In astronomy and celestial navigation, an ephemeris (plural:
ephemerides; from Latin ephemeris, meaning 'diary', from Greek
εφημερίς (ephemeris), meaning 'diary, journal')
gives the positions of naturally occurring astronomical objects as
well as artificial satellites in the sky at a given time or times.
Historically, positions were given as printed tables of values, given
at regular intervals of date and time. Modern ephemerides are often
computed electronically from mathematical models of the motion of
astronomical objects and the Earth. Even though the calculation of
these tables was one of the first applications of mechanical
computers, 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.
2 Modern ephemeris
3 See also
6 External links
A Latin translation of al-Khwārizmī's zīj, page from Corpus Christi
College MS 283
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 – the
Zīj-i Īlkhānī (Ilkhanic Tables) were compiled
Maragheh observatory in Persia.
13th century – 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.
1408 – Chinese ephemeris table (copy in Pepysian Library, Cambridge,
UK (refer book '1434'); Chinese tables believed known to
1496 – the Almanach Perpetuum of Abraão ben Samuel Zacuto (one of
the first books published with a movable type and printing press in
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.
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
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
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.
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.
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.
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
Global Positioning System
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, and the INPOP
(Intégrateur numérique planétaire de l'Observatoire de Paris) by
the French IMCCE.
Ephemeris and Nautical Almanac
Almanac (new name)
Epoch (reference date)
January 0 or March 0
^ ephemeris 1992.
^ "Liddell & Scott Dictionary on Perseus at University of
^ "Dictionary − ephemeris". Merriam-Webster.
^ "ephemeris". Dictionnaire Gaffiot latin-français.
^ Gingerich, Owen (1975). ""Crisis" versus Aesthetic in the Copernican
Revolution" (PDF). Vistas in Astronomy. Elsevier BV. 17 (1): 85–95.
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
^ 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. 14: 470.
^ "INPOP10e, a 4-D planetary ephemeris". IMCCE. Retrieved 2 May
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
Meeus, Jean (1991). Astronomical Algorithms. Willmann-Bell.
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.
Montenbruck, Oliver (1989). Practical
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.
JPL HORIZONS online ephemeris
Introduction to the
Ab urbe condita
Anno Domini / Common Era
Hindu units of time
Hindu units of time (Yuga)
Canon of Kings
Lists of kings
Pre-Julian / Julian
Old Style and New Style dates
Adoption of the Gregorian calendar
Astronomical year numbering
Chinese sexagenary cycle
ISO week date
Winter count (Plains Indians)
Geological history of Earth
Geological time units
Global Standard Stratigraphic Age (GSSA)
Global Boundary Stratotype Section and Point (GSSP)
Law of superposition
Amino acid racemisation
Terminus post quem
Elliptical / Highly elliptical
Inclined / Non-inclined
Orbit of the Moon
About other points
a Semi-major axis
b Semi-minor axis
Q, q Apsides
Ω Longitude of the ascending node
ω Argument of periapsis
ϖ Longitude of the periapsis
M Mean anomaly
ν, θ, f True anomaly
E Eccentric anomaly
L Mean longitude
l True longitude
T Orbital period
n Mean motion
v Orbital speed
Collision avoidance (spacecraft)
Low energy transfer
Transposition, docking, and extraction
Celestial coordinate system
Equatorial coordinate system
Interplanetary Transport Network
Kepler's laws of planetary motion
Orbital state vectors
Specific orbital energy
Specific relative angular momentum
List of orbits
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