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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 a conservative force (where the work done is independent of path), with that of the total potential energy of the system. Mathematically, the theorem states that \langle T \rangle = -\frac12\,\sum_^N \langle\mathbf_k \cdot \mathbf_k\rangle, where T is the total kinetic energy of the N particles, F_k represents the force on the kth 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 , 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 co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanics
Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of an object's position relative to its environment. Theoretical expositions of this branch of physics has its origins in Ancient Greece, for instance, in the writings of Aristotle and Archimedes (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo Galilei, Johannes Kepler, Christiaan Huygens, and Isaac Newton laid the foundation for what is now known as classical mechanics. As a branch of classical physics, mechanics deals with bodies that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as the physical science that deals with the motion of and forces on bodies not in the quantum realm. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrange's Identity
In the algebra, Lagrange's identity, named after Joseph Louis Lagrange, is: \begin \left( \sum_^n a_k^2\right) \left(\sum_^n b_k^2\right) - \left(\sum_^n a_k b_k\right)^2 & = \sum_^ \sum_^n \left(a_i b_j - a_j b_i\right)^2 \\ & \left(= \frac \sum_^n \sum_^n (a_i b_j - a_j b_i)^2\right), \end which applies to any two sets and of real or complex numbers (or more generally, elements of a commutative ring). This identity is a generalisation of the Brahmagupta–Fibonacci identity and a special form of the Binet–Cauchy identity. In a more compact vector notation, Lagrange's identity is expressed as: \left\, \mathbf a \right\, ^2 \left\, \mathbf b \right\, ^2 - (\mathbf \cdot \mathbf )^2 = \sum_ \left(a_i b_j - a_j b_i \right)^2 \, , where a and b are ''n''-dimensional vectors with components that are real numbers. The extension to complex numbers requires the interpretation of the dot product as an inner product or Hermitian dot product. Explicitly, for complex numbers, Lagra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
White Dwarf
A white dwarf is a Compact star, stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very density, dense: in an Earth sized volume, it packs a mass that is comparable to the Sun. No nuclear fusion takes place in a white dwarf; what light it radiates is from its residual heat. The nearest known white dwarf is Sirius B, at 8.6 light years, the smaller component of the Sirius binary star. There are currently thought to be eight white dwarfs among the hundred star systems nearest the Sun. The unusual faintness of white dwarfs was first recognized in 1910. The name ''white dwarf'' was coined by Willem Jacob Luyten in 1922. White dwarfs are thought to be the final stellar evolution, evolutionary state of stars whose mass is not high enough to become a neutron star or black hole. This includes over 97% of the stars in the Milky Way. After the hydrogen-stellar nucleosynthesis, fusing period of a main sequence, main-sequence star of Stellar mass, lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chandrasekhar Limit
The Chandrasekhar limit () is the maximum mass of a stable white dwarf star. The currently accepted value of the Chandrasekhar limit is about (). The limit was named after Subrahmanyan Chandrasekhar. White dwarfs resist gravitational collapse primarily through electron degeneracy pressure, compared to main sequence stars, which resist collapse through thermal pressure. The Chandrasekhar limit is the mass above which electron degeneracy pressure in the star's core is insufficient to balance the star's own gravitational self-attraction.Sean Carroll, Ph.D., Caltech, 2007, The Teaching Company, ''Dark Matter, Dark Energy: The Dark Side of the Universe'', Guidebook Part 2 page 44, Accessed Oct. 7, 2013, "...Chandrasekhar limit: The maximum mass of a white dwarf star, about 1.4 times the mass of the Sun. Above this mass, the gravitational pull becomes too much, and the star collapses to a neutron star or black hole..." Physics Normal stars fuse gravitationally compressed hydrogen in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dark Matter
In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relativity unless more matter is present than can be observed. Such effects occur in the context of Galaxy formation and evolution, formation and evolution of galaxies, gravitational lensing, the observable universe's current structure, mass position in galactic collisions, the motion of galaxies within galaxy clusters, and cosmic microwave background Anisotropy, anisotropies. Dark matter is thought to serve as gravitational scaffolding for cosmic structures. After the Big Bang, dark matter clumped into blobs along narrow filaments with superclusters of galaxies forming a cosmic web at scales on which entire galaxies appear like tiny particles. In the standard Lambda-CDM model of cosmology, the mass–energy equivalence, mass–energy content o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fritz Zwicky
Fritz Zwicky (; ; February 14, 1898 – February 8, 1974) was a Swiss astronomer. He worked most of his life at the California Institute of Technology in the United States of America, where he made many important contributions in theoretical and observational astronomy. In 1933, Zwicky was the first to use the virial theorem to postulate the existence of unseen dark matter, describing it as "'". From p 125: ''"Um, wie beobachtet, einen mittleren Dopplereffekt von 1000 km/sek oder mehr zu erhalten, müsste also die mittlere Dichte im Comasystem mindestens 400 mal grösser sein als die auf Grund von Beobachtungen an leuchtender Materie abgeleitete. Falls sich dies bewahrheiten sollte, würde sich also das überraschende Resultat ergeben, dass dunkle Materie in sehr viel grösserer Dichte vorhanden ist als leuchtende Materie."'' (In order to obtain an average Doppler effect of 1000 km/s or more, as observed, the average density in the Coma system would thus have to be at least 40 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugene Parker
Eugene Newman Parker (June 10, 1927 – March 15, 2022) was an American solar and plasma physicist. In the 1950s he proposed the existence of the solar wind and that the magnetic field in the outer Solar System would be in the shape of a Parker spiral, predictions that were later confirmed by spacecraft measurements. In 1987, Parker proposed the existence of nanoflares, a leading candidate to explain the coronal heating problem. Parker obtained his PhD from Caltech and spent four years as a postdoctoral researcher at the University of Utah. He joined University of Chicago in 1955 and spent the rest of his career there, holding positions in the physics department, the astronomy and astrophysics department, and the Enrico Fermi Institute. Parker was elected to the National Academy of Sciences in 1967. In 2017, NASA named its Parker Solar Probe in his honor, the first NASA spacecraft named after a living person. Biography Parker was born in Houghton, Michigan to Glenn and H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Bader
Richard F. W. Bader (October 15, 1931 – January 15, 2012) was a Canadian quantum chemist, noted for his work on the atoms in molecules theory. This theory attempts to establish a physical basis for many of the working concepts of chemistry, such as atoms in molecules and bonding, in terms of the topology of the electron density function in three-dimensional space. Alongside the eminent chemist Ronald Gillespie, he had a significant influence on inorganic chemistry education in Canada. He was born in 1931 in Kitchener, Ontario, Canada. His parents were Albert Bader and Alvina Bader, who immigrated from Switzerland. His father was a butcher at Burns Pride of Canada and his mother was a housekeeper at Kitchener Hospital of Waterloo. He received a scholarship from McMaster University that allowed him to earn a BSC in 1953. His father was his best supporter who encouraged him and taught him to "never quit" his education and his dream. He finished his master's degree in science ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Ledoux
Paul Ledoux (8 August 1914 – 6 October 1988) was a Belgian astrophysicist best known for his work on stellar stability and variability. With Theodore Walraven, he co-authored a seminal work on stellar oscillations. In 1964 Ledoux was awarded the Francqui Prize for Exact Sciences, and was awarded the Eddington Medal of the Royal Astronomical Society in 1972 for investigations into problems of stellar stability and variable stars A variable star is a star whose brightness as seen from Earth (its apparent magnitude) changes systematically with time. This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are .... He was awarded the Janssen Medal of the French Academy of Sciences in 1976. Ledoux criterion In stellar astrophysics, Ledoux's name is now associated with the criterion under which material in a star becomes unstable to convection in the presence of a gradient of chemical composition. In hom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enrico Fermi
Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian and naturalized American physicist, renowned for being the creator of the world's first artificial nuclear reactor, the Chicago Pile-1, and a member of the Manhattan Project. He has been called the "architect of the nuclear age" and the "architect of the atomic bomb". He was one of very few physicists to excel in both theoretical physics, theoretical and experimental physics. Fermi was awarded the 1938 Nobel Prize in Physics for his work on induced radioactivity by neutron bombardment and for the discovery of transuranium elements. With his colleagues, Fermi filed several patents related to the use of nuclear power, all of which were taken over by the US government. He made significant contributions to the development of statistical mechanics, Quantum mechanics, quantum theory, and nuclear physics, nuclear and particle physics. Fermi's first major contribution involved the field of statistical mechanics. Afte ... [...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] |
Henri Poincaré
Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist", since he excelled in all fields of the discipline as it existed during his lifetime. He has further been called "the Carl Friedrich Gauss, Gauss of History of mathematics, modern mathematics". Due to his success in science, along with his influence and philosophy, he has been called "the philosopher par excellence of modern science". As a mathematician and physicist, he made many original fundamental contributions to Pure mathematics, pure and applied mathematics, mathematical physics, and celestial mechanics. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. Poincaré is regarded as the cr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
