celestial sphere, imaginary sphere of infinite radius with the earth at its center. It is used for describing the positions and motions of stars and other objects. For these purposes, any astronomical object can be thought of as being located at the point where the line of sight from the earth through the object intersects the surface of the celestial sphere. In astronomical coordinate systems, the coordinate axes are great circles on the celestial sphere. In most systems of this type, the reference points are fixed on the sphere, so the two coordinates needed to locate a body are relatively constant.

celestial pole, one of the two points at which the earth's axis of rotation intersects the celestial sphere. The celestial pole is important as a reference point in the equatorial coordinate system; the celestial meridian passes through it, as do the hour circles of the stars. The polestar (see Polaris) lies within 0.5° of the north celestial pole. Although there is no bright star near the south celestial pole, the Southern Cross (see Crux) points directly to it. The altitude of the celestial pole in an observer's hemisphere is equal to the observer's latitude on the earth.

celestial meridian, vertical circle passing through the north celestial pole and an observer's zenith. It is an axis in the altazimuth coordinate system.

celestial mechanics, the study of the motions of astronomical bodies as they move under the influence of their mutual gravitation. Celestial mechanics analyzes the orbital motions of planets, dwarf planets, comets, asteroids, and natural and artificial satellites within the solar system as well as the motions of stars and galaxies. Newton's laws of motion and his theory of universal gravitation are the basis for celestial mechanics; for some objects, general relativity is also important. Calculating the motions of astronomical bodies is a complicated procedure because many separate forces are acting at once, and all the bodies are simultaneously in motion. The only problem that can be solved exactly is that of two bodies moving under the influence of their mutual gravitational attraction (see ephemeris). Since the sun is the dominant influence in the solar system, an application of the two-body problem leads to the simple elliptical orbits as described by Kepler's laws; these laws give a close approximation of planetary motion. More exact solutions, which consider the effects of the planets on each other, cannot be found in a straightforward way. However, methods accounting for these other influences, or perturbations, have been devised; they allow successive refinements of an approximate solution to be made to almost any degree of precision. In computing the motions of stars and the rotations of galaxies, statistical methods are often used. Columbia Univ. astronomer Wallace Eckert was the first to use a computer for orbit calculations; now computers are used for this work almost exclusively.

celestial horizon, one axis of the altazimuth coordinate system. It is the great circle on the celestial sphere midway between the observer's zenith and nadir; it divides the celestial sphere into two equal hemispheres. The observer may be unable to see all the stars that lie above his celestial horizon because of obstructions such as buildings, trees, or mountains; he may be able to see some stars that lie below his celestial horizon because of atmospheric refraction.

celestial equator: see equatorial coordinate system.

Apparent surface of the heavens, on which the stars seem to be fixed. For the purpose of establishing celestial coordinate systems to mark the positions of heavenly bodies, it can be thought of as a real sphere at an infinite distance from Earth. Earth's rotational axis, extended to infinity, touches this sphere at the northern and southern celestial poles, around which the heavens seem to turn. The intersection of the plane of Earth's Equator with the sphere marks the celestial equator.

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Branch of astronomy that deals with the mathematical theory of the motions of celestial bodies. Johannes Kepler's laws of planetary motion (1609–19) and Newton's laws of motion (1687) are fundamental to it. In the 18th century, powerful methods of mathematical analysis were generally successful in accounting for the observed motions of bodies in the solar system. One branch of celestial mechanics deals with the effect of gravitation on rotating bodies, with applications to Earth (see tide) and other objects in space. A modern derivation, called orbital mechanics or flight mechanics, deals with the motions of spacecraft under the influence of gravity, thrust, atmospheric drag, and other forces; it is used to calculate trajectories for ascent into space, achieving orbit, rendezvous, descent, and lunar and interplanetary flights.

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