To locate an object on the sky, astronomers use several different coordinate systems which are similar in concept to the system for plotting a point in a plane. However, the celestial sphere, which is the apparent sphere of the sky, is not a plane: It is the inside of a sphere, and one that rotates relative to Earth's surface. The two most frequently used coordinate systems are the horizon system and the equatorial system, and they are analogous in principle to the grid lines of geographic longitude and latitude. On the celestial sphere, distances are measured in degrees along the arc of a great circle. A great circle, formed by passing a plane through the center of a sphere, divides the sphere into two equal halves. Several features are common to all astronomical coordinate systems. Each has a principal axis, or polar axis, about which the system rotates. The points of intersection of this axis and the celestial sphere are the poles of the system. Perpendicular to the principal axis is a great circle, which is the principal reference circle along which one coordinate is measured. Finally, there are an infinite number of secondary reference circles that are great circles perpendicular to the principal reference circle, and which meet at the poles of the principal axis. The most natural and the easiest coordinate system to visualize is the equatorial system.

## Horizon Coordinate System

The principal axis of this system is defined so it is parallel locally to the direction of gravity. Extended upward, the principle axis intersects the celestial sphere at a point known as the zenith. The principal reference circle, the astronomical horizon, is the great circle marked on the celestial sphere by a plane perpendicular to the zenith-nadir axis and tangent to the Earth at the point of the observer. There are four reference points on the astronomical horizon:

, which are 90north, east, south, and west^{o}from each other.If we project onto the celestial sphere the terrestrial meridian of the longitude passing through the observer's position, it defines the great circle called the celestial meridian. The celestial meridian passes through the north and south points of the horizon as well as the zenith. It also contains the two points that are the intersection of the Earth's axis of rotation extended to the celestial sphere: the north and south celestial poles. The position of the celestial poles relative to the north and south points of the horizon depends upon the observer's latitude. For an observer in the northern hemisphere the angular distance of the north celestial pole above the north point of the horizon is equal to the observer's latitude.

Coordinates in the horizon system are known as azimuth and altitude.

is the angular distance measured along the horizon from the north point. The secondary reference circles in this system are known asAzimuth. Thus azimuth is measured to the foot of the vertical circle passing through the object of interest. The azimuth of the north point is 0vertical circles^{o}; the east point, 90^{o}; the south point, 180^{o}; and the west point, 270^{o}.is the angular distance of the object above or below the horizon measured along a vertical circle. The altitude of the zenith is +90Altitude^{o}, and the nadir, -90^{o}.The major disadvantage of the horizon system is that it is peculiar to the observer and not at all a general system. Also, since the altitude and the azimuth of an object continually change as Earth rotates, one must know the exact location and time at which an altitude and azimuth are measured in order for them to have any meaning to anyone besides the observer. A more general system is the equatorial coordinate system.

## Equatorial Coordinate System

The principal axis of the equatorial system coincides with Earth's axis of rotation. Its poles are the north and south celestial poles, as defined in the preceding section. The principal reference circle is the celestial equator, whereas secondary reference circles are called

. In the horizon system, the horizon and vertical circles remain fixed relative to an observer with the celestial sphere moving relative to them, whereas in this system, the celestial meridian and hour circles are on the celestial sphere and thus rotate with it relative to an observer.hour circlesAs Earth rotates from west to east, stars trace paths from east to west across the sky called diurnal (daily) circles. For an observer located at intermediate latitudes, the sky rotates at an oblique angle, the value depending on the latitude. And the celestial equator passes through the east and west points of the horizon regardless of an observer's latitude.

Coordinates in the equatorial system are called right ascension and declination.

is the angular distance of an object north or south of the celestial equator measured along an hour circle. Thus the declination of the north celestial pole is +90o, and that of the south celestial pole is -90Declination^{o}. The other coordinate is calledand is measured eastward along the celestial equator from the vernal equinox to the foot of the hour circle passing through the object. Theright ascension, so named because the Sun moves through this point on or about March 21, is the point of intersection of the celestial equator with the annual apparent path of the Sun on the celestial sphere, thevernal equinox. Right ascension is measured in units of time rather than degrees of arc. Since a 360ecliptic^{o}rotation by the Earth corresponds to 24^{h}, then 1^{h}equals 15^{o}of arc, or 1^{o}equals 4^{m}, and so on. Finally, the angular distance of the hour circle from the observer's celestial meridian is called theof the star.hour angleIt is obvious that the right ascension and declination of a celestial object remain fixed as the sky rotates. This makes it possible to catalog astronomical objects by right ascensions and declinations in the same way in which places on Earth are cataloged by longitudes and latitudes. Because of precession (Precession of the Equinoxes), the vernal equinox slides westward along the ecliptic by about 50" per year. Thus over a number of years, a star's right ascension and declination change so that cataloged positions are not accurate indefinitely and must be updated periodically to correct for precession.

In addition to the horizon and equatorial systems, there are two less frequently used systems of astronomical coordinates, the ecliptic and the Galactic systems. The principal reference circle for the ecliptic system is the ecliptic, whereas in the Galactic system it is the central plane of our Galaxy. The four systems are summarized in the table below. Although astronomical coordinate systems are necessary in order to make precision observations, a general knowledge of the sky can be obtained with the aid of star charts.

Astronomical Coordinate SystemsCoordinate System Principal Axis Principal Reference Circle Coordinates

(units)Secondary Reference Circles Coordinate

(units)Horizon zenith-nadir astronomical horizon azimuth

(0^{o}-360^{o})vertical circle altitude

(+0^{o}-90^{o})Equatorial north-south celestial pole celestial equator right ascension

(0^{h}-24^{h})hour circle declination

(+0^{o}-90^{o})Ecliptic north-south ecliptic pole ecliptic celestial longitude

(0^{o}-360^{o})no name celestial latitude

(+0^{o}-90^{o})Galactic north-south Galactic pole plane of the Galaxy galactic longitude

(0^{o}-360^{o})no name galactic latitude

(+0^{o}-90^{o})

© 1995, J. C. Evans

Physics & Astronomy Department, George Mason University

Maintained by J. C. Evans; jevans@gmu.edu