerides in Nürnberg, Germany.[6]
  • 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.
  • 1531 – Work of Johannes Stöffler is published posthumously at Tübingen, extending the ephemeris of Regiomontanus through 1551.
  • 1551 – the Prutenic Tables of Erasmus Reinhold were published, based on Copernicus's theories.
  • 1554 – Johannes Stadius published Ephemerides novae et auctae, 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. One of the users of Stadius's tables is Tycho Brahe.
  • 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 yearly by Jean Picard and still extant.
  • 1975 – Owen Gingerich, using modern planetary theory and digital computers, calculates the actual positions of the planets in the 16th Century and graphs the errors in the planetary positions predicted by the ephemerides of Stöffler, Stadius and others. According to Gingerich, the error patterns "are as distinctive as fingerprints and reflect the characteristics of the underlying tables. That is, the error patterns for Stöffler are different from those of Stadius, but the error patterns of Stadius closely resemble those of Maestlin, Magini, Origanus, and others who followed the Copernican parameters."[7]

Modern ephemeris

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.

After introduction of computers in the 1950's it became feasible to use numerical integration to compute ephemerides. The Jet Propulsion Laboratory Development Ephemeris is a prime example. Conventional so-called analytical ephemerides that utilize series expansions for the coordinates have also been developed, but of much increased size and accuracy as compared to the past, by making use of computers to manage the tens of thousands of terms. Ephemeride Lunaire Parisienne and VSOP are examples.

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 since 1981.[8]

Solar System ephemerides are essential for the navigation of spacecraft and for all kinds of space observations of the planets, their natural satellites, stars, and galaxies.

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 Satellite navigation. Software is widely available to assist with this form of navigation; some of this software has a self-contained ephemeris.[9] 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.[10]

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.

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,[11] and the INPOP (Intégrateur numérique planétaire de l'Observatoire de Paris) by the French IMCCE.[12][13]

See also


  1. ^ ephemeris 1992.
  2. ^ ἐφημερίς. Liddell, Henry George; Scott, Robert; A Greek–English Lexicon at the Perseus Project.
  3. ^ "ephemeris". Merriam-Webster.
  4. ^ "ephemeris". Dictionnaire Gaffiot latin-français.
  5. ^ Gingerich, Owen (2017). Arias, Elisa Felicitas; Combrinck, Ludwig; Gabor, Pavel; Hohenkerk, Catherine; Seidelmann, P. Kenneth (eds.). "The Role of Ephemerides from Ptolemy to Kepler". The Science of Time 2016. Astrophysics and Space Science Proceedings. Cham: Springer International Publishing: 17–24. doi:10.1007/978-3-319-59909-0_3. ISBN 978-3-319-59909-0.
  6. ^ Jones, S.S.D.; Howard, John; William, May; Logsdon, Tom; Anderson, Edward; Richey, Michael. "Navigation". Encyclopedia Britannica. Encyclopædia Britannica, inc. Retrieved 13 March 2019.
  7. ^ Gingerich, Owen (1975). ""Crisis" versus Aesthetic in the Copernican Revolution" (PDF). Vistas in Astronomy. Elsevier BV. 17 (1): 85–95. Bibcode:1975VA.....17...85G. doi:10.1016/0083-6656(75)90050-1. Retrieved 23 June 2016.
  8. ^ 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).
  9. ^ American Practical Navigator: An Epitiome of Navigation. Bethesda, MD: National Imagery and Mapping Agency. 2002. p. 270.
  10. ^ "Almanacs and Other Publications — Naval Oceanography Portal". United States Naval Observatory. Retrieved 11 November 2016.
  11. ^ Pitjeva, Elena V. (August 2006). "The dynamical model of the planet motions and EPM ephemerides". Highlights of Astronomy. 2 (14): 470. Bibcode:2007HiA....14..470P. doi:10.1017/S1743921307011453.
  12. ^ "INPOP10e, a 4-D planetary ephemeris". IMCCE. Retrieved 2 May 2013.
  13. ^ Viswanathan, V.; Fienga, A.; Gastineau, M.; Laskar, J. (1 August 2017). "INPOP17a planetary ephemerides". Notes Scientifiques et Techniques de l'Institut de Mécanique Céleste. 108: 108. Bibcode:2017NSTIM.108.....V. doi:10.13140/RG.2.2.24384.43521.


  • 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.

External links

Media files used on this page

Crab Nebula.jpg
This is a mosaic image, one of the largest ever taken by NASA's Hubble Space Telescope, of the Crab Nebula, a six-light-year-wide expanding remnant of a star's supernova explosion. Japanese and Chinese astronomers recorded this violent event in 1054 CE, as did, almost certainly, Native Americans.

The orange filaments are the tattered remains of the star and consist mostly of hydrogen. The rapidly spinning neutron star embedded in the center of the nebula is the dynamo powering the nebula's eerie interior bluish glow. The blue light comes from electrons whirling at nearly the speed of light around magnetic field lines from the neutron star. The neutron star, like a lighthouse, ejects twin beams of radiation that appear to pulse 30 times a second due to the neutron star's rotation. A neutron star is the crushed ultra-dense core of the exploded star.

The Crab Nebula derived its name from its appearance in a drawing made by Irish astronomer Lord Rosse in 1844, using a 36-inch telescope. When viewed by Hubble, as well as by large ground-based telescopes such as the European Southern Observatory's Very Large Telescope, the Crab Nebula takes on a more detailed appearance that yields clues into the spectacular demise of a star, 6,500 light-years away.

The newly composed image was assembled from 24 individual Wide Field and Planetary Camera 2 exposures taken in October 1999, January 2000, and December 2000. The colors in the image indicate the different elements that were expelled during the explosion. Blue in the filaments in the outer part of the nebula represents neutral oxygen, green is singly-ionized sulfur, and red indicates doubly-ionized oxygen.
Author/Creator: ESO, European Southern Observatory, Licence: CC BY 4.0
Artist's impression of "the oldest star of our Galaxy": HE 1523-0901
  • About 13.2 billion years old
  • Approximately 7500 light years far from Earth
  • Published as part of Hamburg/ESO Survey in the May 10 2007 issue of The Astrophysical Journal
Author/Creator: Me, Licence: Copyrighted free use
SVG replacement for File:Spaceship and the Sun.jpg. A stylized illustration of a spaceship and the sun, based on the description of the emblem of the fictional Galactic Empire in Isaac Asimov's Foundation series ("The golden globe with its conventionalized rays, and the oblique cigar shape that was a space vessel"). This image could be used as a icon for science-fiction related articles.
Tabla astronómica de Almanach Perpetuum, obra de Abraham Zacut sobre astronomía
Corpus Christ College MS 283 (1).png
A page from Corpus Christ College MS 283.
This view of the rising Earth greeted the Apollo 8 astronauts as they came from behind the Moon after the fourth nearside orbit. Earth is about five degrees above the horizon in the photo. The unnamed surface features in the foreground are near the eastern limb of the Moon as viewed from Earth. The lunar horizon is approximately 780 kilometers from the spacecraft. Width of the photographed area at the horizon is about 175 kilometers. On the Earth 240,000 miles away, the sunset terminator bisects Africa.
Solar system.jpg
This is a montage of planetary images taken by spacecraft managed by the Jet Propulsion Laboratory in Pasadena, CA. Included are (from top to bottom) images of Mercury, Venus, Earth (and Moon), Mars, Jupiter, Saturn, Uranus and Neptune. The spacecraft responsible for these images are as follows:
  • the Mercury image was taken by Mariner 10,
  • the Venus image by Magellan,
  • the Earth and Moon images by Galileo,
  • the Mars image by Mars Global Surveyor,
  • the Jupiter image by Cassini, and
  • the Saturn, Uranus and Neptune images by Voyager.
  • Pluto is not shown as it is no longer a planet, and no spacecraft has yet visited it when this montage was taken. The inner planets (Mercury, Venus, Earth, Moon, and Mars) are roughly to scale to each other; the outer planets (Jupiter, Saturn, Uranus, and Neptune) are roughly to scale to each other. PIA 00545 is the same montage with Neptune shown larger in the foreground. Actual diameters are given below:
  • Sun (to photosphere) 1,392,684 km
  • Mercury 4,879.4 km
  • Venus 12,103.7 km
  • Earth 12,756.28 km
  • Moon 3,476.2 km
  • Mars 6,804.9 km
  • Jupiter 142,984 km
  • Saturn 120,536 km
  • Uranus 51,118 km
  • Neptune 49,528 km