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Osipkov–Merritt Model
Osipkov–Merritt models (named for Leonid Osipkov and David Merritt) are mathematical representations of spherical stellar systems (galaxies, star clusters, globular clusters etc.). The Osipkov–Merritt formula generates a one-parameter family of phase-space distribution functions that reproduce a specified density profile (representing stars) in a specified gravitational potential (in which the stars move). The density and potential need not be self-consistently related. A free parameter adjusts the degree of velocity anisotropy, from isotropic to completely radial motions. The method is a generalization of Eddington's formula for constructing isotropic spherical models. The method was derived independently by its two eponymous discoverers. Merritt, D. (1985) Spherical stellar systems with spheroidal velocity distributions ''Astron. J.'', 90, 1027 The latter derivation includes two additional families of models (Type IIa, b) with tangentially anisotropic motions. Derivat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, frisbees, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum. Conservation of angular momentum is also why hurricanes form spirals and neutron stars have high rotational rates. In general, conservation limits the possible motion of a system, but it does not uniquely determine it. The three-dimensional angular momentum for a point particle is classically represented as a pseudovector , the cross product of the particle's position vector (relative to some origin) and its momentum vector; the latter is in Newtonian mechanics. Unlike linear momentum, angular m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Binney
James Jeffrey Binney, FRS, FInstP (born 12 April 1950) is a British astrophysicist. He is a professor of physics at the University of Oxford and former head of the Sub-Department of Theoretical Physics as well as an Emeritus Fellow of Merton College. Binney is known principally for his work in theoretical galactic and extragalactic astrophysics, though he has made a number of contributions to areas outside of astrophysics as well. Education and career Binney took a first class BA in the Mathematical Tripos at the University of Cambridge in 1971, then moved to the University of Oxford, reading for a DPhil at Christ Church under Dennis Sciama, which he completed in 1975. He was a visiting scholar at the Institute for Advanced Study, Princeton in 1983–87 and again in the fall of 1989. After holding several post-doctoral positions, including a junior research fellowship at Magdalen College, and a position at Princeton University, Binney returned to Oxford as a university lect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Instability
In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds. Not all systems that are not stable are unstable; systems can also be marginally stable or exhibit limit cycle behavior. In structural engineering, a structure can become unstable when excessive load is applied. Beyond a certain threshold, structural deflections magnify stresses, which in turn increases deflections. This can take the form of buckling or crippling. The general field of study is called structural stability. Atmospheric instability is a major component of all weather systems on Earth. Instability in control systems In the theory of dynamical systems, a state variable in a system is said to be unstable if it evolves without bounds. A system itself is said to be unstable if at least one of its state variables is unstable. In continuous time control theory, a system is unstable if any of the ro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galaxy Cluster
A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. They are the second-largest known gravitationally bound structures in the universe after galaxy filaments and were believed to be the largest known structures in the universe until the 1980s, when superclusters were discovered. One of the key features of clusters is the intracluster medium (ICM). The ICM consists of heated gas between the galaxies and has a peak temperature between 2–15 keV that is dependent on the total mass of the cluster. Galaxy clusters should not be confused with ''galactic clusters'' (also known as open clusters), which are star clusters ''within'' galaxies, or with globular clusters, which typically orbit galaxies. Small aggregates of galaxies are referred to as galaxy groups rather than clusters of galaxies. The galaxy groups and c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dark Matter Halo
According to modern models of physical cosmology, a dark matter halo is a basic unit of cosmological structure. It is a hypothetical region that has decoupled from cosmic expansion and contains gravitationally bound matter. A single dark matter halo may contain multiple virialized clumps of dark matter bound together by gravity, known as subhalos. Modern cosmological models, such as ΛCDM, propose that dark matter halos and subhalos may contain galaxies. The dark matter halo of a galaxy envelops the galactic disc and extends well beyond the edge of the visible galaxy. Thought to consist of dark matter, halos have not been observed directly. Their existence is inferred through observations of their effects on the motions of stars and gas in galaxies and gravitational lensing. Dark matter halos play a key role in current models of galaxy formation and evolution. Theories that attempt to explain the nature of dark matter halos with varying degrees of success include cold dark m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holland Ford
Holland is a geographical regionG. Geerts & H. Heestermans, 1981, ''Groot Woordenboek der Nederlandse Taal. Deel I'', Van Dale Lexicografie, Utrecht, p 1105 and former province on the western coast of the Netherlands. From the 10th to the 16th century, Holland proper was a unified political region within the Holy Roman Empire as a county ruled by the counts of Holland. By the 17th century, the province of Holland had risen to become a maritime and economic power, dominating the other provinces of the newly independent Dutch Republic. The area of the former County of Holland roughly coincides with the two current Dutch provinces of North Holland and South Holland into which it was divided, and which together include the Netherlands' three largest cities: the capital city (Amsterdam), the home of Europe's largest port (Rotterdam), and the seat of government (The Hague). Holland has a population of 6,583,534 as of November 2019, and a population density of 1203/km2. The name ''Hol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Star Cluster
Star clusters are large groups of stars. Two main types of star clusters can be distinguished: globular clusters are tight groups of ten thousand to millions of old stars which are gravitationally bound, while open clusters are more loosely clustered groups of stars, generally containing fewer than a few hundred members, and are often very young. Open clusters become disrupted over time by the gravitational influence of giant molecular clouds as they move through the galaxy, but cluster members will continue to move in broadly the same direction through space even though they are no longer gravitationally bound; they are then known as a stellar association, sometimes also referred to as a ''moving group''. Star clusters visible to the naked eye include the Pleiades, Hyades, and 47 Tucanae. Open cluster Open clusters are very different from globular clusters. Unlike the spherically distributed globulars, they are confined to the galactic plane, and are almost always found wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Collapse
Gravitational collapse is the contraction of an astronomical object due to the influence of its own gravity, which tends to draw matter inward toward the center of gravity. Gravitational collapse is a fundamental mechanism for structure formation in the universe. Over time an initial, relatively smooth distribution of matter will collapse to form pockets of higher density, typically creating a hierarchy of condensed structures such as clusters of galaxies, stellar groups, stars and planets. A star is born through the gradual gravitational collapse of a cloud of interstellar matter. The compression caused by the collapse raises the temperature until thermonuclear fusion occurs at the center of the star, at which point the collapse gradually comes to a halt as the outward thermal pressure balances the gravitational forces. The star then exists in a state of dynamic equilibrium. Once all its energy sources are exhausted, a star will again collapse until it reaches a new equilibrium ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abel Integral Equation
A tautochrone or isochrone curve (from Greek prefixes tauto- meaning ''same'' or iso- ''equal'', and chrono ''time'') is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the curve. The curve is a cycloid, and the time is equal to π times the square root of the radius (of the circle which generates the cycloid) over the acceleration of gravity. The tautochrone curve is related to the brachistochrone curve, which is also a cycloid. The tautochrone problem The tautochrone problem, the attempt to identify this curve, was solved by Christiaan Huygens in 1659. He proved geometrically in his ''Horologium Oscillatorium'', originally published in 1673, that the curve is a cycloid. The cycloid is given by a point on a circle of radius r tracing a curve as the circle rolls along the x axis, as: \begin x &= r(\theta - \sin \theta) \\ y &= r(1 - \cos \theta), \end Huygens al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Potential
In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric potential with mass playing the role of charge. The reference location, where the potential is zero, is by convention infinitely far away from any mass, resulting in a negative potential at any finite distance. In mathematics, the gravitational potential is also known as the Newtonian potential and is fundamental in the study of potential theory. It may also be used for solving the electrostatic and magnetostatic fields generated by uniformly charged or polarized ellipsoidal bodies. Potential energy The gravitational potential (''V'') at a location is the gravitational potential energy (''U'') at that location per unit mass: V = \frac, where ''m'' is the mass of the object. Potential energy is equal (in magnitude, but negative) to the w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ansatz
In physics and mathematics, an ansatz (; , meaning: "initial placement of a tool at a work piece", plural Ansätze ; ) is an educated guess or an additional assumption made to help solve a problem, and which may later be verified to be part of the solution by its results. Use An ansatz is the establishment of the starting equation(s), the theorem(s), or the value(s) describing a mathematical or physical problem or solution. It typically provides an initial estimate or framework to the solution of a mathematical problem, and can also take into consideration the boundary conditions (in fact, an ansatz is sometimes thought of as a "trial answer" and an important technique in solving differential equations). After an ansatz, which constitutes nothing more than an assumption, has been established, the equations are solved more precisely for the general function of interest, which then constitutes a confirmation of the assumption. In essence, an ansatz makes assumptions about the form o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
