Astronomical Ephemeris
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In
astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
and
celestial navigation Celestial navigation, also known as astronavigation, is the practice of position fixing using stars and other celestial bodies that enables a navigator to accurately determine their actual current physical position in space (or on the surface ...
, an ephemeris (pl. ephemerides; ) is a book with tables that gives the
trajectory A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete ...
of naturally occurring
astronomical objects An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often use ...
as well as
artificial satellites A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisotope ...
in the
sky The sky is an unobstructed view upward from the surface of the Earth. It includes the atmosphere and outer space. It may also be considered a place between the ground and outer space, thus distinct from outer space. In the field of astronomy, ...
, i.e., the
position Position often refers to: * Position (geometry), the spatial location (rather than orientation) of an entity * Position, a job or occupation Position may also refer to: Games and recreation * Position (poker), location relative to the dealer * ...
(and possibly
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...
) over
time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, t ...
. 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 computer A mechanical computer is a computer built from mechanical components such as levers and gears rather than electronic components. The most common examples are adding machines and mechanical counters, which use the turning of gears to incremen ...
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 polar coordinate system of
right ascension Right ascension (abbreviated RA; symbol ) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the ( hour circle of the) point in question above the earth. When pai ...
and
declination In astronomy, declination (abbreviated dec; symbol ''δ'') is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declination's angle is measured north or south of t ...
, together with the distance from the origin if applicable. Some of the astronomical phenomena of interest to astronomers are
eclipse An eclipse is an astronomical event that occurs when an astronomical object or spacecraft is temporarily obscured, by passing into the shadow of another body or by having another body pass between it and the viewer. This alignment of three ce ...
s,
apparent retrograde motion Apparent retrograde motion is the apparent motion of a planet in a direction opposite to that of other bodies within its system, as observed from a particular vantage point. Direct motion or prograde motion is motion in the same direction as ...
/planetary stations, planetary es,
sidereal time Sidereal time (as a unit also sidereal day or sidereal rotation period) (sidereal ) is a timekeeping system that astronomers use to locate celestial objects. Using sidereal time, it is possible to easily point a telescope to the proper coor ...
, positions for the mean and true nodes of the moon, the
phases of the Moon Concerning the lunar month of ~29.53 days as viewed from Earth, the lunar phase or Moon phase is the shape of the Moon's directly sunlit portion, which can be expressed quantitatively using areas or angles, or described qualitatively using the t ...
, and the positions of minor
celestial bodies An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...
such as
Chiron In Greek mythology, Chiron ( ; also Cheiron or Kheiron; ) was held to be the superlative centaur amongst his brethren since he was called the "wisest and justest of all the centaurs". Biography Chiron was notable throughout Greek mythology ...
. Ephemerides are used in celestial navigation and astronomy. They are also used by
astrologers Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Di ...
.


History

*1st millennium BC – Ephemerides in
Babylonian astronomy Babylonian astronomy was the study or recording of celestial objects during the early history of Mesopotamia. Babylonian astronomy seemed to have focused on a select group of stars and constellations known as Ziqpu stars. These constellations ...
. *2nd century AD – the ''Almagest'' and the ''Handy Tables'' of
Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of import ...
*8th century AD – the ' of
Ibrāhīm al-Fazārī Ibrahim ibn Habib ibn Sulayman ibn Samura ibn Jundab al-Fazari () (died 777 CE) was an 8th-century Muslim mathematician and astronomer at the Abbasid court of the Caliph Al-Mansur (r. 754–775). He should not to be confused with his son Mu ...
*9th century AD – the ' of
Muḥammad ibn Mūsā al-Khwārizmī Muhammad ( ar, مُحَمَّد;  570 – 8 June 632 CE) was an Arab religious, social, and political leader and the founder of Islam. According to Islamic doctrine, he was a prophet divinely inspired to preach and confirm the monot ...
*12th century AD – the ''
Tables of Toledo The ''Toledan Tables'', or ''Tables of Toledo'', were astronomical tables which were used to predict the movements of the Sun, Moon and planets relative to the fixed stars. They were a collection of mathematic tables that describe different aspec ...
'' – based largely on Arabic ' sources of
Islamic astronomy Islamic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age (9th–13th centuries), and mostly written in the Arabic language. These developments mostly took place in the Middle ...
– were edited by
Gerard of Cremona Gerard of Cremona (Latin: ''Gerardus Cremonensis''; c. 1114 – 1187) was an Italian translator of scientific books from Arabic into Latin. He worked in Toledo, Kingdom of Castile and obtained the Arabic books in the libraries at Toledo. Some of ...
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 The Maragheh observatory ( Persian: رصدخانه مراغه), also spelled Maragha, Maragah, Marageh, and Maraga, was an astronomical observatory established in the mid 13th century under the patronage of the Ilkhanid Hulagu and the directorshi ...
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 The ''Dresden Codex'' is a Maya book, which was believed to be the oldest surviving book written in the Americas, dating to the 11th or 12th century. However, in September 2018 it was proven that the Maya Codex of Mexico, previously known as t ...
'', an extant Mayan ephemeris *1408 – Chinese ephemeris table (copy in Pepysian Library, Cambridge, UK (refer book '1434'); Chinese tables believed known to
Regiomontanus Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), better known as Regiomontanus (), was a mathematician, astrologer and astronomer of the German Renaissance, active in Vienna, Buda and Nuremberg. His contributions were instrumental ...
). *1474 –
Regiomontanus Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), better known as Regiomontanus (), was a mathematician, astrologer and astronomer of the German Renaissance, active in Vienna, Buda and Nuremberg. His contributions were instrumental ...
publishes his day-to-day Ephemerides in Nürnberg, Germany. *1496 – the ''Almanach Perpetuum'' of Abraão ben Samuel Zacuto (one of the first books published with a
movable type Movable type (US English; moveable type in British English) is the system and technology of printing and typography that uses movable components to reproduce the elements of a document (usually individual alphanumeric characters or punctuatio ...
and
printing press A printing press is a mechanical device for applying pressure to an inked surface resting upon a print medium (such as paper or cloth), thereby transferring the ink. It marked a dramatic improvement on earlier printing methods in which the ...
in
Portugal Portugal, officially the Portuguese Republic, In recognized minority languages of Portugal: :* mwl, República Pertuesa is a country located on the Iberian Peninsula, in Southwestern Europe, and whose territory also includes the Macaronesian ...
) *1504 – While shipwrecked on the island of Jamaica,
Christopher Columbus Christopher Columbus * lij, Cristoffa C(or)ombo * es, link=no, Cristóbal Colón * pt, Cristóvão Colombo * ca, Cristòfor (or ) * la, Christophorus Columbus. (; born between 25 August and 31 October 1451, died 20 May 1506) was a ...
successfully predicted a lunar eclipse for the natives, using the ephemeris of the German astronomer
Regiomontanus Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), better known as Regiomontanus (), was a mathematician, astrologer and astronomer of the German Renaissance, active in Vienna, Buda and Nuremberg. His contributions were instrumental ...
. *1531 – Work of Johannes Stöffler is published posthumously at Tübingen, extending the ephemeris of Regiomontanus through 1551. *1551 – the '' Prutenic Tables'' of
Erasmus Reinhold Erasmus Reinhold (22 October 1511 – 19 February 1553) was a German astronomer and mathematician, considered to be the most influential astronomical pedagogue of his generation. He was born and died in Saalfeld, Saxony. He was educated, und ...
were published, based on
Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formula ...
's theories. *1554 – Johannes Stadius published ''Ephemerides novae et auctae'', the first major ephemeris computed according to Copernicus'
heliocentric model Heliocentrism (also known as the Heliocentric model) is the astronomical model in which the Earth and planets revolve around the Sun at the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth a ...
, 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 Equant (or punctum aequans) is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of the planets. The equant is used to explain the observed speed change in different stages of the plan ...
and better explained the
apparent retrograde motion Apparent retrograde motion is the apparent motion of a planet in a direction opposite to that of other bodies within its system, as observed from a particular vantage point. Direct motion or prograde motion is motion in the same direction as ...
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 Tycho Brahe ( ; born Tyge Ottesen Brahe; generally called Tycho (14 December 154624 October 1601) was a Danish astronomer, known for his comprehensive astronomical observations, generally considered to be the most accurate of his time. He was ...
. *1627 – the ''
Rudolphine Tables The ''Rudolphine Tables'' ( la, Tabulae Rudolphinae) consist of a star catalogue and planetary tables published by Johannes Kepler in 1627, using observational data collected by Tycho Brahe (1546–1601). The tables are named in memory of Rudolf ...
'' of Johannes Kepler based on elliptical planetary motion became the new standard. *1679 – ''La
Connaissance des Temps The ''Connaissance des temps'' (English: Knowledge of the Times) is an official yearly publication of astronomical ephemerides in France. Until just after the French Revolution The French Revolution ( ) was a period of radical politic ...
ou calendrier et éphémérides du lever & coucher du Soleil, de la Lune & des autres planètes'', first published yearly by
Jean Picard Jean Picard (21 July 1620 – 12 July 1682) was a French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand. He is principally notable for his accurate measure of the size of the Earth, ba ...
and still extant. *1975 –
Owen Gingerich Owen Jay Gingerich (; born 1930) is professor emeritus of astronomy and of the history of science at Harvard University and a senior astronomer emeritus at the Smithsonian Astrophysical Observatory. In addition to his research and teaching, he has ...
, 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 Michael Maestlin (also Mästlin, Möstlin, or Moestlin) (30 September 1550 – 26 October 1631) was a German astronomer and mathematician, known for being the mentor of Johannes Kepler. He was a student of Philipp Apian and was known as the teac ...
, Magini, Origanus, and others who followed the Copernican parameters."


Modern ephemeris

For scientific uses, a modern planetary ephemeris comprises software that generates positions of planets and often of their satellites,
asteroid An asteroid is a minor planet of the Solar System#Inner solar system, inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic o ...
s, or
comet A comet is an icy, small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process that is called outgassing. This produces a visible atmosphere or Coma (cometary), coma, and sometimes also a Comet ta ...
s, at virtually any time desired by the user. After introduction of computers in the 1950's it became feasible to use
numerical integration In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations ...
to compute ephemerides. The
Jet Propulsion Laboratory Development Ephemeris Jet Propulsion Laboratory Development Ephemeris (abbreved JPL DE(number), or simply DE(number)) designates one of a series of mathematical models of the Solar System produced at the Jet Propulsion Laboratory in Pasadena, California, for use in space ...
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 Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
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
asteroid An asteroid is a minor planet of the Solar System#Inner solar system, inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic o ...
s, most of whose masses and orbits are poorly known, rendering their effect uncertain. Reflecting the continuing influx of new data and observations,
NASA The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research. NASA was established in 1958, succeedi ...
's Jet Propulsion Laboratory ( JPL) has revised its published ephemerides nearly every year since 1981.
Solar System The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...
ephemerides are essential for the navigation of
spacecraft A spacecraft is a vehicle or machine designed to spaceflight, fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including Telecommunications, communications, Earth observation satellite, Earth ...
and for all kinds of space observations of the
planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a ...
s, their
natural satellite A natural satellite is, in the most common usage, an astronomical body that orbits a planet, dwarf planet, or small Solar System body (or sometimes another natural satellite). Natural satellites are often colloquially referred to as ''moons ...
s,
star A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth make ...
s, and
galaxies A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System. ...
. Scientific ephemerides for sky observers mostly contain the positions of celestial bodies in
right ascension Right ascension (abbreviated RA; symbol ) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the ( hour circle of the) point in question above the earth. When pai ...
and
declination In astronomy, declination (abbreviated dec; symbol ''δ'') is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declination's angle is measured north or south of t ...
, because these coordinates are the most frequently used on star maps and telescopes. The
equinox A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears zenith, directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" ...
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 In astronomy, an epoch or reference epoch is a moment in time used as a reference point for some time-varying astronomical quantity. It is useful for the celestial coordinates or orbital elements of a celestial body, as they are subject to pertu ...
, 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 Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; ...
also sometimes contain the apparent inclination of its ring.
Celestial navigation Celestial navigation, also known as astronavigation, is the practice of position fixing using stars and other celestial bodies that enables a navigator to accurately determine their actual current physical position in space (or on the surface ...
serves as a backup to
Satellite navigation A satellite navigation or satnav system is a system that uses satellites to provide autonomous geo-spatial positioning. It allows satellite navigation devices to determine their location ( longitude, latitude, and altitude/ elevation) to hi ...
. Software is widely available to assist with this form of navigation; some of this software has a self-contained ephemeris. 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 A nautical almanac is a publication describing the positions of a selection of celestial bodies for the purpose of enabling navigators to use celestial navigation to determine the position of their ship while at sea. The Almanac specifies for eac ...
'' or ''Air Almanac''. 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 An asteroid is a minor planet of the Solar System#Inner solar system, inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic o ...
s or the
Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width ...
, 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 The Russian Academy of Sciences (RAS; russian: Росси́йская акаде́мия нау́к (РАН) ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across t ...
, and the INPOP (') by the French IMCCE.


See also

*
Almanac An almanac (also spelled ''almanack'' and ''almanach'') is an annual publication listing a set of current information about one or multiple subjects. It includes information like weather forecasts, farmers' planting dates, tide tables, and othe ...
* ''
American Ephemeris and Nautical Almanac ''The American Ephemeris and Nautical Almanac'' was published for the years 1855 to 1980, containing information necessary for astronomers, surveyors, and navigators. It was based on the original British publication, '' The Nautical Almanac and Ast ...
'' ** The ''
Astronomical Almanac ''The Astronomical Almanac''The ''Astronomical Almanac'' for the Year 2015, (United States Naval Observatory/Nautical Almanac Office, 2014) . is an almanac published by the United States Naval Observatory (USNO) and His Majesty's Nautical Almana ...
'' (new name) *
Ephemera Ephemera are transitory creations which are not meant to be retained or preserved. Its etymological origins extends to Ancient Greece, with the common definition of the word being: "the minor transient documents of everyday life". Ambiguous in ...
* Ephemeris time *
Epoch (astronomy) In astronomy, an epoch or reference epoch is a moment in time used as a reference point for some time-varying astronomical quantity. It is useful for the celestial coordinates or orbital elements of a celestial body, as they are subject to per ...
*
Epoch (reference date) In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured. The moment of epoch is usually decided ...
* Fundamental ephemeris * January 0 or March 0 * Keplerian elements *
Nautical almanac A nautical almanac is a publication describing the positions of a selection of celestial bodies for the purpose of enabling navigators to use celestial navigation to determine the position of their ship while at sea. The Almanac specifies for eac ...
*
Osculating orbit In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space at a given moment in time is the gravitational Kepler orbit (i.e. an elliptic or other conic one) that it would have around its central body if perturb ...
*
Ptolemy's table of chords The table of chords, created by the Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's ''Almagest'', a treatise on mathematical astronomy. ...
* Two-line elements *
William of Saint-Cloud William of Saint-Cloud is a French astronomer in the late thirteenth century. He is known for his Almanac prepared around 1292, dedicated to Marie of Brabant, and translated for Joan of Navarre. This almanac, one of the rare witness of astronomical ...


Notes


References

* * * * * * * *


External links


The JPL HORIZONS online ephemerisIntroduction to the JPL ephemerides
* {{Authority control Astronomical tables Astrometry Astronomy books Calendars Celestial navigation