Orbital motion
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orbital motion
(′ör·bəd·əl ′mō·shən)
(physics) Continuous motion of a body in a closed path, such as a circle or an ellipse, about some point.
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Orbital motion
McGraw-Hill Science & Technology Encyclopedia:
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Orbital motion
In astronomy the motion of a material body through space under the influence of its own inertia, a central force, and other forces. Johann Kepler found empirically that the orbital motions of the planets about the Sun are ellipses. Sir Isaac Newton, starting from his laws of motion, proved that an inverse-square gravitational field of force requires a body to move in an orbit that is a circle, ellipse, parabola, or hyperbola.
Two bodies revolving under their mutual gravitational attraction, but otherwise undisturbed, describe orbits of the same shape about a common center of mass. The less massive body has the larger orbit. In the solar system, the Sun and Jupiter have a center of mass just outside the visible disk of the Sun. For each of the other planets, the center of mass of Sun and planet lies within the Sun.
For this reason, it is convenient to consider only the relative motion of a planet of mass m about the Sun of mass M as though the planet had no mass and moved about a center of mass M + m. The orbit so determined is exactly the same shape as the true orbits of planet and Sun about their common center of mass, but it is enlarged in the ratio (M + m)/M. See also Center of mass; Planet.
Orbital velocity v of a planet moving in a relative orbit about the Sun may be expressed by Eq. (1)
1. 
where a is the semimajor axis, and r is the distance from the planet to the Sun. In the special case of a circular orbit, r = a, and the expression becomes Eq. (2). When the eccentricity of an orbit is exactly
2. 
unity, the length of the major axis becomes infinite and the ellipse degenerates into a parabola. The expression for the velocity then becomes Eq. (3). This parabolic velocity is referred
3. 
to as the velocity of escape, since it is the minimum velocity required for a particle to escape from the gravitational attraction of its parent body. See also Escape velocity.
Eccentricities greater than unity occur with hyperbolic orbits. Because in a hyperbola the semimajor axis a is negative, hyperbolic velocities are greater than the escape velocity.
Parabolic and hyperbolic velocities seem to be observed in the motions of some comets and meteors. Aside from the periodic ones, most comets appear to be visitors from cosmic distances, as do about two-thirds of the fainter meteors. It is possible that many of the “parabolic” comets are actually moving in elliptical orbits of extremely long period. The close approach of one of these visitors to a massive planet, such as Jupiter, could change the velocity from parabolic to elliptical if retarded, or from parabolic to hyperbolic if accelerated. It is possible that many of the periodic comets, especially those with periods under 9 years, have been captured in this way. See also Comet; Gravitation; Perturbation (astronomy).
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McGraw-Hill Science & Technology Dictionary
McGraw-Hill Dictionary of Scientific and Technical Terms. Copyright © 2003, 1994, 1989, 1984, 1978, 1976, 1974 by McGraw-Hill Companies, Inc. All rights reserved.
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