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Rosette Orbit
A Klemperer rosette is a gravitational system of heavier and lighter bodies orbiting in a regular repeating pattern around a common barycenter. It was first described by W. B. Klemperer in 1962, and is a special case of a central configuration. Klemperer described the system as follows: The simplest rosette would be a series of four alternating heavier and lighter bodies, 90 degrees from one another, in a rhombic configuration eavy, Light, Heavy, Light where the two larger bodies have the same mass, and likewise the two smaller bodies have the same mass. The number of "mass types" can be increased, so long as the arrangement pattern is cyclic: e.g. 1,2,3 ... 1,2,3 1,2,3,4,5 ... 1,2,3,4,5 1,2,3,3,2,1 ... 1,2,3,3,2,1 etc. Klemperer also mentioned octagonal and rhombic rosettes. While all Klemperer rosettes are vulnerable to destabilization, the hexagonal rosette has extra stability because the "planets" sit in each other's L4 and L5 Lagrangian points. Misuse and mis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Klemperer Rosette
A Klemperer rosette is a gravitational system of heavier and lighter bodies orbiting in a regular repeating pattern around a common barycenter. It was first described by W. B. Klemperer in 1962, and is a special case of a central configuration. Klemperer described the system as follows: The simplest rosette would be a series of four alternating heavier and lighter bodies, 90 degrees from one another, in a rhombic configuration eavy, Light, Heavy, Light where the two larger bodies have the same mass, and likewise the two smaller bodies have the same mass. The number of "mass types" can be increased, so long as the arrangement pattern is cyclic: e.g. 1,2,3 ... 1,2,3 1,2,3,4,5 ... 1,2,3,4,5 1,2,3,3,2,1 ... 1,2,3,3,2,1 etc. Klemperer also mentioned octagonal and rhombic rosettes. While all Klemperer rosettes are vulnerable to destabilization, the hexagonal rosette has extra stability because the "planets" sit in each other's L4 and L5 Lagrangian points. Misuse and missp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two together, may be called a polygon. The segments of a polygonal circuit are called its '' edges'' or ''sides''. The points where two edges meet are the polygon's '' vertices'' (singular: vertex) or ''corners''. The interior of a solid polygon is sometimes called its ''body''. An ''n''-gon is a polygon with ''n'' sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains of simple polygons and they often define a polygon accordingly. A polygonal boundary may be allowed to cross over itself, creating star polygons and other self-intersecting polygons. A polygon is a 2-dimensional example of the more general polytope in any num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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) telescop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentagon
In geometry, a pentagon (from the Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting. A self-intersecting ''regular pentagon'' (or ''star pentagon'') is called a pentagram. Regular pentagons A '' regular pentagon'' has Schläfli symbol and interior angles of 108°. A '' regular pentagon'' has five lines of reflectional symmetry, and rotational symmetry of order 5 (through 72°, 144°, 216° and 288°). The diagonals of a convex regular pentagon are in the golden ratio to its sides. Given its side length t, its height H (distance from one side to the opposite vertex), width W (distance between two farthest separated points, which equals the diagonal length D) and circumradius R are given by: :\begin H &= \frac~t \approx 1.539~t, \\ W= D &= \frac~t\approx 1.618~t, \\ W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fleet Of Worlds
''Fleet of Worlds'' is a science fiction novel by American writers Larry Niven and Edward M. Lerner, part of Niven's Known Space series. The Fleet of Worlds (sub)series, consisting of this book and its four sequels, is named for its opening book. Novel The novel, co-written by Niven and Edward M. Lerner, was released in 2007 and nominated for a Prometheus Award. It is set shortly after the events of the short story " At the Core". The novel concerns the liberation of New Terra from the Concordance of the Pierson's Puppeteers Pierson's Puppeteers, often known just as Puppeteers, are a fictional alien race from American author Larry Niven's ''Known Space'' books. The race first appeared in Niven’s novella '' Neutron Star''. Biology and sociology The sobriquet "Pier .... It also introduces a new intelligent species to Known Space, the Gw'oth. Series The Fleet of World series consists of five books by the same authors: *''Fleet of Worlds'' (2007), * '' Juggler of Worlds'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierson's Puppeteer
Pierson's Puppeteers, often known just as Puppeteers, are a fictional alien race from American author Larry Niven's ''Known Space'' books. The race first appeared in Niven’s novella ''Neutron Star''. Biology and sociology The sobriquet "Pierson's" comes from the name of the human who made first contact in the early 26th century in the ''Known Space'' timeline. According to the Niven story ''The Soft Weapon'', Pierson was a crewman aboard a spaceship at a time when there was a camp revival of the ancient '' Time for Beany'' TV show featuring Cecil the Seasick Sea Serpent, an animated character based on a hand puppet; Pierson accordingly described the alien he had met as a Puppeteer, given some resemblance of the head and neck with Cecil. Puppeteers dealing with humans usually give themselves the names of centaurs and other figures in Greek mythology, such as Nessus, Nike and Chiron. Puppeteers' names for themselves are reportedly highly complex, and unpronounceable by humans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ringworld
''Ringworld'' is a 1970 science fiction novel by Larry Niven, set in his Known Space universe and considered a classic of science fiction literature. ''Ringworld'' tells the story of Louis Wu and his companions on a mission to the Ringworld, a rotating wheel artificial world, an alien construct in space in diameter. Niven later added three sequel novels and then cowrote, with Edward M. Lerner, four prequels and a final sequel; the five latter novels constitute the Fleet of Worlds series. All the novels in the Ringworld series tie into numerous other books set in Known Space. ''Ringworld'' won the Nebula Award in 1970, as well as both the Hugo Award and Locus Award in 1971. Plot summary On planet Earth in 2850 AD, Louis Gridley Wu is celebrating his 200th birthday. Despite his age, Louis is in perfect physical condition due to the longevity drug boosterspice. He meets Nessus, a Pierson's puppeteer, who offers him a mysterious job. Intrigued, Louis eventually accepts. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Larry Niven
Laurence van Cott Niven (; born April 30, 1938) is an American science fiction writer. His best-known works are '' Ringworld'' (1970), which received Hugo, Locus, Ditmar, and Nebula awards, and, with Jerry Pournelle, '' The Mote in God's Eye'' (1974) and '' Lucifer's Hammer'' (1977). The Science Fiction and Fantasy Writers of America named him the 2015 recipient of the Damon Knight Memorial Grand Master Award. His work is primarily hard science fiction, using big science concepts and theoretical physics. It also often includes elements of detective fiction and adventure stories. His fantasy includes the series '' The Magic Goes Away'', rational fantasy dealing with magic as a non-renewable resource. Biography Niven was born in Los Angeles. He is a great-grandson of Edward L. Doheny, an oil tycoon who drilled the first successful well in the Los Angeles City Oil Field in 1892, and also was subsequently implicated in the Teapot Dome scandal. Niven briefly attended ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Center Of Mass
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Velocity
In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object rotates or revolves relative to a point or axis). The magnitude of the pseudovector represents the ''angular speed'', the rate at which the object rotates or revolves, and its direction is normal to the instantaneous plane of rotation or angular displacement. The orientation of angular velocity is conventionally specified by the right-hand rule.(EM1) There are two types of angular velocity. * Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. * Spin angular velocity refers to how fast a rigid body rotates with respect to its center of rotation and is independent of the choice of origin, in contrast to orbital angular v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equilateral
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle. Principal properties Denoting the common length of the sides of the equilateral triangle as a, we can determine using the Pythagorean theorem that: *The area is A=\frac a^2, *The perimeter is p=3a\,\! *The radius of the circumscribed circle is R = \frac *The radius of the inscribed circle is r=\frac a or r=\frac *The geometric center of the triangle is the center of the circumscribed and inscribed circles *The altitude (height) from any side is h=\frac a Denoting the radius of the circumscribed circle as ''R'', we can determine using trigonometry that: *The area of the triangle is \mathrm=\fracR^2 Many of these quantities have simple r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptical Orbit With Objects At L4 And L5
Elliptical may mean: * having the shape of an ellipse, or more broadly, any oval shape ** in botany, having an elliptic leaf shape ** of aircraft wings, having an elliptical planform * characterised by ellipsis (the omission of words), or by concision more broadly * an elliptical trainer, an exercise machine See also * Ellipse (other) In mathematics, an ellipse is a geometrical figure. Ellipse may also refer to: *MacAdam ellipse, an area in a chromaticity diagram * Elliptic leaf shape * Superellipse, a geometric figure As a name, it may also be: * The Ellipse, an area in Wa ... * Ellipsis (other) {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
