eccentricity(redirected from Linear eccentricity)
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orbit, in astronomy, path in space described by a body revolving about a second body where the motion of the orbiting bodies is dominated by their mutual gravitational attraction. Within the solar system, planets, dwarf planets, asteroids, and comets orbit the sun and satellites orbit the planets and other bodies.
From earliest times, astronomers assumed that the orbits in which the planets moved were circular; yet the numerous catalogs of measurements compiled especially during the 16th cent. did not fit this theory. At the beginning of the 17th cent., Johannes Kepler stated three laws of planetary motion that explained the observed data: the orbit of each planet is an ellipse with the sun at one focus; the speed of a planet varies in such a way that an imaginary line drawn from the planet to the sun sweeps out equal areas in equal amounts of time; and the ratio of the squares of the periods of revolution of any two planets is equal to the ratio of the cubes of their average distances from the sun. The orbits of the solar planets, while elliptical, are almost circular; on the other hand, the orbits of many of the extrasolar planets discovered during the 1990s are highly elliptical.
After the laws of planetary motion were established, astronomers developed the means of determining the size, shape, and relative position in space of a planet's orbit. The size and shape of an orbit are specified by its semimajor axis and by its eccentricity. The semimajor axis is a length equal to half the greatest diameter of the orbit. The eccentricity is the distance of the sun from the center of the orbit divided by the length of the orbit's semimajor axis; this value is a measure of how elliptical the orbit is. The position of the orbit in space, relative to the earth, is determined by three factors: (1) the inclination, or tilt, of the plane of the planet's orbit to the plane of the earth's orbit (the ecliptic); (2) the longitude of the planet's ascending node (the point where the planet cuts the ecliptic moving from south to north); and (3) the longitude of the planet's perihelion point (point at which it is nearest the sun; see apsis).
These quantities, which determine the size, shape, and position of a planet's orbit, are known as the orbital elements. If only the sun influenced the planet in its orbit, then by knowing the orbital elements plus its position at some particular time, one could calculate its position at any later time. However, the gravitational attractions of bodies other than the sun cause perturbations in the planet's motions that can make the orbit shift, or precess, in space or can cause the planet to wobble slightly. Once these perturbations have been calculated one can closely determine its position for any future date over long periods of time. Modern methods for computing the orbit of a planet or other body have been refined from methods developed by Newton, Laplace, and Gauss, in which all the needed quantities are acquired from three separate observations of the planet's apparent position.
eccentricitySymbol: e . A measure of the extent to which an elliptical orbit departs from circularity. It is given by the ratio c /2a where c is the distance between the focal points of the ellipse and 2a is the length of the major axis. For a circular orbit e = 0. The planets and most of their satellites have an eccentricity range of 0–0.25 (see table). Many comets and some of the asteroids and planetary satellites have very eccentric orbits. The eccentricity of an orbit varies over a long period due to changing gravitational effects: that of the Earth's orbit varies between about 0.005 to 0.06 in a period of about 100 000 years. See also conic sections.
in a conic section, a number equal to the ratio of a point’s distance from the focus to its distance from a directrix. The eccentricity characterizes the shape of a conic section. For example, two conic sections that have the same eccentricity are similar. The eccentricity of an ellipse is less than unity, that of a hyperbola is greater than unity, and that of a parabola is equal to unity. For the ellipse and hyperbola, the eccentricity may be defined as the ratio of the distances between the foci to the longer or real axis.