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Epicyclic Frequency
In astrophysics, particularly the study of accretion disks, the epicyclic frequency is the frequency at which a radially displaced fluid parcel will oscillate. It can be referred to as a "Rayleigh discriminant". When considering an astrophysical disc with differential rotation \Omega, the epicyclic frequency \kappa is given by : \kappa^ \equiv \frac\frac(R^2 \Omega), where R is the radial co-ordinate.p161, Astrophysical Flows, Pringle and King 2007 This quantity can be used to examine the 'boundaries' of an accretion disc: when \kappa^ becomes negative, then small perturbations to the (assumed circular) orbit of a fluid parcel will become unstable, and the disc will develop an 'edge' at that point. For example, around a Schwarzschild black hole, the innermost stable circular orbit (ISCO) occurs at three times the event horizon, at 6GM/c^. For a Keplerian disk, \kappa = \Omega. Derivation An astrophysical disk can be modeled as a fluid with negligible mass compared to the ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the nature of the heavenly bodies, rather than their positions or motions in space—''what'' they are, rather than ''where'' they are", which is studied in celestial mechanics. Among the subjects studied are the Sun ( solar physics), other stars, galaxies, extrasolar planets, the interstellar medium, and the cosmic microwave background. Emissions from these objects are examined across all parts of the electromagnetic spectrum, and the properties examined include luminosity, density, temperature, and chemical composition. Because astrophysics is a very broad subject, ''astrophysicists'' apply concepts and methods from many disciplines of physics, including classical mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accretion Disk
An accretion disk is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a massive central body. The central body is most frequently a star. Friction, uneven irradiance, magnetohydrodynamic effects, and other forces induce instabilities causing orbiting material in the disk to spiral inward toward the central body. Gravitational and frictional forces compress and raise the temperature of the material, causing the emission of electromagnetic radiation. The frequency range of that radiation depends on the central object's mass. Accretion disks of young stars and protostars radiate in the infrared; those around neutron stars and black holes in the X-ray part of the spectrum. The study of oscillation modes in accretion disks is referred to as diskoseismology. Manifestations Accretion disks are a ubiquitous phenomenon in astrophysics; active galactic nuclei, protoplanetary disks, and gamma ray bursts all involve accretion disks. These di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Strutt, 3rd Baron Rayleigh
John William Strutt, 3rd Baron Rayleigh ( ; 12 November 1842 – 30 June 1919), was an English physicist who received the Nobel Prize in Physics in 1904 "for his investigations of the densities of the most important gases and for his discovery of argon in connection with these studies". He served as president of the Royal Society from 1905 to 1908 and as chancellor of the University of Cambridge from 1908 to 1919. Rayleigh provided the first theoretical treatment of the elastic scattering of light by particles much smaller than the light's wavelength, a phenomenon now known as "Rayleigh scattering", which notably explains why the sky is blue. He studied and described transverse surface waves in solids, now known as "Rayleigh waves". He contributed extensively to fluid dynamics, with concepts such as the Rayleigh number (a dimensionless number associated with natural convection), Rayleigh flow, the Rayleigh–Taylor instability, and Rayleigh's criterion for the stability of Tay ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schwarzschild Black Hole
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero. The solution is a useful approximation for describing slowly rotating astronomical objects such as many stars and planets, including Earth and the Sun. It was found by Karl Schwarzschild in 1916. According to Birkhoff's theorem, the Schwarzschild metric is the most general spherically symmetric vacuum solution of the Einstein field equations. A Schwarzschild black hole or static black hole is a black hole that has neither electric charge nor angular momentum (non-rotating). A Schwarzschild black hole is described by the Schwarzschild metric, and cannot be distinguished from any other Schwarzschild black hole except by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Innermost Stable Circular Orbit
The innermost stable circular orbit (often called the ISCO) is the smallest marginally stable circular orbit in which a test particle can stably orbit a massive object in general relativity. The location of the ISCO, the ISCO-radius (r_), depends on the mass and angular momentum (spin) of the central object. The ISCO plays an important role in black hole accretion disks since it marks the inner edge of the disk. The ISCO should not be confused with the Roche limit, the innermost point where a physical object can orbit before tidal forces break it up. The ISCO is concerned with theoretical ''test particle''s, not real objects. In general terms, the ISCO will be far closer to the central object than the Roche limit. Basic concept In classical mechanics, an orbit is achieved when a test particle's angular momentum is enough to resist the gravity force of the central object. As the test particle approaches the central object, the required amount of angular momentum grows, due to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Event Horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an outside observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact objects that even light cannot escape. At that time, the Newtonian theory of gravitation and the so-called corpuscular theory of light were dominant. In these theories, if the escape velocity of the gravitational influence of a massive object exceeds the speed of light, then light originating inside or from it can escape temporarily but will return. In 1958, David Finkelstein used general relativity to introduce a stricter definition of a local black hole event horizon as a boundary beyond which events of any kind cannot affect an outside observer, leading to information and firewall paradoxes, encouraging the re-examination of the concept of local event horizons and the notion of black holes. Several theories were subsequently d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cylindrical Coordinates
A cylinder () has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology. The shift in the basic meaning—solid versus surface (as in a solid ball versus sphere surface)—has created some ambiguity with terminology. The two concepts may be distinguished by referring to solid cylinders and cylindrical surfaces. In the literature the unadorned term "cylinder" could refer to either of these or to an even more specialized object, the '' right circular cylinder''. Types The definitions and results in this section are taken from the 1913 text ''Plane and Solid Geometry'' by George A. Wentworth and David Eugene Smith . A ' is a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Angular Momentum
In celestial mechanics, the specific relative angular momentum (often denoted \vec or \mathbf) of a body is the angular momentum of that body divided by its mass. In the case of two orbiting bodies it is the vector product of their relative position and relative linear momentum, divided by the mass of the body in question. Specific relative angular momentum plays a pivotal role in the analysis of the two-body problem, as it remains constant for a given orbit under ideal conditions. "Specific" in this context indicates angular momentum per unit mass. The SI unit for specific relative angular momentum is square meter per second. Definition The specific relative angular momentum is defined as the cross product of the relative position vector \mathbf and the relative velocity vector \mathbf . \mathbf = \mathbf\times \mathbf = \frac where \mathbf is the angular momentum vector, defined as \mathbf \times m \mathbf. The \mathbf vector is always perpendicular to the instantaneo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circular Orbit
A circular orbit is an orbit with a fixed distance around the barycenter; that is, in the shape of a circle. In this case, not only the distance, but also the speed, angular speed, Potential energy, potential and kinetic energy are constant. There is no periapsis or apoapsis. This orbit has no Radial orbit, radial version. Listed below is a circular orbit in astrodynamics or celestial mechanics under standard assumptions. Here the centripetal force is the gravitational force, and the axis mentioned above is the line through the Center of mass, center of the central mass perpendicular to the orbital plane. Circular acceleration :wikt:transverse, Transverse acceleration (perpendicular to velocity) causes a change in direction. If it is constant in magnitude and changing in direction with the velocity, circular motion ensues. Taking two derivatives of the particle's coordinates concerning time gives the centripetal acceleration : a\, = \frac \, = where: *v\, is Kinetic e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion) and (the study of water and other liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moment (physics), moments on aircraft, determining the mass flow rate of petroleum through pipeline transport, pipelines, weather forecasting, predicting weather patterns, understanding nebulae in interstellar space, understanding large scale Geophysical fluid dynamics, geophysical flows involving oceans/atmosphere and Nuclear weapon design, modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the nature of the heavenly bodies, rather than their positions or motions in space—''what'' they are, rather than ''where'' they are", which is studied in celestial mechanics. Among the subjects studied are the Sun ( solar physics), other stars, galaxies, extrasolar planets, the interstellar medium, and the cosmic microwave background. Emissions from these objects are examined across all parts of the electromagnetic spectrum, and the properties examined include luminosity, density, temperature, and chemical composition. Because astrophysics is a very broad subject, ''astrophysicists'' apply concepts and methods from many disciplines of physics, including classical mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
