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Schwarzschild Geodesics
In general relativity, Schwarzschild geodesics describe the motion of test particles in the gravitational field of a central fixed mass M, that is, motion in the Schwarzschild metric. Schwarzschild geodesics have been pivotal in the tests of general relativity, validation of Einstein's theory of general relativity. For example, they provide accurate predictions of the Anomalous perihelion precession, anomalous Precession#Relativistic (Einsteinian), precession of the planets in the Solar System and of the deflection of light by gravity. Schwarzschild geodesics pertain only to the motion of particles of masses so small they contribute little to the gravitational field. However, they are highly accurate in many astrophysical scenarios provided that m is many-fold smaller than the central mass M, e.g., for planets orbiting their star. Schwarzschild geodesics are also a good approximation to the relative motion of two bodies of arbitrary mass, provided that the Schwarzschild mass M is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General theory of relativity, relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time in physics, time, or four-dimensional spacetime. In particular, the ''curvature of spacetime'' is directly related to the energy and momentum of whatever is present, including matter and radiation. The relation is specified by the Einstein field equations, a system of second-order partial differential equations. Newton's law of universal gravitation, which describes gravity in classical mechanics, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Longitude
Longitude (, ) is a geographic coordinate that specifies the east- west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians are imaginary semicircular lines running from pole to pole that connect points with the same longitude. The prime meridian defines 0° longitude; by convention the International Reference Meridian for the Earth passes near the Royal Observatory in Greenwich, south-east London on the island of Great Britain. Positive longitudes are east of the prime meridian, and negative ones are west. Because of the Earth's rotation, there is a close connection between longitude and time measurement. Scientifically precise local time varies with longitude: a difference of 15° longitude corresponds to a one-hour difference in local time, due to the differing position in relation to the Sun. Comparing local time to an absol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mercury (planet)
Mercury is the first planet from the Sun. It is a rocky planet with a trace atmosphere. While it is the List of Solar System objects by size, smallest and least massive planet of the Solar System, its surface gravity is slightly higher than that of Mars. The surface of Mercury is similar to Earth's Moon, heavily Impact crater, cratered, with expansive rupes system, generated from thrust faults, and bright ray systems, formed by ejecta. Its largest crater, Caloris Planitia, has a diameter of , which is about one-third the diameter of the planet (). Being the most inferior planet, inferior orbiting planet it appears in Earth's sky, always close to the Sun, either as a "morning star" or an "evening star". It stays most of the time the closest to all other planets and is the planet with the highest delta-v needed to travel to from all other planets of the Solar System. Mercury's sidereal year (88.0 Earth days) and sidereal day (58.65 Earth days) are in a 3:2 ratio. This relation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reduced Mass
In physics, reduced mass is a measure of the effective inertial mass of a system with two or more particles when the particles are interacting with each other. Reduced mass allows the two-body problem to be solved as if it were a one-body problem. Note, however, that the mass determining the gravitational force is ''not'' reduced. In the computation, one mass ''can'' be replaced with the reduced mass, if this is compensated by replacing the other mass with the sum of both masses. The reduced mass is frequently denoted by \mu ( mu), although the standard gravitational parameter is also denoted by \mu (as are a number of other physical quantities). It has the dimensions of mass, and SI unit kg. Reduced mass is particularly useful in classical mechanics. Equation Given two bodies, one with mass ''m''1 and the other with mass ''m''2, the equivalent one-body problem, with the position of one body with respect to the other as the unknown, is that of a single body of mass \m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Relative 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 instant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamilton's Principle
In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action. It states that the dynamics of a physical system are determined by a variational problem for a functional based on a single function, the Lagrangian, which may contain all physical information concerning the system and the forces acting on it. The variational problem is equivalent to and allows for the derivation of the '' differential'' equations of motion of the physical system. Although formulated originally for classical mechanics, Hamilton's principle also applies to classical fields such as the electromagnetic and gravitational fields, and plays an important role in quantum mechanics, quantum field theory and criticality theories. Mathematical formulation Hamilton's principle states that the true evolution of a system described by generalized coordinates between two specified states and at two specified times and is a stationary point (a point where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constant Of Motion
In mechanics, a constant of motion is a physical quantity conserved throughout the motion, imposing in effect a constraint on the motion. However, it is a ''mathematical'' constraint, the natural consequence of the equations of motion, rather than a ''physical'' constraint (which would require extra constraint forces). Common examples include energy, linear momentum, angular momentum and the Laplace–Runge–Lenz vector (for inverse-square force laws). Applications Constants of motion are useful because they allow properties of the motion to be derived without solving the equations of motion. In fortunate cases, even the trajectory of the motion can be derived as the intersection of isosurfaces corresponding to the constants of motion. For example, Poinsot's construction shows that the torque-free rotation of a rigid body is the intersection of a sphere (conservation of total angular momentum) and an ellipsoid (conservation of energy), a trajectory that might be otherw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Totally Geodesic
This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. The following articles may also be useful; they either contain specialised vocabulary or provide more detailed expositions of the definitions given below. * Connection * Curvature * Metric space * Riemannian manifold See also: * Glossary of general topology * Glossary of differential geometry and topology * List of differential geometry topics Unless stated otherwise, letters ''X'', ''Y'', ''Z'' below denote metric spaces, ''M'', ''N'' denote Riemannian manifolds, , ''xy'', or , xy, _X denotes the distance between points ''x'' and ''y'' in ''X''. Italic ''word'' denotes a self-reference to this glossary. ''A caveat'': many terms in Riemannian and metric geometry, such as ''convex function'', ''convex set'' and others, do not have exactly the same meaning as in general mathematical usage. __NOTOC__ A Affine connection Al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton Versus Schwarzschild Trajectories
Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: People * Newton (surname), including a list of people with the surname * Newton (given name), including a list of people with the given name Arts and entertainment * ''Newton'' (film), a 2017 Indian film * Newton (band), Spanish electronic music group * ''Newton'' (Blake), a print by William Blake * ''Newton'' (Paolozzi), a 1995 bronze sculpture by Eduardo Paolozzi * Cecil Newton (''Coronation Street''), a character in the British soap opera ''Coronation Street'' * Curtis Newton, "real" name of pulp magazine character Captain Future * George Newton, a character in the film series ''Beethoven'' * Newton Gearloose, a Disney character, nephew of Gyro Gearloose * Newton, a character in ''The Mighty Hercules'' animated series Places Australia * Newton, South Australia Canada * Newton, Edmonton, Alberta * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black Hole
A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. The boundary (topology), boundary of no escape is called the event horizon. A black hole has a great effect on the fate and circumstances of an object crossing it, but has no locally detectable features according to general relativity. In many ways, a black hole acts like an ideal black body, as it reflects no light. Quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with thermal radiation, the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is of the Orders of magnitude (temperature), order of billionths of a kelvin for stellar black holes, making it essentially impossible to observe directly. Objects whose gravitational fields are too strong for ... [...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] |
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] |
