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] }

- 1st millennium BC – Ephemerides in Babylonian astronomy.
- 2nd century AD – the
*Almagest*and the*Handy Tables*of Ptolemy - 8th century AD – the
of Ibrāhīm al-Fazārī*zīj* - 9th century AD – the
of Muḥammad ibn Mūsā al-Khwārizmī*zīj* - 12th century AD – the
*Tables of Toledo*– based largely on Arabicsources of Islamic astronomy – were edited by Gerard of Cremona to form the standard European ephemeris until the*zīj**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.
^{ [7] } - 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."
^{ [8] }

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.^{ [9] }

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.^{ [10] } 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*.^{ [11] }

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,^{ [12] } and the INPOP (* Intégrateur numérique planétaire de l'Observatoire de Paris *) by the French IMCCE.

- Almanac
*American Ephemeris and Nautical Almanac*- The
*Astronomical Almanac*(new name)

- The
- 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

- ↑ ephemeris 1992.
- ↑ ἐφημερίς . Liddell, Henry George ; Scott, Robert ;
*A Greek–English Lexicon*at the Perseus Project. - ↑ "ephemeris".
*Merriam-Webster*. - ↑ "ephemeris".
*Dictionnaire Gaffiot latin-français*. - ↑ 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.**50**: 17–24. doi:10.1007/978-3-319-59909-0_3. ISBN 978-3-319-59909-0. - ↑ Jones, S.S.D.; Howard, John; William, May; Logsdon, Tom; Anderson, Edward; Richey, Michael. "Navigation".
*Encyclopedia Britannica*. Encyclopædia Britannica, inc. Retrieved 13 March 2019. - ↑ Hoskin, Michael (28 November 1996).
*The Cambridge Illustrated History of Astronomy*. Cambridge University Press. p. 89. ISBN 9780521411585. - ↑ 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. - ↑ 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). - ↑
*American Practical Navigator: An Epitiome of Navigation*. Bethesda, MD: National Imagery and Mapping Agency. 2002. p. 270. - ↑ "Almanacs and Other Publications — Naval Oceanography Portal". United States Naval Observatory . Retrieved 11 November 2016.
- ↑ 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 . - ↑ "INPOP10e, a 4-D planetary ephemeris". IMCCE. Retrieved 2 May 2013.
- ↑ 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.

The **ecliptic** is the plane of Earth's orbit around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars. The ecliptic is an important reference plane and is the basis of the ecliptic coordinate system.

The **zodiac** is a belt-shaped region of the sky that extends approximately 8° north or south of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The paths of the Moon and visible planets are within the belt of the zodiac.

In astronomy and navigation, the **celestial sphere** is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, which may be centered on Earth or the observer. If centered on the observer, half of the sphere would resemble a hemispherical screen over the observing location.

The **equatorial coordinate system** is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere, a primary direction towards the vernal equinox, and a right-handed convention.

The **ecliptic coordinate system** is a celestial coordinate system commonly used for representing the apparent positions, orbits, and pole orientations of Solar System objects. Because most planets and many small Solar System bodies have orbits with only slight inclinations to the ecliptic, using it as the fundamental plane is convenient. The system's origin can be the center of either the Sun or Earth, its primary direction is towards the vernal (March) equinox, and it has a right-hand convention. It may be implemented in spherical or rectangular coordinates.

In astronomy, **axial tilt**, also known as **obliquity**, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbital plane. It differs from orbital inclination. At an obliquity of 0 degrees, the two axes point in the same direction; that is, the rotational axis is perpendicular to the orbital plane.

In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the **epicycle** was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. In particular it explained the apparent retrograde motion of the five planets known at the time. Secondarily, it also explained changes in the apparent distances of the planets from the Earth.

**Barycentric Dynamical Time** is a relativistic coordinate time scale, intended for astronomical use as a time standard to take account of time dilation when calculating orbits and astronomical ephemerides of planets, asteroids, comets and interplanetary spacecraft in the Solar System. TDB is now defined as a linear scaling of Barycentric Coordinate Time (TCB). A feature that distinguishes TDB from TCB is that TDB, when observed from the Earth's surface, has a difference from Terrestrial Time (TT) that is about as small as can be practically arranged with consistent definition: the differences are mainly periodic, and overall will remain at less than 2 milliseconds for several millennia.

**Johannes Stöffler** was a German mathematician, astronomer, astrologer, priest, maker of astronomical instruments and professor at the University of Tübingen.

* De revolutionibus orbium coelestium* is the seminal work on the heliocentric theory of the astronomer Nicolaus Copernicus (1473–1543) of the Polish Renaissance. The book, first printed in 1543 in Nuremberg, Holy Roman Empire, offered an alternative model of the universe to Ptolemy's geocentric system, which had been widely accepted since ancient times.

The * Toledan Tables*, or

The * Alfonsine Tables*, sometimes spelled

**Spherical astronomy**, or **positional astronomy**, is a branch of observational astronomy used to locate astronomical objects on the celestial sphere, as seen at a particular date, time, and location on Earth. It relies on the mathematical methods of spherical geometry and the measurements of astrometry.

**Copernican heliocentrism** is the name given to the astronomical model developed by Nicolaus Copernicus and published in 1543. This model positioned the Sun at the center of the Universe, motionless, with Earth and the other planets orbiting around it in circular paths, modified by epicycles, and at uniform speeds. The Copernican model displaced the geocentric model of Ptolemy that had prevailed for centuries, which had placed Earth at the center of the Universe.

The * Prutenic Tables*, were an ephemeris by the astronomer Erasmus Reinhold published in 1551. They are sometimes called the

**Jet Propulsion Laboratory Development Ephemeris** designates one of a series of mathematical models of the Solar System produced at the Jet Propulsion Laboratory in Pasadena, California, for use in spacecraft navigation and astronomy. The models consist of numeric representations of positions, velocities and accelerations of major Solar System bodies, tabulated at equally spaced intervals of time, covering a specified span of years. Barycentric rectangular coordinates of the Sun, eight major planets and Pluto, and geocentric coordinates of the Moon are tabulated.

**Erland Myles Standish Jr.** is a mathematical astronomer largely working in the field of solar system dynamics and celestial mechanics. He is a former professor at Yale University and had worked for the Jet Propulsion Laboratory.

A **tropical year** is the time that the Sun takes to return to the same position in the sky of a celestial body of the Solar System such as the Earth, completing a full cycle of seasons; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice. It is the type of year used by tropical solar calendars. The solar year is one type of astronomical year and particular orbital period. Another type is the sidereal year, which is the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars, resulting in a duration of 20 minutes longer than the tropical year, because of the precession of the equinoxes.

**Johannes Stadius** or **Estadius**, was a Flemish astronomer, astrologer, and mathematician. He was one of the important late 16th-century makers of ephemerides, which gave the positions of astronomical objects in the sky at a given time or times.

A **fundamental ephemeris** of the Solar System is a model of the objects of the system in space, with all of their positions and motions accurately represented. It is intended to be a high-precision primary reference for prediction and observation of those positions and motions, and which provides a basis for further refinement of the model. It is generally not intended to cover the entire life of the Solar System; usually a short-duration time span, perhaps a few centuries, is represented to high accuracy. Some long ephemerides cover several millennia to medium accuracy.

- 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.

Wikimedia Commons has media related to Ephemeris . |

- The JPL HORIZONS online ephemeris
- Introduction to the JPL ephemerides
- "Ephemerides-IMCEE".
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