# Astronomical coordinate systems

In astronomy, a celestial coordinate system or astronomical coordinate systems is a coordinate system for determining a position in the sky, usually expressed in decimal or pseudo-sexagesimal notation (the base unit of right ascension, however, being sidereal time, equivalent at 15°).

There are several systems, using a coordinate grid projected onto the celestial sphere, analogous to the geographic coordinate systems used on the Earth’s surface. The celestial coordinate systems differ only in the choice of the reference plane, which divides the sky into two hemispheres along a great circle (the reference plane of the geographic coordinate system is the earth’s equator). Each system is named after its reference plane:

• Horizontal coordinate system.
• Equatorial coordinate system.
• Ecliptic coordinate system.
• Galactic coordinate system.
• Supergalactic coordinate system.

## Table lists the common coordinate systems in use by the astronomical community

Coordinate systemCenter point
(origin)
Fundamental plane
(0° latitude)
PolesCoordinatesPrimary direction
(0° longitude)
LatitudeLongitude
Horizontal (also called altaz or el-az)ObserverHorizonZenith, nadirAltitude (a) or elevationAzimuth (A)North or south point of horizon
EquatorialCenter of the Earth (geocentric), or Sun (heliocentric)Celestial equatorCelestial polesDeclination (δ)Right ascension (α)
or hour angle (h)
March equinox
EclipticEclipticEcliptic polesEcliptic latitude (β)Ecliptic longitude (λ)
GalacticCenter of the SunGalactic planeGalactic polesGalactic latitude (b)Galactic longitude (l)Galactic Center
SupergalacticSupergalactic planeSupergalactic polesSupergalactic latitude (SGB)Supergalactic longitude (SGL)Intersection of supergalactic plane and galactic plane

#### Functions

A celestial coordinate system has the function of determining a position in the sky. There are several systems, using a coordinate grid projected onto the celestial sphere, analogous to the geographic coordinate systems used on the Earth’s surface.

The celestial coordinate systems differ only in the choice of reference plane, which divides the sky into two hemispheres along a great circle (the reference plane of the geographic coordinate system is the Earth’s equator). Each system is named after its reference plane.

## The systems of astronomical coordinate

##### Horizontal coordinate system

The horizontal coordinate system, also called local system or alt-azimuth coordinate system, is a system of celestial coordinates used in astronomy by an observer on the ground. The system, centered on the observer, separates the sky into two hemispheres: one located above the observer and the other located below, hidden by the ground. The circle separating the two hemispheres, called the celestial horizon, locates the horizontal plane. The altitude (or elevation, “h”) and the azimuth (A), which constitute the two main coordinates of this system, are defined from this plane.

Altitude is the angle between the object and the observer’s local horizon. For visible objects, this angle is between 0° (horizon) and 90° (zenith).

Azimuth is the angle of the object around the horizon. It is a circle divided into 360° drawn on the horizontal plane from north to east (exceptions to this convention exist).
This coordinate system has the advantage of being simple and local. It is easy to establish at a given place from the moment the observer knows where one of the cardinal points is. This is the reason why it is particularly used by ground-based telescopes with azimuthal mounting, that is to say most of the most recent telescopes.

Horizontal coordinates use a celestial sphere centered on the observer. Azimuth is measured eastward from the north point (sometimes from the south point) of the horizon; altitude is the angle above the horizon. TWCarlson, CC BY-SA 3.0, via Wikimedia Commons

##### Equatorial coordinate system

The equatorial coordinate system is a celestial coordinate system whose values ​​are independent of the position of the observer. This is also true for ecliptic and galactic coordinate systems. This system uses the projection of the Earth’s equator on the celestial sphere as a reference plane. This projection is called the celestial equator. It divides the sky into two hemispheres, each having as its axis of reference the projection of a terrestrial pole, perpendicular to the celestial equator. From these divisions, the system makes it possible to establish two angular coordinates: right ascension and declination.

Right ascension (α) is the angle measured on the celestial equator from an axis pointing to a reference point, the vernal point, corresponding to the intersection between the celestial equator and the ecliptic. From this axis, the angle is measured towards the East and has 24 main divisions of 15° each, called “hours”. Each hour is divided into minutes and seconds. This division of the angle into hours, minutes and seconds makes it easy to determine how long (in sidereal time) it will take for a star to reach a certain point in the sky.

The declination (δ) is the angle measured perpendicularly between the celestial equator and the observed celestial object. It is measured in degrees, positive for objects in the northern hemisphere and negative for those in the southern hemisphere. The declination thus varies from -90° (south pole) to +90° (north pole) passing through 0° at the celestial equator. Right ascension and declination are the astronomical equivalents of longitude and latitude.

Geocentric equatorial coordinates. The origin is the centre of the Earth. The fundamental plane is the plane of the Earth’s equator. The primary direction (the x axis) is the vernal equinox. A right-handed convention specifies a y axis 90° to the east in the fundamental plane; the z axis is the north polar axis. The reference frame does not rotate with the Earth, rather, the Earth rotates around the z axis. Tfr000 (talk) 19:24, 23 April 2012 (UTC), CC BY-SA 3.0, via Wikimedia Commons

##### Ecliptic coordinate system

The ecliptic coordinate system is a coordinate system suitable for celestial objects: it uses the ecliptic plane (plane of the Earth’s orbit around the Sun) as a reference plane. This plane makes an angle of approximately 23° with the Earth’s equatorial plane, due to the tilt of the Earth’s axis of rotation. This frame is a two-dimensional spherical system.

The ecliptic longitude (λ) is the angle between the vernal point (the same as for the equatorial coordinate system), the center of the coordinate system (the sun) and the projection of the object on this plane. This angle is measured in degrees.
The ecliptic latitude (β) represents the angle between the plane of the ecliptic, the center of the frame (the sun) and the object.
This system can be centered on the Earth, the Sun or any other body. It is especially useful for objects located in the solar system.

The obliquity, or inclination of Earth’s equator against the ecliptic, amounts eps[ilon] = 23deg 26′ 21.448″ (2000.0) and changes very slightly with time, due to gravitational perturbations of Earth’s motion. Knowing this quantity, the transformation formulae from equatorial to ecliptical coordinates are quite simply given (mathematically, by a rotation around the “X” axis pointing to the vernal equinox by angle eps):

cos be * cos le = cos Dec * cos RA
cos be * sin le = cos Dec * sin RA * cos eps + sin Dec * sin eps
sin be = – cos Dec * sin RA * sin eps + sin Dec * cos eps

and the reverse transformation: cos Dec * cos RA = cos be * cos le
cos Dec * sin RA = cos be * sin le * cos eps – sin be * sin eps
sin Dec = cos be * sin le * sin eps + sin be * cos eps

Ecliptical coordinates are most frequently used for solar system calculations such as: planetary and cometary orbits and appearances.

##### For this purpose, two ecliptical systems are used:
• The heliocentric coordinate system with the Sun in its center.
• The geocentric one with the Earth in its origin, which can be transferred into each other by a coordinate translation.

Ecliptic coordinate system (celestial) Joshua Cesa, CC BY 3.0, via Wikimedia Commons

##### Galactic coordinate system

Galactic coordinates are suitable for objects located in our galaxy and not located in the near vicinity of the Sun. Galactic coordinates are a location made using a latitude and longitude defined so that the galactic plane corresponds to the equator, and the origin of the longitudes corresponds to the galactic center. The galactic coordinate system is a celestial coordinate system that takes into account the rotation of the Galaxy on itself. We are also talking here about galactic longitude and latitude. The reference plane of this system is the plane of the Galaxy centered on the galactic center. The galactic north pole has been defined by convention in the equatorial reference frame by a right ascension of 12 h 51 min 26.282 s and a declination of 27°07′42.01″. In this plane, the reference direction of the measurement is the direction of the center of the Galaxy.

Galactic longitude (l) is the angle between this direction of reference and the projection of the object on the plane of the galaxy. The galactic longitude is 0° in the direction of the center of the Galaxy.
Galactic latitude (b) is the measure of the angle between the reference plane and the object with the Sun at the center. It measures in degrees the height of this object from 0° in the reference plane to 90° at the galactic north pole.

Ilustration of the galactic coordinates use the Sun as the origin. Galactic longitude (ℓ) is measured with primary direction from the Sun to the center of the galaxy in the galactic plane, while the galactic latitude (b) measures the angle of the object above the galactic plane. Brews ohare, CC BY-SA 3.0, via Wikimedia Commons

##### Supergalactic coordinate system

The supergalactic coordinate system is a system of spherical celestial coordinates used on the scale of a hundred million light-years. Its equator is defined from the supergalactic plane, which was first observed in the 18th century but confirmed only in the 1970s. This is the approximate plane of the Virgo Supercluster.

The observed supergalactic plane is more or less perpendicular to the plane of the Milky Way, the angle between the two being 84.5 degrees (°). It crosses the constellations of Cassiopeia (in the galactic plane), of the Giraffe, of the Big Dipper, of Berenike’s Hair (near the galactic north pole), of Virgo, of the Centaur, of the Compass (in the galactic plane), the Southern Triangle, the Peacock, the Indian, the Crane, the Sculptor (near the galactic south pole), the Whale, the Pisces, Andromeda and Perseus.

Galaxies and galaxy clusters plotted in the supergalactic plane < 50 million lightyears distance. RobbertMoolhuijsen, CC BY-SA 4.0, via Wikimedia Commons

Ptolemy (85 – 165), Mathematician, Geographer, Astronomer and Astrologer

Photo credit (main picture): Jim slater307 (CC BY-SA 4.0) via equinox

Main photo description: Celestial Equator (blue), Ecliptic Plane (red), and Galactic Equator (yellow) projected on the Celestial Sphere, showing the inclinations of their respective poles and equators.