Orbit

In physics, an orbit is the gravitationally curved path of an object about a point in space, for example the orbit of a planet about a star. Orbits of planets are typically elliptical, and the central mass being orbited is at a focal point of the ellipse.

Current understanding of the mechanics of orbital motion is based on Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of space-time, with orbits following geodesics. For ease of calculation, relativity is commonly approximated by the force-based theory of universal gravitation based on Kepler's laws of planetary motion.

History

Historically, the apparent motions of the planets were described geometrically (without regard to gravity) in terms of epicycles, which are the sums of numerous circular motions. Theories of this kind predicted paths of the planets moderately well, until Johannes Kepler was able to show that the motions of planets were elliptical motions.

The celestial spheres model is a geocentric model of the solar system originally used to explain the apparent motion of the planets in the sky. It posited the existence of perfect moving spheres or rings to which the stars and planets were attached. After the planets' motions were more accurately measured, theoretical mechanisms such as deferent and epicycles were added. Although it was capable of accurately predicting the planets' positions in the sky, more and more epicycles were required as the measurements became more accurate, hence the model became more and more unwieldy.

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Group action

In mathematics, a symmetry group is an abstraction used to describe the symmetries of an object. A group action formalizes the relationship between the group and the symmetries of the object. It relates each element of the group to a particular transformation of the object.

In this case, the group is also called a permutation group (especially if the set is finite or not a vector space) or transformation group (especially if the set is a vector space and the group acts like linear transformations of the set). A permutation representation of a group G is a representation of G as a group of permutations of the set (usually if the set is finite), and may be described as a group representation of G by permutation matrices. It is the same as a group action of G on an ordered basis of a vector space.

A group action is an extension to the notion of a symmetry group in which every element of the group "acts" like a bijective transformation (or "symmetry") of some set, without being identified with that transformation. This allows for a more comprehensive description of the symmetries of an object, such as a polyhedron, by allowing the same group to act on several different sets of features, such as the set of vertices, the set of edges and the set of faces of the polyhedron.

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Orbit (horse)

Orbit (foaled 1885) was a Thoroughbred racehorse. He was trained at Kingsclere by John Porter for the 1st Duke of Westminster. As a three-year-old he won the Eclipse Stakes.

Breeding

Orbit was the son of Epsom Derby and Champion Stakes winner Bend Or. His dam was Fair Alice, a daughter of July Stakes winner Cambuscan.

Racing career

Orbit won three races as a two-year-old; the Criterion Nursery Handicap at Newmarket, the Kempton Park Champion Nursery Handicap and the Daveridge Stakes. Orbit started his three-year-old career by winning the Craven Stakes at Newmarket by ¾ length from Cotillon. His next race came in the 2000 Guineas at Newmarket. Friar's Balsam started as the 1/3 favourite for the race, with Ayrshire at 100/12 and Orbit at 100/8. Orbit ran on well in the closing stages to finish in third place. Ayrshire won the race by two lengths from Johnny Morgan, who was a head in front of Orbit. After winning the 2000 Guineas win Ayrshire started as the 5/6 favourite for the Epsom Derby and Orbit was second favourite at 11/2. Orbit could only finish in fifth place, over seven lengths behind winner Ayrshire. He then finished second in the Triennial Stakes at Ascot. Orbit started as the 9/4 favourite for the Eclipse Stakes and in the final 100 yards of the race Orbit gradually edged away from stablemate Ossory and beat him by a length.