horizon coordinate system: see altazimuth coordinate system.

galactic coordinate system, astronomical coordinate system in which the principal axis is the galactic equator (the intersection of the plane of the Milky Way with the celestial sphere) and the reference points are the north galactic pole and the zero point on the galactic equator; the coordinates of a celestial body are its galactic longitude and galactic latitude. In the IAU galactic coordinate system, introduced in 1958 by the International Astronomical Union, the zero point on the galactic equator has the equatorial coordinates R.A. 17^h39.3^m and Dec. -28°55'; this lies in the direction of the center of our galaxy, the Milky Way.

equatorial coordinate system, the most commonly used astronomical coordinate system for indicating the positions of stars or other celestial objects on the celestial sphere. The celestial sphere is an imaginary sphere with the observer at its center. It represents the entire sky; all celestial objects other than the earth are imagined as being located on its inside surface. If the earth's axis is extended, the points where it intersects the celestial sphere are called the celestial poles; the north celestial pole is directly above the earth's North Pole, and the south celestial pole directly above the earth's South Pole. The great circle on the celestial sphere halfway between the celestial poles is called the celestial equator; it can be thought of as the earth's equator projected onto the celestial sphere. It divides the celestial sphere into the northern and southern skies. An important reference point on the celestial equator is the vernal equinox, the point at which the sun crosses the celestial equator in March.

To designate the position of a star, the astronomer considers an imaginary great circle passing through the celestial poles and through the star in question. This is the star's hour circle, analogous to a meridian of longitude on earth. The astronomer then measures the angle between the vernal equinox and the point where the hour circle intersects the celestial equator. This angle is called the star's right ascension and is measured in hours, minutes, and seconds rather than in the more familiar degrees, minutes, and seconds. (There are 360 degrees or 24 hours in a full circle.) The right ascension is always measured eastward from the vernal equinox. Next the observer measures along the star's hour circle the angle between the celestial equator and the position of the star. This angle is called the declination of the star and is measured in degrees, minutes, and seconds north or south of the celestial equator, analogous to latitude on the earth. Right ascension and declination together determine the location of a star on the celestial sphere. The right ascensions and declinations of many stars are listed in various reference tables published for astronomers and navigators. Because a star's position may change slightly (see proper motion and precession of the equinoxes), such tables must be revised at regular intervals. By definition, the vernal equinox is located at right ascension 0^h and declination 0°.

Another useful reference point is the sigma point, the point where the observer's celestial meridian intersects the celestial equator. The right ascension of the sigma point is equal to the observer's local sidereal time. The angular distance from the sigma point to a star's hour circle is called its hour angle; it is equal to the star's right ascension minus the local sidereal time. Because the vernal equinox is not always visible in the night sky (especially in the spring), whereas the sigma point is always visible, the hour angle is used in actually locating a body in the sky.

ecliptic coordinate system, an astronomical coordinate system in which the principal coordinate axis is the ecliptic, the apparent path of the sun through the heavens. The ecliptic poles are the two points at which a line perpendicular to the plane of the ecliptic through the center of the earth strikes the surface of the celestial sphere. The north ecliptic pole lies in the constellation Draco.

astronomical coordinate systems. A coordinate system is a method of indicating positions. Each coordinate is a quantity measured from some starting point along some line or curve, called a coordinate axis. There are four basic systems of astronomical coordinates: the equatorial coordinate system, the altazimuth coordinate system, the celestial or ecliptic coordinate system, and the galactic coordinate system. These systems are based on three common principles: (1) all stars are considered to be located on the inner surface of the celestial sphere, the imaginary sphere centered on the earth and representing the entire sky; (2) each coordinate axis is a great circle on the celestial sphere; and (3) coordinate measurements of an object to be located are made along two great circles, one a coordinate axis and the other perpendicular to it and passing through the object. Measurements are made either in degrees or in hours.

altazimuth coordinate system or horizon coordinate system, astronomical coordinate system in which the position of a body on the celestial sphere is described relative to an observer's celestial horizon and zenith. The coordinates of a body in this system are its altitude and azimuth. Altitude is measured from the celestial horizon along the vertical circle through the body and the zenith of the observer. Azimuth is measured along the celestial horizon from the observer's south point (the point on the horizon directly south of him) to the point where the body's vertical circle intersects the horizon. Because the earth rotates on its axis, the altitude and azimuth of a celestial body are constantly changing.

In astronomy, a galactic latitude or longitude, useful for describing the relative positions and motions of components of the Milky Way Galaxy. Galactic latitude is measured in degrees north or south of the plane of the Milky Way. Galactic longitude is measured in degrees east of the galactic centre in the constellation Sagittarius.

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Investigation of geometric objects using coordinate systems. Because René Descartes was the first to apply algebra to geometry, it is also known as Cartesian geometry. It springs from the idea that any point in two-dimensional space can be represented by two numbers and any point in three-dimensional space by three. Because lines, circles, spheres, and other figures can be thought of as collections of points in space that satisfy certain equations, they can be explored via equations and formulas rather than graphs. Most of analytic geometry deals with the conic sections. Because these are defined using the notion of fixed distance, each section can be represented by a general equation derived from the distance formula.

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