ASTRONOMICAL COORDINATE SYSTEMS

DEFINITIONS

Celestial Sphere - A hypothetical spherical shell of infinite radius, centered on the earth, which represents the sky and upon which celestial bodies appear projected.

Great Circle - A circle defined by the intersection of the surface of a sphere and any plane which passes through the center of the sphere (and therefore divides the sphere equally into halves).

Fundamental Great Circle - A great circle which forms the basis of a spherical coordinate system, e.g., the equator on the earth. Any great circle on a sphere may serve as a fundamental great circle. In practice however the fundamental great circle is usually chosen to have some special physical significance.

Pole - Either of the two points on a sphere defined by the intersection of that sphere and an axis passing through the center of the sphere, perpendicular to the plane of the fundamental great circle.

Secondary Great Circle - Any great circle passing through the poles of a spherical coordinate system. Secondary great circles are therefore perpendicular to the fundamental great circle of a spherical coordinate system at their two points of intersection.

Latitude-Like Coordinate (of a point) - The angular distance measured along the secondary great circle passing through a point between the fundamental great circle and that point.

Longitude-Like Coordinate (of a point) - The angular distance measured along the fundamental great circle between some arbitrarily chosen reference point (origin) and the secondary great circle passing through a point.

Horizon or Altitude-Azimuth Coordinate System - A spherical coordinate system used mostly for informal purposes in astronomy, the physical basis of which is the local direction of the gravitational force.

Horizon - The fundamental great circle of the horizon system, defined by the intersection of the celestial sphere and a level plane passing through the observer. (The local direction of gravity is perpendicular to and therefore determines the orientation of a level plane.)

Zenith - The upper pole of the horizon system.

Nadir - The lower pole of the horizon system.

Vertical Circle - A secondary great circle in the horizon system. Such a circle passes through the zenith and nadir and is vertical since it is perpendicular to the horizon.

Altitude - The latitude-like coordinate in the horizon system. It is measured along the vertical circle of a point from the horizon up to that point. It is therefore positive for objects above the horizon and negative for objects below the horizon.

Azimuth - The longitude-like coordinate in the horizon system. It is measured eastward from the northward direction on the horizon to the vertical circle of a point. It can range therefore from 0° through 360°.

Equatorial Coordinate System - The spherical coordinate system usually used for locating objects with a telescope. The physical basis of this system is the earth's rotation.

Celestial Equator - The fundamental great circle of the equatorial system, defined by the intersection of the earth's equatorial plane and the celestial sphere. (The earth's equatorial plane is that plane passing through the earth's center which is perpendicular to the earth's axis of rotation and which passes through the earth's equator.)

Ecliptic - The sun's apparent path on the celestial sphere. Hence this is also the projection of the earth's orbital plane onto the sky. The ecliptic is a great circle.

Vernal Equinox - That intersection point of the celestial equator and ecliptic through which the sun passes when crossing the equator from south to north. Hence this is the sun's position at the beginning of northern spring. (The term is also applied to the time at which this crossing occurs.)

North and South Celestial Poles - The poles of the equatorial coordinate system. These are those points at which the earth's axis of rotation intersects the celestial sphere.

Hour Circle - A secondary great circle in the equatorial system. Such a circle therefore passes through the celestial poles and is perpendicular to the celestial equator.

Celestial Meridian - A great circle passing through the zenith, nadir, north and south celestial poles, and north and south points of the horizon. It is both a vertical circle and an hour circle and is therefore perpendicular to both the celestial equator and horizon. The celestial meridian bisects the sky into eastern and western halves.

Declination (*) - The latitude-like coordinate in the equatorial system. It is measured along the hour circle of a point from the celestial equator to that point. It is positive for points north of the celestial equator and negative for points south. The declination of a star is not affected by either the observer's position nor by the passage of time (except for a slow precessional effect). The declination is one of the two coordinates used in pointing a telescope.

Right Ascension (") - A longitude-like coordinate in the equatorial system. It is measured along the celestial equator eastward from the vernal equinox to the hour circle of a point. It is measured in units of time and therefore can range from 0 hours to 24 hours. It is not affected by either the observer's position nor by the passage of time (except for a slow precessional effect).

Hour Angle (HA) - Another longitude-like coordinate in the equatorial system. It is measured in units of time westward along the celestial equator from the celestial meridian to the hour circle of a point. Unlike the right ascension it does depend both upon the observer's position and also upon the time. A star's hour angle can be thought of both as an angle and also as the elapsed time since that star crossed the celestial meridian. The hour angle is one of the two coordinates used in pointing a telescope.

Local Sidereal Time (LST) - The hour angle of the vernal equinox or, equivalently, the right ascension of points on the celestial meridian. LST is dependent upon the observer's position and is constantly changing with time.

Ecliptic Coordinate System - The spherical coordinate system often used for describing the positions of solar system objects.  The physical basis of this system is the earth's orbital motion about the sun.

Galactic Coordinate System - The spherical coordinate system often used for studies of galactic structure or for specifying positions within a galactic framework.  The physical basis of this system is galactic structure and rotation.

RELATIONSHIPS TO REMEMBER

1. LST = α + HA

This relationship is extremely important to the observational astronomer. In order to properly aim his telescope he must know a star's hour angle (HA) and declination (*). A star's declination is fixed and can be obtained from a catalog but its hour angle constantly changes as the earth rotates. Thus the astronomer begins with the star's right ascension (") which, like declination, is fixed and can be found in a catalog. Then using the local sidereal time (LST) which is obtained from his sidereal clock the astronomer calculates the star's hour angle using the above equation.

2. For any observer the altitude of the north celestial pole is equal to the observer's latitude, i.e., hNCP = φobs.  

3. Star maps are drawn to show the celestial sphere as it is actually seen (from the inside looking out). Thus with north at the top and south at the bottom, east is to the left and west to the right, opposite to the convention for geographical maps.