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Tisserand's Parameter
Tisserand's parameter (or Tisserand's invariant) is a value calculated from several orbital elements ( semi-major axis, orbital eccentricity and inclination) of a relatively small object and a larger " perturbing body". It is used to distinguish different kinds of orbits. The term is named after French astronomer Félix Tisserand, and applies to restricted three-body problems in which the three objects all differ greatly in mass. Definition For a small body with semi-major axis a\,\!, orbital eccentricity e\,\!, and orbital inclination i\,\!, relative to the orbit of a perturbing larger body with semimajor axis a_P, the parameter is defined as follows: :T_P\ = \frac + 2\cos i\sqrt The quasi-conservation of Tisserand's parameter is a consequence of Tisserand's relation. Applications * TJ, Tisserand's parameter with respect to Jupiter as perturbing body, is frequently used to distinguish asteroids (typically T_J > 3) from Jupiter-family comets (typically 2< T_J < 3 [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Elements
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same orbit, but certain schemes, each consisting of a set of six parameters, are commonly used in astronomy and orbital mechanics. A real orbit and its elements change over time due to gravitational perturbations by other objects and the effects of general relativity. A Kepler orbit is an idealized, mathematical approximation of the orbit at a particular time. Keplerian elements The traditional orbital elements are the six Keplerian elements, after Johannes Kepler and his laws of planetary motion. When viewed from an inertial frame, two orbiting bodies trace out distinct trajectories. Each of these trajectories has its focus at the common center of mass. When viewed from a non-inertial frame centered on one of the bodies, only the trajec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scattered Disc
The scattered disc (or scattered disk) is a distant circumstellar disc in the Solar System that is sparsely populated by icy small solar system bodies, which are a subset of the broader family of trans-Neptunian objects. The scattered-disc objects (SDOs) have orbital eccentricities ranging as high as 0.8, inclinations as high as 40°, and perihelia greater than . These extreme orbits are thought to be the result of gravitational "scattering" by the gas giants, and the objects continue to be subject to perturbation by the planet Neptune. Although the closest scattered-disc objects approach the Sun at about 30–35 AU, their orbits can extend well beyond 100 AU. This makes scattered objects among the coldest and most distant objects in the Solar System. The innermost portion of the scattered disc overlaps with a torus-shaped region of orbiting objects traditionally called the Kuiper belt, but its outer limits reach much farther away from the Sun and farther above and b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perihelion And Aphelion
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any elliptic orbit. The name for each apsis is created from the prefixes ''ap-'', ''apo-'' (), or ''peri-'' (), each referring to the farthest and closest point to the primary body the affixing necessary suffix that describes the primary body in the orbit. In this case, the suffix for Earth is ''-gee'', so the apsides' names are ''apogee'' and ''perigee''. For the Sun, its suffix is ''-helion'', so the names are ''aphelion'' and ''perihelion''. According to Newton's laws of motion, all periodic orbits are ellipses. The barycenter of the two bodies may lie well within the bigger body—e.g., the Earth–Moon barycenter is about 75% of the way from Earth's center to its surface. If, compared to the larger mass, the smaller mass is negligible (e.g., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sungrazing Comet
A sungrazing comet is a comet that passes extremely close to the Sun at perihelion – sometimes within a few thousand kilometres of the Sun's surface. Although small sungrazers can completely evaporate during such a close approach to the Sun, larger sungrazers can survive many perihelion passages. However, the strong evaporation and tidal forces they experience often lead to their fragmentation. Up until the 1880s, it was thought that all bright comets near the Sun were the repeated return of a single sungrazing comet. Then, German astronomer Heinrich Kreutz and American astronomer Daniel Kirkwood determined that, instead of the return of the same comet, each appearance was a different comet, but each were related to a group of comets that had separated from each other at an earlier passage near the Sun (at perihelion). Very little was known about the population of sungrazing comets until 1979 when coronagraphic observations allowed the detection of sungrazers. As of Octob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kozai Mechanism
In celestial mechanics, the Kozai mechanism is a dynamical phenomenon affecting the orbit of a binary system perturbed by a distant third body under certain conditions. It is also known as the von Zeipel-Kozai-Lidov, Lidov–Kozai mechanism, Kozai–Lidov mechanism, or some combination of Kozai, Lidov–Kozai, Kozai–Lidov or von Zeipel-Kozai-Lidov effect, oscillations, cycles, or resonance. This effect causes the orbit's argument of pericenter to oscillate about a constant value, which in turn leads to a periodic exchange between its eccentricity and inclination. The process occurs on timescales much longer than the orbital periods. It can drive an initially near-circular orbit to arbitrarily high eccentricity, and ''flip'' an initially moderately inclined orbit between a prograde and a retrograde motion. The effect has been found to be an important factor shaping the orbits of irregular satellites of the planets, trans-Neptunian objects, extrasolar planets, and multiple star ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resonance
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an Oscillation, oscillating force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher Amplitude, amplitude than when the same force is applied at other, non-resonant frequencies. Frequencies at which the response amplitude is a relative maximum are also known as resonant frequencies or resonance frequencies of the system. Small periodic forces that are near a resonant frequency of the system have the ability to produce large amplitude oscillations in the system due to the storage of vibrational energy. Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, orbital resonance, acoustic resonance, Electromagnetic radiation, electromagnet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conserved Quantity
In mathematics, a conserved quantity of a dynamical system is a function of the dependent variables, the value of which remains constant along each trajectory of the system. Not all systems have conserved quantities, and conserved quantities are not unique, since one can always produce another such quantity by applying a suitable function, such as adding a constant, to a conserved quantity. Since many laws of physics express some kind of conservation, conserved quantities commonly exist in mathematical models of physical systems. For example, any classical mechanics model will have mechanical energy as a conserved quantity as long as the forces involved are conservative. Differential equations For a first order system of differential equations :\frac = \mathbf f(\mathbf r, t) where bold indicates vector quantities, a scalar-valued function ''H''(r) is a conserved quantity of the system if, for all time and initial conditions in some specific domain, :\frac = 0 Note that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three-body Problem
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation. The three-body problem is a special case of the -body problem. Unlike two-body problems, no general closed-form solution exists, as the resulting dynamical system is chaotic for most initial conditions, and numerical methods are generally required. Historically, the first specific three-body problem to receive extended study was the one involving the Moon, Earth, and the Sun. In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three particles. Mathematical description The mathematical statement of the three-body problem can be given in terms of the Newtonian equations of motion for vector positions \mathbf = (x_i, y_i, z_i) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian Mechanics
Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta''. Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical and quantum mechanics. Overview Phase space coordinates (p,q) and Hamiltonian H Let (M, \mathcal L) be a mechanical system with the configuration space M and the smooth Lagrangian \mathcal L. Select a standard coordinate system (\boldsymbol,\boldsymbol) on M. The quantities \textstyle p_i(\boldsymbol,\boldsymbol,t) ~\stackrel~ / are called ''momenta''. (Also ''generalized momenta'', ''conjugate momenta'', and ''canonical momenta''). For a time instant t, the Legendre transformat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles-Eugène Delaunay
Charles-Eugène Delaunay (9 April 1816 – 5 August 1872) was a French astronomer and mathematician. His lunar motion studies were important in advancing both the theory of planetary motion and mathematics. Life Born in Lusigny-sur-Barse, France, to Jacques‐Hubert Delaunay and Catherine Choiselat, Delaunay studied under Jean-Baptiste Biot at the Sorbonne. He worked on the mechanics of the Moon as a special case of the three-body problem. He published two volumes on the topic, each of 900 pages in length, in 1860 and 1867. The work hints at chaos in the system, and clearly demonstrates the problem of so-called "small denominators" in perturbation theory. His infinite series expression for finding the position of the Moon converged too slowly to be of practical use but was a catalyst in the development of functional analysisO'Connor & Edmund and computer algebra. Delaunay became director of the Paris Observatory in 1870 but drowned in a boating accident near Cherbourg, F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial support of Charles Scribner, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed in 1911 on William Street in Princeton. Its first book was a new 1912 edition of John Witherspoon's ''Lectures on Moral Philosophy.'' History Princeton University Press was founded in 1905 by a recent Princeton graduate, Whitney Darrow, with financial support from another Princetonian, Charles Scribner II. Darrow and Scribner purchased the equipment and assumed the operations of two already existing local publishers, that of the ''Princeton Alumni Weekly'' and the Princeton Press. The new press printed both local newspapers, university documents, ''The Daily Princetonian'', and later added book publishing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Milky Way
The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye. The term ''Milky Way'' is a translation of the Latin ', from the Greek ('), meaning "milky circle". From Earth, the Milky Way appears as a band because its disk-shaped structure is viewed from within. Galileo Galilei first resolved the band of light into individual stars with his telescope in 1610. Until the early 1920s, most astronomers thought that the Milky Way contained all the stars in the Universe. Following the 1920 Great Debate between the astronomers Harlow Shapley and Heber Curtis, observations by Edwin Hubble showed that the Milky Way is just one of many galaxies. The Milky Way is a barred spiral galaxy with an estimated D25 isophotal diameter of , but only about 1,000 light years thick at the spiral arms (more at the bulge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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