# eccentricity

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## orbit

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.

### Planetary Orbits

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.

### Nonplanetary Orbits

The laws of planetary orbits also apply to the orbits of comets, natural satellites, artificial satellites, and space probes. The orbits of comets are very elongated; some are long ellipses, some are nearly parabolic (see parabola), and some may be hyperbolic. When the orbit of a newly discovered comet is calculated, it is first assumed to be a parabola and then corrected to its actual shape when more measured positions are obtained. Natural satellites that are close to their primaries tend to have nearly circular orbits in the same plane as that of the planet's equator, while more distant satellites may have quite eccentric orbits with large inclinations to the planet's equatorial plane. Because of the moon's proximity to the earth and its large relative mass, the earth-moon system is sometimes considered a double planet. It is the center of the earth-moon system, rather than the center of the earth itself, that describes an elliptical orbit around the sun in accordance with Kepler's laws. All of the planets and most of the satellites in the solar system move in the same direction in their orbits, counterclockwise as viewed from the north celestial pole; some satellites, probably captured asteroids, have retrograde motion, i.e., they revolve in a clockwise direction.
Eccentricity

## eccentricity

Symbol: 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.
Collins Dictionary of Astronomy © Market House Books Ltd, 2006
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Eccentricity

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.

## eccentricity

[‚ek·sən′tris·əd·ē]
(mathematics)
The ratio of the distance of a point on a conic from the focus to the distance from the directrix.
(mechanics)
The distance of the geometric center of a revolving body from the axis of rotation.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## Eccentricity

weird family, presented in grotesque domesticity. [TV: Terrace, I, 29]
Boynton, Nanny
travels with set of Encyclopaedia Britannica to settle disputes. [Am. Lit.: “Percy” in Stories, 634–644]
Dick, Mr.
odd but harmless old gentleman. [Br. Lit.: David Copperfield]
Doolittle, Doctor
veterinarian who talks to animals. [Children’s Lit.: Dr. Doolittle]
Flite, Miss
“ancient” ward in Chancery. [Br. Lit.: Bleak House]
Great-Aunt Dymphna
outlandish dresser who pointedly doesn’t eat meat. [Children’s Lit.: The Growing Summer, Fisher 124–127]
Havisham, Miss
jilted bride turns into witchlike old woman. [Br. Lit.: Great Expectations]
Longstocking, Pippi
outrageous, rebellious, imaginative child. [Children’s Lit.: Pippi Longstocking]
individualist; only girl “out of line.” [Children’s Lit.: Madeline, Fisher, 196]
delightfully pixilated old woman manages to exploit the Parisian exploiters. [Fr. Lit.: The Madwoman of Chaillot, Benét, 618]
Pickwick, Mr. (Samuel)
jolly “conformist” who understands anything but the obvious. [Br. Lit.: Pickwick Papers]
Poppins, Mary
English nanny who practises levitation, flies up chimneys, etc. [Children’s Lit.: Mary Poppins, Fisher, 218]
Salus, St. Simeon
behaved queerly to share outcasts’ contempt. [Christian Hagiog.: Attwater, 311]

## eccentricity

1. deviation from a circular path or orbit
2. a measure of the noncircularity of an elliptical orbit, the distance between the foci divided by the length of the major axis
3. Geometry a number that expresses the shape of a conic section: the ratio of the distance of a point on the curve from a fixed point (the focus) to the distance of the point from a fixed line (the directrix)
4. the degree of displacement of the geometric centre of a rotating part from the true centre, esp of the axis of rotation of a wheel or shaft
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
References in periodicals archive ?
* eccentricity did not influence the real diameter of reamed hole.
where [[sigma].sub.BA], [[sigma].sub.PA], [[sigma].sub.AEij], [[sigma].sub.TDij], [[sigma].sub.SDDij] are RMS of vehicle body vertical acceleration (BVA), pitch angle (PA), airgap eccentricity (AE), tyre deformation (TD), and suspension dynamic deflections (SDD).
13, the fundamental frequency of pre-stressed concrete beam showed no obvious changes with the increase of pre-stress value under the same eccentricity. When the pre-stress value increased from 0 kN to 200 kN, the fundamental frequency of concrete beams only rose by about 5%.
Figure 5 shows that flow coefficient also decreases with increase in relief track depth ratio and for a given relief track depth ratio flow coefficient increases with increase in eccentricity ratio.
Figure 6 represents the effect of fluid inertia on the SFD fluid film reaction forces at small eccentricity ratios.
In the case of dynamic eccentricity, the length of the airgap can be expressed as follows [27]:
Moreover, the inertia force of leakage flow at 90[degrees] is smaller than that at 270[degrees], which implies that the leakage flow is nonuniform in the circumferential direction because of eccentricity and the circumferential force is nonuniform too.
Figures 15 to 18 show the thermal patterns for Ta=33[degrees]C, E=0.48 x [10.sup.-3] gm/[cm.sup.2]min, case I and stage V for different eccentricity [d.sub.1]=0, 0.25, 0.5 and 0.75 respectively.
The presence of the eccentricity and ellipticity in the construction of cable has different effects on the distribution of the electric field strength at the conductor and the insulation.
From the table 1 it is seen that eccentricity increases with increase in the magnitude of asymmetry.
Also if x and y are vertices of a connected graph G and Aut(G), then d(x,y)=d( (x), (y)) [1,5].Thus to determine the eccentricity of the vertices of P(n,m), it is enough to determine the eccentricity of exactly one vertex on the inner and outer cycle.

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