Planetary Motion
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Planetary Motion
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion. For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital ...
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Animation Of C/2018 Y1 Orbit 1600-2500
Animation is a method by which image, still figures are manipulated to appear as Motion picture, moving images. In traditional animation, images are drawn or painted by hand on transparent cel, celluloid sheets to be photographed and exhibited on film. Today, most animations are made with computer-generated imagery (CGI). Computer animation can be very detailed Computer animation#Animation methods, 3D animation, while Traditional animation#Computers and traditional animation, 2D computer animation (which may have the look of traditional animation) can be used for stylistic reasons, low bandwidth, or faster real-time renderings. Other common animation methods apply a stop motion technique to two- and three-dimensional objects like cutout animation, paper cutouts, puppets, or Clay animation, clay figures. A cartoon is an animated film, usually a short film, featuring an cartoon, exaggerated visual style. The style takes inspiration from comic strips, often featuring anthropomorphi ...
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Geodesic
In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight line". The noun '' geodesic'' and the adjective ''geodetic'' come from ''geodesy'', the science of measuring the size and shape of Earth, though many of the underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between two points on the Earth's surface. For a spherical Earth, it is a segment of a great circle (see also great-circle distance). The term has since been generalized to more abstract mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph. In a Riemannian manifold or submanifold, geodesics are characterised by the property of having vanishin ...
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Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the greatest mathematicians and physicists and among the most influential scientists of all time. He was a key figure in the philosophical revolution known as the Enlightenment. His book (''Mathematical Principles of Natural Philosophy''), first published in 1687, established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for developing infinitesimal calculus. In the , Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint for centuries until it was superseded by the theory of relativity. Newton used his mathematical description of gravity to derive Kepler's laws of planetary motion, account for ...
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Kepler Orbits
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books ''Astronomia nova'', ''Harmonice Mundi'', and ''Epitome Astronomiae Copernicanae''. These works also provided one of the foundations for Newton's theory of universal gravitation. Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting (or Keplerian) telescope, and ...
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Astronomical Unit
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits the Sun, from a maximum (aphelion) to a minimum (perihelion) and back again once each year. The astronomical unit was originally conceived as the average of Earth's aphelion and perihelion; however, since 2012 it has been defined as exactly (see below for several conversions). The astronomical unit is used primarily for measuring distances within the Solar System or around other stars. It is also a fundamental component in the definition of another unit of astronomical length, the parsec. History of symbol usage A variety of unit symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union (IAU) had used the symbol ''A'' to denote a length equal to the astronomical ...
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About
About may refer to: * About (surname) * About.com, an online source for original information and advice * about.me, a personal web hosting service * ''abOUT'', a Canadian LGBT online magazine * ''About Magazine'', a Texas-based digital platform covering LGBT news * About URI scheme, an internal URI scheme * About box, a dialog box that displays information related to a computer software * About equal sign, symbol used to indicate values are approximately equal See also * About Face (other) * About Last Night (other) * About Time (other) * About us (other) * About You (other) * ''about to The ''going-to'' future is a grammatical construction used in English to refer to various types of future occurrences. It is made using appropriate forms of the expression ''to be going to''.Fleischman, Suzanne, ''The Future in Thought and Langua ...
'', one of the future constructions in English grammar * {{disambiguation ...
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Focus (geometry)
In geometry, focuses or foci (), singular focus, are special points with reference to which any of a variety of curves is constructed. For example, one or two foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola. In addition, two foci are used to define the Cassini oval and the Cartesian oval, and more than two foci are used in defining an ''n''-ellipse. Conic sections Defining conics in terms of two foci An ellipse can be defined as the locus of points for which the sum of the distances to two given foci is constant. A circle is the special case of an ellipse in which the two foci coincide with each other. Thus, a circle can be more simply defined as the locus of points each of which is a fixed distance from a single given focus. A circle can also be defined as the circle of Apollonius, in terms of two different foci, as the locus of points having a fixed ratio of distances to the two foci. A parabola is a li ...
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Epicycle
In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle (, meaning "circle moving on another circle") was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. In particular it explained the apparent retrograde motion of the five planets known at the time. Secondarily, it also explained changes in the apparent distances of the planets from the Earth. It was first proposed by Apollonius of Perga at the end of the 3rd century BC. It was developed by Apollonius of Perga and Hipparchus of Rhodes, who used it extensively, during the 2nd century BC, then formalized and extensively used by Ptolemy in his 2nd century AD astronomical treatise the '' Almagest''. Epicyclical motion is used in the Antikythera mechanism, an ancient Greek astronomical device for compensating for the elliptical orbit of the Moon, moving faster at perigee and slower at apogee than circular orbits would, using fo ...
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Circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. Usually, the radius is required to be a positive number. A circle with r=0 (a single point) is a degenerate case. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. Specifically, a circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a '' disc''. A circle may also be defined as a special ki ...
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Solar System
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar System" and "solar system" structures in theinaming guidelines document. The name is commonly rendered in lower case ('solar system'), as, for example, in the ''Oxford English Dictionary'' an''Merriam-Webster's 11th Collegiate Dictionary''. is the gravity, gravitationally bound system of the Sun and the objects that orbit it. It Formation and evolution of the Solar System, formed 4.6 billion years ago from the gravitational collapse of a giant interstellar molecular cloud. The solar mass, vast majority (99.86%) of the system's mass is in the Sun, with most of the Jupiter mass, remaining mass contained in the planet Jupiter. The four inner Solar System, inner system planets—Mercury (planet), Mercury, Venus, Earth and Mars—are terrest ...
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Johannes Kepler
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books ''Astronomia nova'', ''Harmonice Mundi'', and ''Epitome Astronomiae Copernicanae''. These works also provided one of the foundations for Newton's theory of universal gravitation. Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting (or Keplerian) telescope, an ...
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Copernicus
Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulated a model of the universe that placed the Sun rather than Earth at its center. In all likelihood, Copernicus developed his model independently of Aristarchus of Samos, an ancient Greek astronomer who had formulated such a model some eighteen centuries earlier. The publication of Copernicus's model in his book ' (''On the Revolutions of the Celestial Spheres''), just before his death in 1543, was a major event in the history of science, triggering the Copernican Revolution and making a pioneering contribution to the Scientific Revolution. Copernicus was born and died in Royal Prussia, a region that had been part of the Kingdom of Poland since 1466. A polyglot and polymath, he obtained a doctorate in canon law and was a mathematician, astro ...
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