|
N-body Units
''N''-body units are a completely self-contained system of units used for ''N''-body simulations of self-gravitating systems in astrophysics. In this system, the base physical units are chosen so that the total mass, ''M'', the gravitational constant, ''G'', and the virial radius, ''R'', are normalized. The underlying assumption is that the system of ''N'' objects (stars) satisfies the virial theorem In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by potential forces, with that of the total potential energy of the system. .... The consequence of standard ''N''-body units is that the velocity dispersion of the system, ''v'', is \scriptstyle \frac\sqrt and that the dynamical or crossing time, ''t'', is \scriptstyle 2\sqrt . The use of standard ''N''-body units was advocated by Michel Hénon in 1971. Early adopters of this system of units included H. Cohn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Length
Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system the base unit for length is the metre. Length is commonly understood to mean the most extended dimension of a fixed object. However, this is not always the case and may depend on the position the object is in. Various terms for the length of a fixed object are used, and these include height, which is vertical length or vertical extent, and width, breadth or depth. Height is used when there is a base from which vertical measurements can be taken. Width or breadth usually refer to a shorter dimension when length is the longest one. Depth is used for the third dimension of a three dimensional object. Length is the measure of one spatial dimension, whereas area is a measure of two dimensions (length square ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple definitions which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a measure of the body's inertia, meaning the resistance to acceleration (change of velocity) when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Systems Of Measurement
A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Systems of measurement in use include the International System of Units or (the modern form of the metric system), the British imperial system, and the United States customary system. History The French Revolution gave rise to the metric system, and this has spread around the world, replacing most customary units of measure. In most systems, length (distance), mass, and time are ''base quantities''. Later science developments showed that an electromagnetic quantity such as electric charge or electric current could be added to extend the set of base quantities. Gaussian units have only length, mass, and time as base quantities, with no separate electromagnetic dimension. Other quantities, such as power and speed, are derived from the base set: for example, spe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-body Simulation
In physics and astronomy, an ''N''-body simulation is a simulation of a dynamical system of particles, usually under the influence of physical forces, such as gravity (see ''n''-body problem for other applications). ''N''-body simulations are widely used tools in astrophysics, from investigating the dynamics of few-body systems like the Earth-Moon-Sun system to understanding the evolution of the large-scale structure of the universe. In physical cosmology, ''N''-body simulations are used to study processes of non-linear structure formation such as galaxy filaments and galaxy halos from the influence of dark matter. Direct ''N''-body simulations are used to study the dynamical evolution of star clusters. Nature of the particles The 'particles' treated by the simulation may or may not correspond to physical objects which are particulate in nature. For example, an N-body simulation of a star cluster might have a particle per star, so each particle has some physical significa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Constant
The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity. In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance. In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor (also referred to as the stress–energy tensor). The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately The modern notation of Newton's law involving was introduced in the 1890s by C. V. Boys. The first impl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virial Theorem
In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by potential forces, with that of the total potential energy of the system. Mathematically, the theorem states \left\langle T \right\rangle = -\frac12\,\sum_^N \bigl\langle \mathbf_k \cdot \mathbf_k \bigr\rangle where is the total kinetic energy of the particles, represents the force on the th particle, which is located at position , and angle brackets represent the average over time of the enclosed quantity. The word virial for the right-hand side of the equation derives from ''vis'', the Latin word for "force" or "energy", and was given its technical definition by Rudolf Clausius in 1870. The significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems that defy an exact solution, such as those considered in statistical mechanics; thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virial Theorem
In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by potential forces, with that of the total potential energy of the system. Mathematically, the theorem states \left\langle T \right\rangle = -\frac12\,\sum_^N \bigl\langle \mathbf_k \cdot \mathbf_k \bigr\rangle where is the total kinetic energy of the particles, represents the force on the th particle, which is located at position , and angle brackets represent the average over time of the enclosed quantity. The word virial for the right-hand side of the equation derives from ''vis'', the Latin word for "force" or "energy", and was given its technical definition by Rudolf Clausius in 1870. The significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems that defy an exact solution, such as those considered in statistical mechanics; thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michel Hénon
Michel Hénon (; 23 July 1931, Paris – 7 April 2013, Nice) was a French mathematician and astronomer. He worked for a long time at the Nice Observatory. In astronomy, Hénon is well known for his contributions to stellar dynamics. In the late 1960s and early 1970s he made important contributions on the dynamical evolution of star clusters, in particular globular clusters. He developed a numerical technique using Monte Carlo methods to follow the dynamical evolution of a spherical star cluster much faster than the so-called ''n''-body methods. In mathematics, he is well known for the Hénon map, a simple discrete dynamical system that exhibits chaotic behavior. He published a two-volume work on the restricted three-body problem. In 1978 he was awarded the '' Prix Jean Ricard''. See also *N-body units References External links Hénon's publications(a partial list from NASA Astrophysics Data System). A discussionof Hénon's equation, contains further links. Simulationof H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lecture Notes In Physics
''Lecture Notes in Physics'' (LNP) is a book series published by Springer Science+Business Media in the field of physics, including articles related to both research and teaching. It was established in 1969. See also * ''Lecture Notes in Computer Science'' * ''Lecture Notes in Mathematics ''Lecture Notes in Mathematics'' is a book series in the field of mathematics, including articles related to both research and teaching. It was established in 1964 and was edited by A. Dold, Heidelberg and B. Eckmann, Zürich. Its publisher is Sp ...'' External links * Publications established in 1969 Physics books Series of books Springer Science+Business Media books {{physics-book-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Edinburgh
The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 1582 and officially opened in 1583, it is one of Scotland's four ancient universities and the sixth-oldest university in continuous operation in the English-speaking world. The university played an important role in Edinburgh becoming a chief intellectual centre during the Scottish Enlightenment and contributed to the city being nicknamed the " Athens of the North." Edinburgh is ranked among the top universities in the United Kingdom and the world. Edinburgh is a member of several associations of research-intensive universities, including the Coimbra Group, League of European Research Universities, Russell Group, Una Europa, and Universitas 21. In the fiscal year ending 31 July 2021, it had a total income of £1.176 billion, of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Cosmology
Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fundamental questions about its Cosmogony, origin, structure, Chronology of the universe, evolution, and ultimate fate.For an overview, see Cosmology as a science originated with the Copernican principle, which implies that astronomical object, celestial bodies obey identical physical laws to those on Earth, and Newtonian mechanics, which first allowed those physical laws to be understood. Physical cosmology, as it is now understood, began with the development in 1915 of Albert Einstein's general relativity, general theory of relativity, followed by major observational discoveries in the 1920s: first, Edwin Hubble discovered that the universe contains a huge number of external Galaxy, galaxies beyond the Milky Way; then, work by Vesto Sli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Systems Of Units
A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Systems of measurement in use include the International System of Units or (the modern form of the metric system), the British imperial system, and the United States customary system. History The French Revolution gave rise to the metric system, and this has spread around the world, replacing most customary units of measure. In most systems, length (distance), mass, and time are ''base quantities''. Later science developments showed that an electromagnetic quantity such as electric charge or electric current could be added to extend the set of base quantities. Gaussian units have only length, mass, and time as base quantities, with no separate electromagnetic dimension. Other quantities, such as power and speed, are derived from the base set: for example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
