View source for Ephemeris

{{short description|Table of positions of astronomical objects at given times}}
{{For|the 18th-century Greek newspaper|Efimeris{{!}}''Efimeris''}}
{{Use dmy dates|date=November 2016}}

In [[astronomy]] and [[celestial navigation]], an '''ephemeris''' ({{IPAc-en|ɪ|ˈ|f|ɛ|m|ər|ɪ|s}}; {{plural form|'''ephemerides'''}} {{IPAc-en|ˌ|ɛ|f|ə|ˈ|m|ɛr|ɪ|ˌ|d|iː|z}}; {{etymology|la|{{wikt-lang|la|ephemeris}}|diary}}, {{etymology|grc|''{{wikt-lang|grc|ἐφημερίς}}'' ({{grc-transl|ἐφημερίς}})|diary, journal}})<ref>{{LSJ|e)fhmeri/s|ἐφημερίς|cite}}.</ref><ref>{{cite Merriam-Webster|ephemeris}}</ref><ref>{{cite web |title=ephemeris |url=https://lexilogos.com/latin/gaffiot.php?q=ephemeris |website=Dictionnaire Gaffiot latin-français}}</ref> is a book with tables that gives the [[trajectory]] of naturally occurring [[astronomical object]]s and [[artificial satellite]]s in the [[sky]], i.e., the [[apparent place|position]] (and possibly [[velocity]]) over [[time]]. 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 [[history of computing|first applications]] of [[mechanical computer]]s. 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 coordinate system|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 [[eclipse]]s, [[apparent retrograde motion]]/planetary stations, planetary {{linktext|ingress}}es, [[sidereal time]], positions for the mean and true [[Lunar node|nodes of the moon]], the [[phases of the Moon]], and the positions of minor [[celestial bodies]] such as [[2060 Chiron|Chiron]].

Ephemerides are used in celestial navigation and astronomy. They are also used by [[Astrology|astrologers]].<ref>{{Cite journal |last=Gingerich |first=Owen |date=2017 |editor-last=Arias |editor-first=Elisa Felicitas |editor2-last=Combrinck |editor2-first=Ludwig |editor3-last=Gabor |editor3-first=Pavel |editor4-last=Hohenkerk |editor4-first=Catherine |editor5-last=Seidelmann |editor5-first=P. Kenneth |title=The Role of Ephemerides from Ptolemy to Kepler   |url=https://link.springer.com/chapter/10.1007%2F978-3-319-59909-0_3  |journal=The Science of Time 2016 |series=Astrophysics and Space Science Proceedings |volume=50 |language=en |location=Cham |publisher=Springer International Publishing |pages=17–24 |doi=10.1007/978-3-319-59909-0_3 |bibcode=2017ASSP...50...17G |isbn=978-3-319-59909-0|url-access=subscription }}</ref> [[GPS signals]] include ephemeris data used to calculate the position of satellites in orbit.

== History ==
[[Image:Corpus Christ College MS 283 (1).png|thumb|A Latin translation of [[al-Khwārizmī]]'s ''{{Transliteration|ar|zīj}}'', page from [[Corpus Christi College, Cambridge|Corpus Christi College]] MS 283]]
[[Image:Tablas alfonsies.jpg|thumb|[[Alfonsine tables]]]]
[[Image:AlmanachPerpetuum.jpg|thumb|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 ''{{Transliteration|ar|[[zīj]]}}'' of [[Ibrāhīm al-Fazārī]]
*9th century AD – the ''{{Transliteration|ar|zīj}}'' of [[Muḥammad ibn Mūsā al-Khwārizmī]]
*11th century AD – the ''{{Transliteration|ar|zīj}}'' of [[Ibn Yunus]]
*12th century AD – the ''[[Tables of Toledo]]'' – based largely on Arabic ''{{Transliteration|ar|zīj}}'' sources of [[Astronomy in medieval Islam|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 astronomy|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.<ref>{{cite web |last1=Jones |first1=S.S.D. |last2=Howard |first2=John |last3=William |first3=May |last4=Logsdon |first4=Tom |last5=Anderson |first5=Edward |last6=Richey |first6=Michael |title=Navigation |url=https://www.britannica.com/technology/navigation-technology |website=Encyclopedia Britannica |publisher=Encyclopædia Britannica, inc. |access-date=13 March 2019}}</ref>     
*1496 – the ''Almanach Perpetuum'' of [[Abraham Zacuto|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]].<ref>{{cite book |last=Hoskin |first=Michael |url=https://books.google.com/books?id=rH1iQgAACAAJ |title=The Cambridge Illustrated History of Astronomy |date=28 November 1996 |publisher=Cambridge University Press |pages=89|isbn=9780521411585 }}</ref>
*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]], [[Giovanni Antonio Magini|Magini]], [[David Origanus|Origanus]], and others who followed the Copernican parameters."<ref>{{cite journal |last=Gingerich |first=Owen |date=1975 |title="Crisis" versus Aesthetic in the Copernican Revolution |url=https://dash.harvard.edu/bitstream/handle/1/4258973/Crisis%20vs%20Aesthetic%20OGingrich.pdf |journal=Vistas in Astronomy |publisher=[[Elsevier BV]] |volume=17 |issue=1 |pages=85–95 |doi=10.1016/0083-6656(75)90050-1 |bibcode=1975VA.....17...85G |s2cid=20888261 |access-date=23 June 2016}}</ref>

== Modern ephemeris ==
For scientific uses, a modern planetary ephemeris comprises software that generates positions of planets and often of their satellites, [[asteroid]]s, or [[comet]]s, at virtually any time desired by the user.

After introduction of electronic computers in the 1950s 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 (planets)|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 variation|secular phenomena]] which cannot adequately be considered by ephemerides. The greatest uncertainties in the positions of planets are caused by the perturbations of numerous [[asteroid]]s, 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 [[Jet Propulsion Laboratory Development Ephemeris|published ephemerides]] nearly every year since 1981.<ref>[[Georgij A. Krasinsky]] and [[Victor A. Brumberg]], ''Secular Increase of Astronomical Unit from Analysis of the Major Planet Motions, and its Interpretation'' [https://link.springer.com/article/10.1007/s10569-004-0633-z Celestial Mechanics and Dynamical Astronomy 90: 267–288, (2004)].</ref>

[[Solar System]] ephemerides are essential for the navigation of [[spacecraft]] and for all kinds of space observations of the [[planet]]s, their [[natural satellite]]s, [[star]]s, and [[Galaxy|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 (celestial coordinates)|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.<ref>{{cite book | title = American Practical Navigator: An Epitiome of Navigation | date = 2002 | page = 270 | publisher = National Imagery and Mapping Agency | location = Bethesda, MD | url = http://msi.nga.mil/NGAPortal/MSI.portal?_nfpb=true&_pageLabel=msi_portal_page_62&pubCode=0002}}</ref> 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''.<ref>{{Cite web| title = Almanacs and Other Publications — Naval Oceanography Portal| access-date = 11 November 2016| url = http://www.usno.navy.mil/USNO/astronomical-applications/publications| publisher = [[United States Naval Observatory]]| archive-date = 27 January 2022| archive-url = https://web.archive.org/web/20220127194119/https://www.usno.navy.mil/USNO/astronomical-applications/publications| url-status = dead}}</ref>

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 [[asteroid]]s 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]],<ref>{{cite journal|last=Pitjeva|first=Elena V.|title=The dynamical model of the planet motions and EPM ephemerides|journal=Highlights of Astronomy|date=August 2006|volume=2|issue=14|pages=470|doi=10.1017/S1743921307011453|bibcode=2007HiA....14..470P|doi-access=free}}</ref> and the INPOP (''{{lang|fr|Intégrateur numérique planétaire de l'[[Observatoire de Paris]]}}'') by the French [[IMCCE]].<ref>{{cite web|title=INPOP10e, a 4-D planetary ephemeris|url=http://www.imcce.fr/inpop/|publisher=IMCCE|access-date=2 May 2013}}</ref><ref>{{cite journal |last1=Viswanathan |first1=V. |last2=Fienga |first2=A. |last3=Gastineau |first3=M. |last4=Laskar |first4=J. |title=INPOP17a planetary ephemerides |journal=Notes Scientifiques et Techniques de l'Institut de Mécanique Céleste |date=1 August 2017 |volume=108 |pages=108 |doi=10.13140/RG.2.2.24384.43521 |bibcode=2017NSTIM.108.....V }}</ref>

== See also ==
{{Div col|colwidth=26em}}
* [[Almanac]]
* ''[[American Ephemeris and Nautical Almanac]]''
** The ''[[Astronomical Almanac]]'' (new name)
* [[Ephemera]]
* [[Ephemeris time]]
* [[Epoch (astronomy)]]
* [[Epoch (reference date)]]
* [[Fundamental ephemeris]]
* [[January 0]] or [[March 0]]
* [[Keplerian elements]]
* [[Nautical almanac]]
* [[Osculating orbit]]
* [[Ptolemy's table of chords]]
* [[Two-line elements]]
* [[William of Saint-Cloud]]
{{Div col end}}

== Notes ==
{{Reflist}}

== References ==
* {{cite book
 | first = Peter | last = Duffett-Smith
 | title = Astronomy With Your Personal Computer
 | publisher = [[Cambridge University Press]]
 | year = 1990
 | isbn = 0-521-38995-X}}
* {{cite dictionary
 | year = 1992
 | title = ephemeris
 | encyclopedia = American Heritage Dictionary of the English Language
 | edition = 3rd
 | publisher = [[Houghton Mifflin]]
 | location = Boston
 | ref = {{harvid|ephemeris|1992}}
}}
* {{cite book
 | first = Hugh | last = MacCraig
 | title = The 200 Year Ephemeris
 | publisher = Macoy Publishing Company
 | year = 1949}}
* {{cite book
 | first = Jean | last = Meeus
 | title = Astronomical Algorithms
 | publisher = Willmann-Bell
 | year = 1991
 | isbn = 0-943396-35-2}}
* {{cite book
 | first = Neil F. | last = Michelsen
 | title = Tables of Planetary Phenomena
 | publisher = ACS Publications, Inc.
 | year = 1990
 | isbn = 0-935127-08-9}}
* {{cite book
 | first = Neil F. | last = Michelsen
 | title = The American Ephemeris for the 21st Century - 2001 to 2100 at Midnight
 | publisher = Astro Computing Services
 | year = 1982
 | isbn = 0-917086-50-3 }}
* {{cite book
 | first = Oliver | last = Montenbruck
 | title = Practical Ephemeris Calculations
 | publisher = [[Springer-Verlag]]
 | year = 1989
 | isbn = 0-387-50704-3 }}
* {{cite book
 | first = Kenneth
 | last = Seidelmann
 | title = Explanatory supplement to the astronomical almanac
 | publisher = University Science Books
 | year = 2006
 | isbn = 1-891389-45-9
 | url-access = registration
 | url = https://archive.org/details/explanatorysuppl00pken
 }}

== External links ==
{{commons}}
*[http://ssd.jpl.nasa.gov/?horizons The JPL HORIZONS online ephemeris]
*[https://web.archive.org/web/20050226015740/http://ssd.jpl.nasa.gov/iau-comm4/README Introduction to the JPL ephemerides] (archived 26 February 2005)
*{{Cite web|title=Ephemerides-IMCEE|url=https://www.imcce.fr/services/ephemerides/|access-date=|website=}}

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[[Category:Astrology]]
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