Celestial coordinate system

Encyclopedia

In astronomy

, a

for mapping positions on the celestial sphere

.

There are different celestial coordinate systems each using a system of spherical coordinates projected on the celestial sphere

, in analogy to the geographic coordinate system

used on the surface of the Earth

. The coordinate systems differ only in their choice of the fundamental plane

, which divides the sky into two equal hemisphere

s along a great circle

. For example, the fundamental plane of the geographic system is the Earth's equator

. Each coordinate system is named for its choice of fundamental plane.

divides the sphere into two equal hemispheres and defines the baseline for the equivalent latitude

in the coordinates. This defines equivalent to the equator

in the geographic coordinate system

(GCS). The two points located 90° from the fundamental plane are termed the poles. The coordinate column gives the coordinate system's equivalents to the latitude and longitude

in GCS, respectively.

The

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 that at which 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.

and astrology

divorced, particularly in the West.

The ecliptic system describes the planets' orbital movement around the sun, and centers on the barycenter of the solar system (i.e. very close to the sun). The fundamental plane is the plane of the Earth's orbit, called the ecliptic plane. The system is primarily used for computing the positions of planets and other solar system bodies, as well as defining their orbital elements

.

Φ, the conversion equations are:

where

angle (or zenith distance, i.e. the 90° complement of Altitude). The inverse trigonometric function

s are then used to get the values of the coordinates.

NOTE: Inverse cosine is dual valued, i.e. 160° and 200° both have the same cosine. The above needs to be corrected. If H < 180 (or Pi radians) then Az = 360 - Az as derived from the above equation.

Astronomy

Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

, a

**celestial coordinate system**is a coordinate systemCoordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by...

for mapping positions on the celestial sphere

Celestial sphere

In astronomy and navigation, the celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with the Earth and rotating upon the same axis. All objects in the sky can be thought of as projected upon the celestial sphere. Projected upward from Earth's equator and poles are the...

.

There are different celestial coordinate systems each using a system of spherical coordinates projected on the celestial sphere

Celestial sphere

In astronomy and navigation, the celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with the Earth and rotating upon the same axis. All objects in the sky can be thought of as projected upon the celestial sphere. Projected upward from Earth's equator and poles are the...

, in analogy to the geographic coordinate system

Geographic coordinate system

A geographic coordinate system is a coordinate system that enables every location on the Earth to be specified by a set of numbers. The coordinates are often chosen such that one of the numbers represent vertical position, and two or three of the numbers represent horizontal position...

used on the surface of the Earth

Earth

Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

. The coordinate systems differ only in their choice of the fundamental plane

Fundamental plane (spherical coordinates)

The fundamental plane in a spherical coordinate system is a plane which divides the sphere into two hemispheres. The latitude of a point is then the angle between the fundamental plane and the line joining the point to the centre of the sphere....

, which divides the sky into two equal hemisphere

Sphere

A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...

s along a great circle

Great circle

A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as opposed to a general circle of a sphere where the plane is not required to pass through the center...

. For example, the fundamental plane of the geographic system is the Earth's equator

Equator

An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

. Each coordinate system is named for its choice of fundamental plane.

## Coordinate systems

The following table lists the standard coordinate systems in use by the astronomy community. The fundamental planeFundamental plane (spherical coordinates)

The fundamental plane in a spherical coordinate system is a plane which divides the sphere into two hemispheres. The latitude of a point is then the angle between the fundamental plane and the line joining the point to the centre of the sphere....

divides the sphere into two equal hemispheres and defines the baseline for the equivalent latitude

Latitude

In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...

in the coordinates. This defines equivalent to the equator

Equator

An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

in the geographic coordinate system

Geographic coordinate system

A geographic coordinate system is a coordinate system that enables every location on the Earth to be specified by a set of numbers. The coordinates are often chosen such that one of the numbers represent vertical position, and two or three of the numbers represent horizontal position...

(GCS). The two points located 90° from the fundamental plane are termed the poles. The coordinate column gives the coordinate system's equivalents to the latitude and longitude

Longitude

Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....

in GCS, respectively.

Coordinate system | Fundamental plane | Poles | Coordinates |
---|---|---|---|

Horizontal Horizontal coordinate system The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane. This coordinate system divides the sky into the upper hemisphere where objects are visible, and the lower hemisphere where objects cannot be seen since the earth is in... (also called Alt/Az or Az/El) |
horizon Horizon The horizon is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not. At many locations, the true horizon is obscured by trees, buildings, mountains, etc., and the resulting... |
zenith Zenith The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e... /nadir Nadir The nadir is the direction pointing directly below a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface there. Since the concept of being below is itself somewhat vague, scientists define the nadir in more rigorous... |
elevation (also called altitude) - azimuth - meridian Meridian (astronomy) This article is about the astronomical concept. For other uses of the word, see Meridian.In the sky, a meridian is an imaginary great circle on the celestial sphere. It passes through the north point on the horizon, through the celestial pole, up to the zenith, through the south point on the... |

Equatorial Equatorial coordinate system The equatorial coordinate system is a widely-used method of mapping celestial objects. It functions by projecting the Earth's geographic poles and equator onto the celestial sphere. The projection of the Earth's equator onto the celestial sphere is called the celestial equator... |
celestial equator Celestial equator The celestial equator is a great circle on the imaginary celestial sphere, in the same plane as the Earth's equator. In other words, it is a projection of the terrestrial equator out into space... |
celestial pole Celestial pole The north and south celestial poles are the two imaginary points in the sky where the Earth's axis of rotation, indefinitely extended, intersects the imaginary rotating sphere of stars called the celestial sphere... s |
declination Declination In astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and... - right ascension Right ascension Right ascension is the astronomical term for one of the two coordinates of a point on the celestial sphere when using the equatorial coordinate system. The other coordinate is the declination.-Explanation:... or hour angle Hour angle In astronomy and celestial navigation, the hour angle is one of the coordinates used in the equatorial coordinate system to give the position of a point on the celestial sphere.... |

Ecliptic Ecliptic coordinate system The ecliptic coordinate system is a celestial coordinate system that uses the ecliptic for its fundamental plane. The ecliptic is the path that the sun appears to follow across the celestial sphere over the course of a year. It is also the intersection of the Earth's orbital plane and the celestial... |
ecliptic Ecliptic The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun... |
ecliptic pole Ecliptic pole The ecliptic pole is the point on the celestial sphere where the sphere meets the imaginary line perpendicular to the ecliptic plane, the path the Earth travels on its orbit around the Sun.There are two ecliptic poles:... s |
ecliptic latitude - ecliptic longitude |

Galactic Galactic coordinate system The galactic coordinate system is a celestial coordinate system which is centered on the Sun and is aligned with the apparent center of the Milky Way galaxy. The "equator" is aligned to the galactic plane... |
galactic plane Galactic plane The galactic plane is the plane in which the majority of a disk-shaped galaxy's mass lies. The directions perpendicular to the galactic plane point to the galactic poles... |
galactic poles | galactic latitude - galactic longitude |

Supergalactic Supergalactic coordinate system Supergalactic coordinates are coordinates in a spherical coordinate system which was designed to have its equator aligned with the supergalactic plane, a major structure in the local universe formed by the preferential distribution of nearby galaxy clusters towards a plane... |
supergalactic plane | Supergalactic poles | supergalactic latitude, supergalactic longitude |

### Horizontal system

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 "fixed" 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 distant stars and galaxies. 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 that at which 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

Nutation

Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...

, and "true of date," which include nutation.

### Ecliptical system

The ecliptic system was one of the old coordinate systems used for star maps before astronomyAstronomy

Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

and astrology

Astrology

Astrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world...

divorced, particularly in the West.

The ecliptic system describes the planets' orbital movement around the sun, and centers on the barycenter of the solar system (i.e. very close to the sun). The fundamental plane is the plane of the Earth's orbit, called the ecliptic plane. The system is primarily used for computing the positions of planets and other solar system bodies, as well as defining their orbital elements

Orbital elements

Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are generally considered in classical two-body systems, where a Kepler orbit is used...

.

### Galactic system

The galactic coordinate system uses the approximate plane of our galaxy as its fundamental plane. The solar system is still the center of the coordinate system, and the zero point is defined as the direction towards the galactic center. Galactic latitude resembles the elevation above the galactic plane and galactic longitude determines direction relative to the center of the galaxy.### Supergalactic system

The supergalactic coordinate system corresponds to a fundamental plane which contains a higher than average number of local galaxies in the sky as seen from Earth.### Equatorial to horizontal coordinates

Let*H*be the hour angle and*δ*the declination in equatorial coordinates. Suppose the need is to compute the altitude*a*and the azimuth*A*in horizontal coordinates. Then, for an observer at latitudeLatitude

In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...

Φ, the conversion equations are:

where

*θ*is the zenithZenith

The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...

angle (or zenith distance, i.e. the 90° complement of Altitude). The inverse trigonometric function

Trigonometric function

In mathematics, the trigonometric functions are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle...

s are then used to get the values of the coordinates.

NOTE: Inverse cosine is dual valued, i.e. 160° and 200° both have the same cosine. The above needs to be corrected. If H < 180 (or Pi radians) then Az = 360 - Az as derived from the above equation.

## See also

- Axial tiltAxial tiltIn astronomy, axial tilt is the angle between an object's rotational axis, and a line perpendicular to its orbital plane...
- Azimuth
- InclinationInclinationInclination in general is the angle between a reference plane and another plane or axis of direction.-Orbits:The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit...
- Kozai effect
- Orbital inclination changeOrbital inclination changeOrbital inclination change is an orbital maneuver aimed at changing the inclination of an orbiting body's orbit. This maneuver is also known as an orbital plane change as the plane of the orbit is tipped. This maneuver requires a change in the orbital velocity vector at the orbital nodes Orbital...

## External links

*This article was originally based on Jason Harris' Astroinfo which comes along with KStars*KStarsKStars is a planetarium program using the KDE Platform for Unix-like computer operating systems. It provides an accurate graphical representation of the night sky, from any location on Earth, at any date and time...

, a KDE Desktop Planetarium for LinuxLinuxLinux is a Unix-like computer operating system assembled under the model of free and open source software development and distribution. The defining component of any Linux system is the Linux kernel, an operating system kernel first released October 5, 1991 by Linus Torvalds...

/KDEKDEKDE is an international free software community producing an integrated set of cross-platform applications designed to run on Linux, FreeBSD, Microsoft Windows, Solaris and Mac OS X systems...

.