Astronomical coordinate systems

In astronomy, coordinate systems are used for specifying positions of celestial objects (satellites, planets, stars, galaxies, etc.) relative to a given reference frame, based on physical reference points available to a situated observer (e.g. the true horizon and north to an observer on Earth's surface).^[1] Coordinate systems in astronomy can specify an object's relative position in three-dimensional space or plot merely by its direction on a celestial sphere, if the object's distance is unknown or trivial.

Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate system used on the surface of Earth. These differ in their choice of fundamental plane, which divides the celestial sphere into two equal hemispheres along a great circle. Rectangular coordinates, in appropriate units, have the same fundamental ( $x, y$ ) plane and primary ( $x$ -axis) direction, such as an axis of rotation. Each coordinate system is named after its choice of fundamental plane.

Coordinate systems

The following table lists the common coordinate systems in use by the astronomical community. The fundamental plane divides the celestial sphere into two equal hemispheres and defines the baseline for the latitudinal coordinates, similar to the equator in the geographic coordinate system. The poles are located at ±90° from the fundamental plane. The primary direction is the starting point of the longitudinal coordinates. The origin is the zero distance point, the "center of the celestial sphere", although the definition of celestial sphere is ambiguous about the definition of its center point.

Coordinate system^[2]	Center point (origin)	Fundamental plane (0° latitude)	Poles	Coordinates		Primary direction (0° longitude)
Coordinate system^[2]	Center point (origin)	Fundamental plane (0° latitude)	Poles	Latitude	Longitude	Primary direction (0° longitude)
Horizontal (also called alt-az or el-az)	Observer	Horizon	Zenith, nadir	Altitude ( $a$ ) or elevation	Azimuth ( $A$ )	North or south point of horizon
Equatorial	Center of the Earth (geocentric), or Sun (heliocentric)	Celestial equator	Celestial poles	Declination ( $δ$ )	Right ascension ( $α$ ) or hour angle ( $h$ )	March equinox
Ecliptic	Center of the Earth (geocentric), or Sun (heliocentric)	Ecliptic	Ecliptic poles	Ecliptic latitude ( $β$ )	Ecliptic longitude ( $λ$ )	March equinox
Galactic	Center of the Sun	Galactic plane	Galactic poles	Galactic latitude ( $b$ )	Galactic longitude ( $l$ )	Galactic Center
Supergalactic		Supergalactic plane	Supergalactic poles	Supergalactic latitude ( $SGB$ )	Supergalactic longitude ( $SGL$ )	Intersection of supergalactic plane and galactic plane

Horizontal system

Equatorial (red) and horizontal (blue) celestial coordinates

The horizontal, or altitude-azimuth, system is based on the position of the observer on Earth, which revolves around its own axis once per sidereal day (23 hours, 56 minutes and 4.091 seconds) in relation to the star background. The positioning of a celestial object by the horizontal system varies with time, but is a useful coordinate system for locating and tracking objects for observers on Earth. It is based on the position of stars relative to an observer's ideal horizon.

Equatorial system

The equatorial coordinate system is centered at Earth's center, but fixed relative to the celestial poles and the March equinox. The coordinates are based on the location of stars relative to Earth's equator if it were projected out to an infinite distance. The equatorial describes the sky as seen from the Solar System, and modern star maps almost exclusively use equatorial coordinates.

The equatorial system is the normal coordinate system for most professional and many amateur astronomers having an equatorial mount that follows the movement of the sky during the night. Celestial objects are found by adjusting the telescope's or other instrument's scales so that they match the equatorial coordinates of the selected object to observe.

Popular choices of pole and equator are the older B1950 and the modern J2000 systems, but a pole and equator "of date" can also be used, meaning one appropriate to the date under consideration, such as when a measurement of the position of a planet or spacecraft is made. There are also subdivisions into "mean of date" coordinates, which average out or ignore nutation, and "true of date," which include nutation.