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Polytrope
In astrophysics, a polytrope refers to a solution of the Lane–Emden equation in which the pressure depends upon the density in the form P = K \rho^ = K \rho^, where is pressure, is density and is a Constant (mathematics), constant of Proportionality (mathematics), proportionality. The constant is known as the polytropic index; note however that the polytropic index has an alternative definition as with ''n'' as the exponent. This relation need not be interpreted as an equation of state, which states ''P'' as a function of both ρ and ''T'' (the temperature); however in the particular case described by the polytrope equation there are other additional relations between these three quantities, which together determine the equation. Thus, this is simply a relation that expresses an assumption about the change of pressure with radius in terms of the change of density with radius, yielding a solution to the Lane–Emden equation. Sometimes the word ''polytrope'' may refer t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equation Of State
In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars. Though there are many equations of state, none accurately predicts properties of substances under all conditions. The quest for a universal equation of state has spanned three centuries. Overview At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polytropic Index
A polytropic process is a thermodynamic process that obeys the relation: p V^ = C where ''p'' is the pressure, ''V'' is volume, ''n'' is the polytropic index, and ''C'' is a constant. The polytropic process equation describes expansion and compression processes which include heat transfer. Particular cases Some specific values of ''n'' correspond to particular cases: * n=0 for an isobaric process, * n=+\infty for an isochoric process. In addition, when the ideal gas law applies: * n=1 for an isothermal process, * n=\gamma for an isentropic process. Where \gamma is the ratio of the heat capacity at constant pressure (C_P) to heat capacity at constant volume (C_V). Equivalence between the polytropic coefficient and the ratio of energy transfers For an ideal gas in a closed system undergoing a slow process with negligible changes in kinetic and potential energy the process is polytropic, such that p v^ = C where ''C'' is a constant, K = \frac, \gamma = \frac, and with the po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Murnaghan Equation Of State
The Murnaghan equation of state is a relationship between the volume of a body and the pressure to which it is subjected. This is one of many state equations that have been used in earth sciences and shock physics to model the behavior of matter under conditions of high pressure. It owes its name to Francis D. Murnaghan who proposed it in 1944 to reflect material behavior under a pressure range as wide as possible to reflect an experimentally established fact: the more a solid is compressed, the more difficult it is to compress further. The Murnaghan equation is derived, under certain assumptions, from the equations of continuum mechanics. It involves two adjustable parameters: the modulus of incompressibility ''K''0 and its first derivative with respect to the pressure, ''K'''0, both measured at ambient pressure. In general, these coefficients are determined by a regression on experimentally obtained values of volume ''V'' as a function of the pressure ''P''. These experimenta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lane–Emden Equation
In astrophysics, the Lane–Emden equation is a dimensionless form of Poisson's equation for the gravitational potential of a Newtonian self-gravitating, spherically symmetric, polytropic fluid. It is named after astrophysicists Jonathan Homer Lane and Robert Emden. The equation reads where \xi is a dimensionless radius and \theta is related to the density, and thus the pressure, by \rho=\rho_c\theta^n for central density \rho_c. The index n is the polytropic index that appears in the polytropic equation of state, P = K \rho^\, where P and \rho are the pressure and density, respectively, and K is a constant of proportionality. The standard boundary conditions are \theta(0)=1 and \theta'(0)=0. Solutions thus describe the run of pressure and density with radius and are known as polytropes of index n. If an isothermal fluid (polytropic index tends to infinity) is used instead of a polytropic fluid, one obtains the Emden–Chandrasekhar equation. Applications Physically, hydro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subrahmanyan Chandrasekhar
Subrahmanyan Chandrasekhar (; 19 October 1910 – 21 August 1995) was an Indian Americans, Indian-American theoretical physicist who made significant contributions to the scientific knowledge about the structure of stars, stellar evolution and black holes. He was awarded the 1983 Nobel Prize in Physics along with William Alfred Fowler, William A. Fowler for theoretical studies of the physical processes of importance to the structure and evolution of the stars. His mathematical treatment of stellar evolution yielded many of the current theoretical models of the later evolutionary stages of massive stars and black holes. Many concepts, institutions and inventions, including the Chandrasekhar limit and the Chandra X-ray Observatory, Chandra X-Ray Observatory, are named after him. Chandrasekhar worked on a wide variety of problems in physics during his lifetime, contributing to the contemporary understanding of stellar structure, white dwarfs, stellar dynamics, stochastic process, r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terrestrial Planet
A terrestrial planet, tellurian planet, telluric planet, or rocky planet, is a planet that is composed primarily of silicate, rocks or metals. Within the Solar System, the terrestrial planets accepted by the IAU are the inner planets closest to the Sun: Mercury, Venus, Earth and Mars. Among astronomers who use the geophysical definition of a planet, two or three planetary-mass satellites – Earth's Moon, Io, and sometimes Europa – may also be considered terrestrial planets. The large rocky asteroids Pallas and Vesta are sometimes included as well, albeit rarely. The terms "terrestrial planet" and "telluric planet" are derived from Latin words for Earth (''Terra'' and ''Tellus''), as these planets are, in terms of structure, ''Earth-like''. Terrestrial planets are generally studied by geologists, astronomers, and geophysicists. Terrestrial planets have a solid planetary surface, making them substantially different from larger gaseous planets, which are composed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neutron Star
A neutron star is the gravitationally collapsed Stellar core, core of a massive supergiant star. It results from the supernova explosion of a stellar evolution#Massive star, massive star—combined with gravitational collapse—that compresses the core past white dwarf star density to that of Atomic nucleus, atomic nuclei. Surpassed only by black holes, neutron stars are the second smallest and densest known class of stellar objects. Neutron stars have a radius on the order of and a mass of about . Stars that collapse into neutron stars have a total mass of between 10 and 25 solar masses (), or possibly more for those that are especially rich in Metallicity, elements heavier than hydrogen and helium. Once formed, neutron stars no longer actively generate heat and cool over time, but they may still evolve further through Stellar collision, collisions or Accretion (astrophysics), accretion. Most of the basic models for these objects imply that they are composed almost entirely o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model (abstract)
The term conceptual model refers to any model that is formed after a wikt:concept#Noun, conceptualization or generalization process. Conceptual models are often abstractions of things in the real world, whether physical or social. Semantics, Semantic studies are relevant to various stages of process of concept formation, concept formation. Semantics is fundamentally a study of concepts, the meaning that thinking beings give to various elements of their experience. Overview Concept models and conceptual models The value of a conceptual model is usually directly proportional to how well it corresponds to a past, present, future, actual or potential state of affairs. A concept model (a model of a concept) is quite different because in order to be a good model it need not have this real world correspondence. In artificial intelligence, conceptual models and conceptual graphs are used for building expert systems and knowledge-based systems; here the analysts are concerned to repres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stellar Core
A stellar core is the extremely hot, dense region at the center of a star. For an ordinary main sequence star, the core region is the volume where the temperature and pressure conditions allow for energy production through thermonuclear fusion of hydrogen into helium. This energy in turn counterbalances the mass of the star pressing inward; a process that self-maintains the conditions in Thermal equilibrium, thermal and hydrostatic equilibrium. The minimum temperature required for stellar hydrogen fusion exceeds 107 Kelvin, K (), while the density at the core of the Sun is over . The core is surrounded by the stellar envelope, which transports energy from the core to the stellar atmosphere where it is radiated away into space. Main sequence Main sequence stars are distinguished by the primary energy-generating mechanism in their central region, which joins four hydrogen nuclei to form a single helium atom through thermonuclear fusion. The Sun is an example of this class of star ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virginia Louise Trimble
Virginia Louise Trimble (born November 15, 1943) is an American astronomer specializing in the structure and evolution of stars and galaxies, and the history of astronomy. She has published more than 600 works in Astrophysics, and dozens of other works in the history of other sciences. She is famous for an annual review of astronomy and astrophysics research that was published in the Publications of the Astronomical Society of the Pacific, and often gives summary reviews at astrophysical conferences. In 2018, she was elected a Patron of the American Astronomical Society, for her many years of intellectual, organizational, and financial contributions to the society. Life Trimble "grew up the only child of a chemist father and a mother with a flair for language, within easy driving distance of both UCLA and Caltech." While attending UCLA in 1962, she was the subject of a ''Life'' article titled "Behind a Lovely Face, a 180 I.Q." The following year, she was selected to promote ''Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Red Giant
A red giant is a luminous giant star of low or intermediate mass (roughly 0.3–8 solar masses ()) in a late phase of stellar evolution. The stellar atmosphere, outer atmosphere is inflated and tenuous, making the radius large and the surface temperature around or lower. The appearance of the red giant is from yellow-white to reddish-orange, including the stellar classification, spectral types K and M, sometimes G, but also S-type star, class S stars and most carbon stars. Red giants vary in the way by which they generate energy: * most common red giants are stars on the red-giant branch (RGB) that are still stellar nucleosynthesis, fusing hydrogen into helium in a shell surrounding an inert helium core * red-clump stars in the cool half of the horizontal branch, fusing helium into carbon in their cores via the triple-alpha process * asymptotic-giant-branch (AGB) stars with a helium burning shell outside a degenerate carbon–oxygen core, and a hydrogen-burning shell just beyo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
