|
Zero-velocity Surface
The zero-velocity surface is a concept that relates to the N-body problem of gravity. It represents a surface a body of given energy cannot cross, since it would have zero velocity on the surface. It was first introduced by George William Hill. The zero-velocity surface is particularly significant when working with weak gravitational interactions among orbiting bodies. Three-body problem In the circular restricted three-body problem two heavy masses orbit each other at constant radial distance and angular velocity, and a particle of negligible mass is affected by their gravity. By shifting to a rotating coordinate system where the masses are stationary a centrifugal force is introduced. Energy and momentum are not conserved separately in this coordinate system, but the Jacobi integral remains constant: :C=\omega^2 (x^2+y^2) + 2 \left(\frac+\frac\right) - \left(\dot x^2+\dot y^2+\dot z^2\right) where \omega is the rotation rate, x,y the particle's location in the rotating coordinate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobi Const Zero Velocity Suface Curve
Jacobi may refer to: * People with the surname Jacobi (surname), Jacobi Mathematics: * Jacobi sum, a type of character sum * Jacobi method, a method for determining the solutions of a diagonally dominant system of linear equations * Jacobi eigenvalue algorithm, a method for calculating the eigenvalues and eigenvectors of a real symmetric matrix * Jacobi elliptic functions, a set of doubly-periodic functions * Jacobi polynomials, a class of orthogonal polynomials * Jacobi symbol, a generalization of the Legendre symbol * Jacobi coordinates, a simplification of coordinates for an n-body system * Jacobi identity for non-associative binary operations * Jacobi's formula for the derivative of the determinant of a matrix * Jacobi triple product an identity in the theory of theta functions * Jacobi's theorem (other) (various) Other: * Jacobi Medical Center, New York * Jacobi (grape), another name for the French/German wine grape Pinot Noir Précoce * Jacobi (crater), a lunar impac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Low-energy Transfer
A low-energy transfer, or low-energy trajectory, is a route in space that allows spacecraft to change orbits using significantly less fuel than traditional transfers. These routes work in the Earth–Moon system and also in other systems, such as between the moons of Jupiter. The drawback of such trajectories is that they take longer to complete than higher-energy (more-fuel) transfers, such as Hohmann transfer orbits. Low-energy transfers are also known as Weak Stability Boundary trajectories, and include ballistic capture trajectories. Low-energy transfers follow special pathways in space, sometimes referred to as the Interplanetary Transport Network. Following these pathways allows for long distances to be traversed for little change in velocity, or . Example missions Missions that have used low-energy transfers include: * ''Hiten'', from JAXA * '' SMART-1'', from ESA * ''Genesis'', from NASA. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Low-energy Transfer
A low-energy transfer, or low-energy trajectory, is a route in space that allows spacecraft to change orbits using significantly less fuel than traditional transfers. These routes work in the Earth–Moon system and also in other systems, such as between the moons of Jupiter. The drawback of such trajectories is that they take longer to complete than higher-energy (more-fuel) transfers, such as Hohmann transfer orbits. Low-energy transfers are also known as Weak Stability Boundary trajectories, and include ballistic capture trajectories. Low-energy transfers follow special pathways in space, sometimes referred to as the Interplanetary Transport Network. Following these pathways allows for long distances to be traversed for little change in velocity, or . Example missions Missions that have used low-energy transfers include: * ''Hiten'', from JAXA * '' SMART-1'', from ESA * ''Genesis'', from NASA. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hill Sphere
The Hill sphere of an astronomical body is the region in which it dominates the attraction of satellites. To be retained by a planet, a moon must have an orbit that lies within the planet's Hill sphere. That moon would, in turn, have a Hill sphere of its own. Any object within that distance would tend to become a satellite of the moon, rather than of the planet itself. One simple view of the extent of the Solar System is the Hill sphere of the Sun with respect to local stars and the galactic nucleus. In more precise terms, the Hill sphere approximates the gravitational sphere of influence of a smaller body in the face of perturbations from a more massive body. It was defined by the American astronomer George William Hill, based on the work of the French astronomer Édouard Roche. In the example to the right, the Earth's Hill sphere extends between the Lagrange points and , which lie along the line of centers of the two bodies. The region of influence of the smaller body is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Group
The Local Group is the galaxy group that includes the Milky Way. It has a total diameter of roughly , and a total mass of the order of . It consists of two collections of galaxies in a "dumbbell" shape: the Milky Way and its satellites form one lobe, and the Andromeda Galaxy and its satellites constitute the other. The two collections are separated by about and are moving toward one another with a velocity of . The group itself is a part of the larger Virgo Supercluster, which may be a part of the Laniakea Supercluster. The exact number of galaxies in the Local Group is unknown as some are occluded by the Milky Way; however, at least 80 members are known, most of which are dwarf galaxies. The two largest members, the Andromeda Galaxy and the Milky Way, are both spiral galaxies with masses of about solar masses each. Each has its own system of satellite galaxies: * The Andromeda Galaxy's satellite system consists of Messier 32 (M32), Messier 110 (M110), NGC 147, NGC 185, A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galaxy Cluster
A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. They are the second-largest known gravitationally bound structures in the universe after galaxy filaments and were believed to be the largest known structures in the universe until the 1980s, when superclusters were discovered. One of the key features of clusters is the intracluster medium (ICM). The ICM consists of heated gas between the galaxies and has a peak temperature between 2–15 keV that is dependent on the total mass of the cluster. Galaxy clusters should not be confused with ''galactic clusters'' (also known as open clusters), which are star clusters ''within'' galaxies, or with globular clusters, which typically orbit galaxies. Small aggregates of galaxies are referred to as galaxy groups rather than clusters of galaxies. The galaxy groups and c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hubble Expansion
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving away from Earth. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit toward the red end of the visible spectrum. Hubble's law is considered the first observational basis for the expansion of the universe, and today it serves as one of the pieces of evidence most often cited in support of the Big Bang model. The motion of astronomical objects due solely to this expansion is known as the Hubble flow. It is described by the equation , with ''H''0 the constant of proportionality—the Hubble constant—between the "proper distance" ''D'' to a galaxy, which can change over time, unlike the comoving distance, and its speed of separation ''v'', i.e. the derivative of proper distance with respect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galaxy
A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System. Galaxies, averaging an estimated 100 million stars, range in size from dwarfs with less than a hundred million stars, to the largest galaxies known – supergiants with one hundred trillion stars, each orbiting its galaxy's center of mass. Most of the mass in a typical galaxy is in the form of dark matter, with only a few percent of that mass visible in the form of stars and nebulae. Supermassive black holes are a common feature at the centres of galaxies. Galaxies are categorized according to their visual morphology as elliptical, spiral, or irregular. Many are thought to have supermassive black holes at their centers. The Milky Way's central black hole, known as Sagittarius A*, has a mass four million times greater than the Sun. As o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrange Points
In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Mathematically, this involves the solution of the restricted three-body problem in which two bodies are far more massive than the third. Normally, the two massive bodies exert an unbalanced gravitational force at a point, altering the orbit of whatever is at that point. At the Lagrange points, the gravitational forces of the two large bodies and the centrifugal force balance each other. This can make Lagrange points an excellent location for satellites, as few orbit corrections are needed to maintain the desired orbit. Small objects placed in orbit at Lagrange points are in equilibrium in at least two directions relative to the center of mass of the large bodies. For any combination of two orbital bodies there are five Lagrange points, L1 to L5, all in the orbital plane of the two lar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-body Problem
In physics, the -body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally.Leimanis and Minorsky: Our interest is with Leimanis, who first discusses some history about the -body problem, especially Ms. Kovalevskaya's 1868–1888 twenty-year complex-variables approach, failure; Section 1: "The Dynamics of Rigid Bodies and Mathematical Exterior Ballistics" (Chapter 1, "The motion of a rigid body about a fixed point (Euler and Poisson equations)"; Chapter 2, "Mathematical Exterior Ballistics"), good precursor background to the -body problem; Section 2: "Celestial Mechanics" (Chapter 1, "The Uniformization of the Three-body Problem (Restricted Three-body Problem)"; Chapter 2, "Capture in the Three-Body Problem"; Chapter 3, "Generalized -body Problem"). Solving this problem has been motivated by the desire to understand the motions of the Sun, Moon, planets, and visible stars. In the 20th century, unde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobi Integral
In celestial mechanics, Jacobi's integral (also known as the Jacobi integral or Jacobi constant) is the only known conserved quantity for the circular restricted three-body problem.Bibliothèque nationale de France Unlike in the two-body problem, the energy and momentum of the system are not conserved separately and a general analytical solution is not possible. The integral has been used to derive numerous solutions in special cases. It was named after German mathematician . Definition Synodic system One of the suitable coordinate systems used is the so-called ''syn ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotating Reference Frame
A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article considers only frames rotating about a fixed axis. For more general rotations, see Euler angles.) Fictitious forces All non-inertial reference frames exhibit fictitious forces; rotating reference frames are characterized by three: * the centrifugal force, * the Coriolis force, and, for non-uniformly rotating reference frames, * the Euler force. Scientists in a rotating box can measure the speed and direction of their rotation by measuring these fictitious forces. For example, Léon Foucault was able to show the Coriolis force that results from Earth's rotation using the Foucault pendulum. If Earth were to rotate many times faster, these fictitious forces could be felt by humans, as they are when on a spinning carousel. Relating rotating frames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
