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An ephemeris (plural: ephemerides) (from the Greek word ephemeros = daily) is a table of values that gives the positions of astronomical objects in the sky at a given time or times. Different kinds are used for astronomy and astrology. Even though this was also one of the first applications of mechanical computers, an ephemeris will still often be a simple printed table.

The position is given to astronomers in a Spherical polar coordinate system of right ascension and declination or to astrologer in longitude along the zodiacal ecliptic, and sometimes declination. Astrological positions may be given for either noon or midnight.

An ephemeris may also provide data on astronomical phenomena of interest to astrologers and astronomers such as eclipses, apparent retrogradation/planetary stations, planetary ingresses, sidereal time, positions for the Mean and True nodes of the moon, the phases of the Moon, and sometimes even the position(s) of Chiron, Lilith, and other minor or imaginary celestial bodies. Some ephemerides also contain a monthly aspectarian, while others often include the declination of the planets as well as their longitudes, right ascensions or Cartesian coordinates.

Contents 1 History 2 Scientific ephemeris 3 Astrological ephemeris 4 References 5 See also 6 External links

In 1554, Johannes Stadius published a well-known work known as Ephemerides novae at auctae that attempted to give accurate planetary positions. The effort was not entirely successful, and there were, for example, periodic errors in Stadius’ Mercury positions of up to ten degrees.

For scientific uses, a modern planetary ephemeris comprises software that generates positions of the planets and often of their satellites, or of asteroids or comets at virtually any time desired by the user. Often there is an option to find the velocities of the bodies of interest, as well.

Typically, such ephemerides cover several centuries, past and future; the future ones can be covered because celestial mechanics is an accurate theory. Nevertheless, there are secular phenomena, factors that cannot adequately be considered by ephemerides. The biggest uncertainties on planetary positions are due to the perturbations of numerous asteroids, most of whose masses are poorly known, rendering their effect uncertain. Therefore, despite efforts to overcome these uncertainties, the JPL has to revise its published ephemerides at intervals of 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 position of the mentioned celestial body in right ascension and declination, because these coordinates are the most often 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 the one of the "standard" equinoxes, typically J2000.0, B1950.0, or J1900. Star maps are almost always in 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.

An ephemeris is usually only correct for a particular location on the Earth. In many cases the differences are too small to matter, but for nearby asteroids or the Moon they can be quite important.

GPS navigation satellites transmit electronic ephemeris data consisting of health and exact location data that GPS receivers then use (together with the signal's elapsed travel time to the receiver) to calculate their own location on Earth using trilateration.

The majority of astrologers study tropical astrology, involving planetary positions referenced to the vernal (spring) equinox position along the ecliptic (the equinox being the nexus of Earth's rotational plane and Earth's orbital plane around the Sun). However, as this position in the ecliptic moves backwards over time, (precession of the equinoxes), at a rate of ca. 1 degree per 72 years, astrologers require ephemerides which display planetary positions offset by that amount. Astrologers refer to their twelve 30-degree sectors of the tropical Zodiac as Signs, to distinguish them from the sectors of the sidereal Zodiac, referred to by astronomers as the Constellations through which the ecliptic appears. A small minority of astrologers who study sidereal astrology use the same ephemerides as astronomers.

Though astrology is and always has been geocentric, heliocentric astrology is an emerging field; for this purpose a standard ephemeris cannot be utilized, and because of this specialized heliocentric ephemerides must be calculated and used instead of the default geocentric ephemerides that are used in standard Western astrology to construct the astrological chart/natal chart.

• Duffett-Smith, Peter (1990). Astronomy With Your Personal Computer. Cambridge University Press. ISBN 0-521-38995-X. 

• MacCraig, Hugh (1949). The 200 Year Ephemeris. Macoy Publshing Company. (no ISBN indicated). 

• 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. 

• American Ephemeris and Nautical Almanac
• Ephemeris time
• Epoch (astronomy)
• Epoch (reference date)
• Jet Propulsion Laboratory Developmental Ephemeris
• Global Positioning System
• Almanac

• The JPL HORIZONS online ephemeris
• Introduction to the JPL ephemerides
• The effect of asteroidal perturbations on the long term accuracy of ephemerides.
• Kharin, A. S. and Kolesnik, Y. B.; On the Errors of the Ephemerides Derived from Optical Observations of Planets. (1990), IAU SYMP.141 P.189, 1989.
• Source code for computing ephemerides - by Steve Moshier
• A Free 3200 Year Ephemeris Provided by Astro.com -- Based out of Zürich, Switzerland (available in 8 languages)
• The Original 3,000 Year High-Precision Daily Astrological Online Ephemeris from Khaldea.com -- 600BC to 2400AD -- Calculated for Midnight GMT; also with an Aspectarian included for years 1900 to 2005
• Interactive orrery and ephemeris provided by Fourmilab in Switzerland.
• Online Ephemeris from 1891 to 2100 -- A simple ephemeris that is very easy to use and extremely accurate. All times are for Midnight (00:00 Hours) Greenwich Mean Time (UTC).
• Monthly Ephemeris
• Daily ephemeris, at the TAU AstroClub web site

v • d • e Orbits
Types	General Box · Circular · Non-inclined · Elliptic (Highly Elliptical) · Graveyard · Hyperbolic trajectory · Inclined · Osculating · Parabolic trajectory · Capture · Escape · Semi-synchronous · Subsynchronous · Synchronous · Parking Geocentric Geosynchronous · Geostationary · Sun-synchronous · Low Earth · Medium Earth · Molniya · Near equatorial · Moon · Polar · Tundra Other Areosynchronous · Areostationary · Halo · Lissajous · Lunar · Heliocentric · Heliosynchronous
v • d • e Parameters Classical orbital elements     Inclination   Longitude of the ascending node    Eccentricity        Argument of periapsis         Semi-major axis   Mean anomaly at epoch Other parameters  True anomaly    Semi-minor axis    Linear eccentricity  Eccentric anomaly  Mean longitude    True longitude  Orbital period
Maneuvers	Bi-elliptic transfer · Geostationary transfer · Gravity assist · Hohmann transfer · Inclination change · Phasing · Rendezvous
Related topics	Apsis · Celestial coordinate system · Delta-v budget · Epoch · Ephemeris · Equatorial coordinate system · Gravity turn · Ground track · Interplanetary Transport Network · Kepler's laws of planetary motion · Lagrangian point · n-body problem · Oberth effect · Orbit equation · Orbital state vectors · Perturbation · Retrograde and direct motion · Specific orbital energy · Specific relative angular momentum
List of orbits