In astronomy and celestial navigation, an ephemeris (plural: ephemerides) 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, meaning 'diary' and from Greek, Modern εφημερίς (ephemeris), meaning '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 computed electronically, from mathematical models of the motion of astronomical objects and the Earth. However, 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 positions of minor celestial bodies such as Chiron.

Ephemerides are used in celestial navigation and astronomy. They are also used by some astrologers.


Corpus Christ College MS 283 (1)
A Latin translation of al-Khwārizmī's zīj, page from Corpus Christi College MS 283
Page from Almanach Perpetuum

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.

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 for the past 20 years.[7]

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 the Global Positioning System. Software is widely available to assist with this form of navigation; some of this software has a self-contained ephemeris.[8] 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.[9]

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.

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

See also


  1. ^ ephemeris 1992.
  2. ^ "Liddell & Scott Dictionary on Perseus at University of Chicago".
  3. ^ "Dictionary − ephemeris". Merriam-Webster.
  4. ^ "ephemeris". Dictionnaire Gaffiot latin-français.
  5. ^ Jones, S.S.D.; Howard, John; William, May; Logsdon, Tom; Anderson, Edward; Richey, Michael. "Navigation". Encyclopedia Britannica. Encyclopædia Britannica, inc. Retrieved 13 March 2019.
  6. ^ Gingerich, Owen (1975). ""Crisis" versus Aesthetic in the Copernican Revolution" (PDF). Vistas in Astronomy. Elsevier BV. 17 (1): 85–95. Retrieved 23 June 2016.
  7. ^ 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).
  8. ^ American Practical Navigator: An Epitiome of Navigation. Bethesda, MD: National Imagery and Mapping Agency. 2002. p. 270.
  9. ^ "Almanacs and Other Publications — Naval Oceanography Portal". United States Naval Observatory. Retrieved 11 November 2016.
  10. ^ Pitjeva, Elena V. (August 2006). "The dynamical model of the planet motions and EPM ephemerides". Highlights of Astronomy. 14: 470. Bibcode:2007HiA....14..470P. doi:10.1017/S1743921307011453.
  11. ^ "INPOP10e, a 4-D planetary ephemeris". IMCCE. Retrieved 2 May 2013.


  • 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

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 Astronomical Ephemeris, with which it merged to form The Astronomical Almanac, published from the year 1981 to the present.

Astronomical Almanac

The Astronomical Almanac is an almanac published by the United States Naval Observatory (USNO) and Her Majesty's Nautical Almanac Office (HMNAO); it also includes data supplied by many scientists from around the world. It is considered a worldwide resource for fundamental astronomical data, often being the first publication to incorporate new International Astronomical Union resolutions. The almanac largely contains solar system ephemeris and catalogs of selected stellar and extragalactic objects. The material appears in sections, each section addressing a specific astronomical category. The book also includes references to the material, explanations, and examples. It is available one year in advance of its date.

The Astronomical Almanac Online is a companion to the printed volume. It is designed to broaden the scope of the publication, not duplicate the data. In addition to ancillary information, the Astronomical Almanac Online extends the printed version by providing data best presented in machine-readable form.

The Explanatory Supplement to the Astronomical Almanac, currently in its third edition (2013), provides detailed discussion of usage and data reduction methods used by the Almanac. It covers its history, significance, sources, methods of computation, and use of the data. Because the Astronomical Almanac prints primarily positional data, this book goes into great detail on techniques to get astronomical positions. Earlier editions of the supplement were published in 1961 and in 1992.

Barycentric Dynamical Time

Barycentric Dynamical Time (TDB, from the French Temps Dynamique Barycentrique) 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 (since 2006) 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.TDB applies to the Solar-System-barycentric reference frame, and was first defined in 1976 as a successor to the (non-relativistic) former standard of ephemeris time (adopted by the IAU in 1952 and superseded 1976). In 2006, after a history of multiple time-scale definitions and deprecation since the 1970s, a redefinition of TDB was approved by the IAU. The 2006 IAU redefinition of TDB as an international standard expressly acknowledged that the long-established JPL ephemeris time argument Teph, as implemented in JPL Development Ephemeris DE405, "is for practical purposes the same as TDB defined in this Resolution" (By 2006, ephemeris DE405 had already been in use for a few years as the official basis for planetary and lunar ephemerides in the Astronomical Almanac; it was the basis for editions for 2003 through 2014; in the edition for 2015 it is superseded by DE430).

C/2014 E2 (Jacques)

C/2014 E2 (Jacques), provisionally designated as S002692, is a long-period comet discovered by the Brazilian astronomers Cristóvão Jacques Lage de Faria, Eduardo Pimentel and João Ribeiro de Barros on the night of 13 March 2014. It was the second comet discovered by the SONEAR Observatory team after comet C/2014 A4.

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 produce ephemeris data.

Dynamical time scale

In time standards, dynamical time is the time-like argument of a dynamical theory; and a dynamical time scale in this sense is the realization of a time-like argument based on a dynamical theory: that is, the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via a theory of its motion. A first application of this concept of dynamical time was the definition of the ephemeris time scale (ET).In the late 19th century it was suspected, and in the early 20th century it was established, that the rotation of the Earth (i.e. the length of the day) was both irregular on short time scales, and was slowing down on longer time scales. The suggestion was made, that observation of the position of the Moon, Sun and planets and comparison of the observations with their gravitational ephemerides would be a better way to determine a uniform time scale. A detailed proposal of this kind was published in 1948 and adopted by the IAU in 1952 (see Ephemeris time - history).

Using data from Newcomb's Tables of the Sun (based on the theory of the apparent motion of the Sun by Simon Newcomb, 1895, as retrospectively used in the definition of ephemeris time), the SI second was defined in 1960 as:

the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.Caesium atomic clocks became operational in 1955, and their use provided further confirmation that the rotation of the earth fluctuated randomly. This confirmed the unsuitability of the mean solar second of Universal Time as a precision measure of time interval. After three years of comparisons with lunar observations it was determined that the ephemeris second corresponded to 9,192,631,770 ± 20 cycles of the caesium resonance. In 1967/68 the length of the SI second was redefined to be 9,192,631,770 cycles of the caesium resonance, equal to the previous measurement result for the ephemeris second (see Ephemeris time - redefinition of the second).

In 1976, however, the IAU resolved that the theoretical basis for ephemeris time was wholly non-relativistic, and therefore, beginning in 1984 ephemeris time would be replaced by two further time scales with allowance for relativistic corrections. Their names, assigned in 1979, emphasized their dynamical nature or origin, Barycentric Dynamical Time (TDB) and Terrestrial Dynamical Time (TDT). Both were defined for continuity with ET and were based on what had become the standard SI second, which in turn had been derived from the measured second of ET.

During the period 1991–2006, the TDB and TDT time scales were both redefined and replaced, owing to difficulties or inconsistencies in their original definitions. The current fundamental relativistic time scales are Geocentric Coordinate Time (TCG) and Barycentric Coordinate Time (TCB); both of these have rates that are based on the SI second in respective reference frames (and hypothetically outside the relevant gravity well), but on account of relativistic effects, their rates would appear slightly faster when observed at the Earth's surface, and therefore diverge from local earth-based time scales based on the SI second at the Earth's surface. Therefore, the currently defined IAU time scales also include Terrestrial Time (TT) (replacing TDT, and now defined as a re-scaling of TCG, chosen to give TT a rate that matches the SI second when observed at the Earth's surface), and a redefined Barycentric Dynamical Time (TDB), a re-scaling of TCB to give TDB a rate that matches the SI second at the Earth's surface.

Ephemeris time

The term ephemeris time (often abbreviated ET) can in principle refer to time in connection with any astronomical ephemeris. In practice it has been used more specifically to refer to:

a former standard astronomical time scale adopted in 1952 by the IAU, and superseded in the 1970s. This time scale was proposed in 1948, to overcome the drawbacks of irregularly fluctuating mean solar time. The intent was to define a uniform time (as far as was then feasible) based on Newtonian theory (see below: Definition of ephemeris time (1952)). Ephemeris time was a first application of the concept of a dynamical time scale, in which the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via the dynamical theory of its motion.

a modern relativistic coordinate time scale, implemented by the JPL ephemeris time argument Teph, in a series of numerically integrated Development Ephemerides. Among them is the DE405 ephemeris in widespread current use. The time scale represented by Teph is closely related to, but distinct (by an offset and constant rate) from, the TCB time scale currently adopted as a standard by the IAU (see below: JPL ephemeris time argument Teph).Most of the following sections relate to the ephemeris time of the 1952 standard.

An impression has sometimes arisen that ephemeris time was in use from 1900: this probably arose because ET, though proposed and adopted in the period 1948–1952, was defined in detail using formulae that made retrospective use of the epoch date of 1900 January 0 and of Newcomb's Tables of the Sun.The ephemeris time of the 1952 standard leaves a continuing legacy, through its ephemeris second which became closely duplicated in the length of the current standard SI second (see below: Redefinition of the second).

JPL Horizons On-Line Ephemeris System

JPL Horizons On-Line Ephemeris System provides easy access to key Solar System data and flexible production of highly accurate ephemerides for Solar System objects.

Osculating elements at a given epoch are always an approximation to an object's orbit (i.e. an unperturbed conic orbit or a "two-body" orbit). The real orbit (or the best approximation to such) considers perturbations by all planets, a few of the larger asteroids, a few other usually small physical forces, and requires numerical integration.

Jet Propulsion Laboratory (JPL) ephemerides do not use things such as periods, eccentricities, etc. Instead, JPL integrates the equations of motion in Cartesian coordinates (x,y,z), and adjusts the initial conditions in order to fit modern, highly accurate measurements of planetary positions.As of August 2015, Horizons now uses ephemeris DE431.

JPL Small-Body Database

The JPL Small-Body Database (SBDB) is an astronomy database about small Solar System bodies. It is maintained by Jet Propulsion Laboratory (JPL) and NASA and provides data for all known asteroids and several comets, including orbital parameters and diagrams, physical diagrams, and lists of publications related to the small body. The database is updated on a daily basis.

Jet Propulsion Laboratory Development Ephemeris

The name Jet Propulsion Laboratory Development Ephemeris (followed by a number), the abbreviation JPL DE(number), or just DE(number) designates one of a series of models of the Solar System produced at the Jet Propulsion Laboratory in Pasadena, California, primarily for purposes of spacecraft navigation and astronomy. The models consist of computer 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.

DE405, created in May 1997, include both nutations and librations, and is considered the fundamental planetary and lunar ephemerides of The Astronomical Almanac. It is very large at 62.4 Megabytes, so smaller, more targeted versions have been created based on DE405.

List of non-standard dates

There are several non-standard dates that are used in calendars. Some are used sarcastically, some for scientific or mathematical purposes, and some for exceptional or fictional calendars.

Paul Herget

Paul Herget (January 30, 1908 – August 27, 1981) was an American astronomer.Herget taught astronomy at the University of Cincinnati. He was a pioneer in the use of machine methods, and eventually digital computers, in the solving of scientific and specifically astronomical problems (for example, in the calculation of ephemeris tables for minor planets). The asteroid 1751 Herget is named in his honour, while 1755 Lorbach was named for his wife.During World War II he applied these same talents to the war effort, helping to locate U-boats by means of the application of spherical trigonometry.

Herget established the Minor Planet Center at the university after the war in 1947. He was also named director of the Cincinnati Observatory. The Minor Planet Center was eventually relocated in 1978 to the Smithsonian Astrophysical Observatory in Cambridge, Massachusetts, where it still operates.


The second (symbol: s) is the base unit of time in the International System of Units (SI), commonly understood and historically defined as ​1⁄86400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each. Analog clocks and watches often have sixty tick marks on their faces, representing seconds, and a "second hand" to mark the passage of time in seconds. Digital clocks and watches often have a two-digit seconds counter. The second is also part of several other units of measurement like meters per second for velocity, meters per second per second for acceleration, and per second for frequency.

Although the historical definition of the unit was based on this division of the Earth's rotation cycle, the formal definition in the International System of Units (SI) is a much steadier timekeeper: it is defined by taking the fixed numerical value of the caesium frequency ∆νCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s−1.

Because the Earth's rotation varies and is also slowing ever so slightly, a leap second is periodically added to clock time to keep clocks in sync with Earth's rotation.

Multiples of seconds are usually counted in hours and minutes. Fractions of a second are usually counted in tenths or hundredths. In scientific work, small fractions of a second are counted in milliseconds (thousandths), microseconds (millionths), nanoseconds (billionths), and sometimes smaller units of a second. An everyday experience with small fractions of a second is a 1-gigahertz microprocessor which has a cycle time of 1 nanosecond. Camera shutter speeds are often expressed in fractions of a second, such as ​1⁄30 second or ​1⁄1000 second.

Sexagesimal divisions of the day from a calendar based on astronomical observation have existed since the third millennium BC, though they were not seconds as we know them today. Small divisions of time could not be counted back then, so such divisions were figurative. The first timekeepers that could count seconds accurately were pendulum clocks invented in the 17th century. Starting in the 1950s, atomic clocks became better timekeepers than earth's rotation, and they continue to set the standard today.

Terrestrial Time

Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth.

For example, the Astronomical Almanac uses TT for its tables of positions (ephemerides) of the Sun, Moon and planets as seen from Earth. In this role, TT continues Terrestrial Dynamical Time (TDT or TD), which in turn succeeded ephemeris time (ET). TT shares the original purpose for which ET was designed, to be free of the irregularities in the rotation of Earth.

The unit of TT is the SI second, the definition of which is currently based on the caesium atomic clock, but TT is not itself defined by atomic clocks. It is a theoretical ideal, and real clocks can only approximate it.

TT is distinct from the time scale often used as a basis for civil purposes, Coordinated Universal Time (UTC). TT indirectly underlies UTC, via International Atomic Time (TAI). Because of the historical difference between TAI and ET when TT was introduced, TT is approximately 32.184 s ahead of TAI.

The Nautical Almanac

The Nautical Almanac has been the familiar name for a series of official British almanacs published under various titles since the first issue of The Nautical Almanac and Astronomical Ephemeris, for 1767: this was the first nautical almanac to contain data dedicated to the convenient determination of longitude at sea. It was originally published from the Royal Greenwich Observatory in England. A detailed account of how the publication was produced in its earliest years has been published by the National Maritime Museum.Since 1958 (with the issue for the year 1960), Her Majesty's Nautical Almanac Office and the US Naval Observatory have jointly published a unified Nautical Almanac, for use by the navies of both countries.

Time standard

A time standard is a specification for measuring time: either the rate at which time passes; or points in time; or both. In modern times, several time specifications have been officially recognized as standards, where formerly they were matters of custom and practice. An example of a kind of time standard can be a time scale, specifying a method for measuring divisions of time. A standard for civil time can specify both time intervals and time-of-day.

Standardized time measurements are made using a clock to count periods of some period changes, which may be either the changes of a natural phenomenon or of an artificial machine.

Historically, time standards were often based on the Earth's rotational period. From the late 18 century to the 19th century it was assumed that the Earth's daily rotational rate was constant. Astronomical observations of several kinds, including eclipse records, studied in the 19th century, raised suspicions that the rate at which Earth rotates is gradually slowing and also shows small-scale irregularities, and this was confirmed in the early twentieth century. Time standards based on Earth rotation were replaced (or initially supplemented) for astronomical use from 1952 onwards by an ephemeris time standard based on the Earth's orbital period and in practice on the motion of the Moon. The invention in 1955 of the caesium atomic clock has led to the replacement of older and purely astronomical time standards, for most practical purposes, by newer time standards based wholly or partly on atomic time.

Various types of second and day are used as the basic time interval for most time scales. Other intervals of time (minutes, hours, and years) are usually defined in terms of these two.

Tropical year

A tropical year (also known as a solar year) is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice. Because of the precession of the equinoxes, the seasonal cycle does not remain exactly synchronized with the position of the Earth in its orbit around the Sun. As a consequence, the tropical year is about 20 minutes shorter than the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars (the sidereal year).

Since antiquity, astronomers have progressively refined the definition of the tropical year. The entry for "year, tropical" in the Astronomical Almanac Online Glossary (2015) states:

the period of time for the ecliptic longitude of the Sun to increase 360 degrees. Since the Sun's ecliptic longitude is measured with respect to the equinox, the tropical year comprises a complete cycle of seasons, and its length is approximated in the long term by the civil (Gregorian) calendar. The mean tropical year is approximately 365 days, 5 hours, 48 minutes, 45 seconds.

An equivalent, more descriptive, definition is "The natural basis for computing passing tropical years is the mean longitude of the Sun reckoned from the precessionally moving equinox (the dynamical equinox or equinox of date). Whenever the longitude reaches a multiple of 360 degrees the mean Sun crosses the vernal equinox and a new tropical year begins" (Borkowski 1991, p. 122).

The mean tropical year in 2000 was 365.24219 ephemeris days; each ephemeris day lasting 86,400 SI seconds. This is 365.24217 mean solar days (Richards 2013, p. 587).


In precise timekeeping, ΔT (Delta T, delta-T, deltaT, or DT) is a measure of the cumulative effect of the departure of the Earth's rotation period from the fixed-length day of atomic time. Formally it is the time difference obtained by subtracting Universal Time (UT, defined by the Earth's rotation) from Terrestrial Time (TT, independent of the Earth's rotation): ΔT = TT − UT. The value of ΔT for the start of 1902 is approximately zero; for 2002 it is about 64 seconds. So the Earth's rotations over that century took about 64 seconds longer than would be required for days of atomic time.

Key topics
Astronomic time
Geologic time
Genetic methods
Linguistic methods
Related topics
Gravitational orbits
Orbital mechanics

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