Secular Resonance
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Secular Resonance
A secular resonance is a type of orbital resonance between two bodies with synchronized precessional frequencies. In celestial mechanics, secular refers to the long-term motion of a system, and resonance is periods or frequencies being a simple numerical ratio of small integers. Typically, the synchronized precessions in secular resonances are between the rates of change of the argument of the periapses or the rates of change of the longitude of the ascending nodes of two system bodies. Secular resonances can be used to study the long-term orbital evolution of asteroids and their families within the asteroid belt. Description Secular resonances occur when the precession of two orbits is synchronised (a precession of the perihelion, with frequency g, or the ascending node, with frequency s, or both). A small body (such as a small Solar System body) in secular resonance with a much larger one (such as a planet) will precess at the same rate as the large body. Over relatively sho ...
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Orbital Resonance
In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relationship is found between a pair of objects (binary resonance). The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, whereby the orbit and the swing both have a natural frequency, and the body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies (i.e., their ability to alter or constrain each other's orbits). In most cases, this results in an ''unstable'' interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be self-correcting and thus stable. Examples are the 1:2:4 resonance o ...
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Astronomical Body
An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often used interchangeably. However, an astronomical body or celestial body is a single, tightly bound, contiguous entity, while an astronomical or celestial ''object'' is a complex, less cohesively bound structure, which may consist of multiple bodies or even other objects with substructures. Examples of astronomical objects include planetary systems, star clusters, nebulae, and galaxies, while asteroids, moons, planets, and stars are astronomical bodies. A comet may be identified as both body and object: It is a ''body'' when referring to the frozen nucleus of ice and dust, and an ''object'' when describing the entire comet with its diffuse coma and tail. History Astronomical objects such as stars, planets, nebulae, asteroids and com ...
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Asteroid Belt
The asteroid belt is a torus-shaped region in the Solar System, located roughly between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies, of many sizes, but much smaller than planets, called asteroids or minor planets. This asteroid belt is also called the main asteroid belt or main belt to distinguish it from other asteroid populations in the Solar System such as near-Earth asteroids and trojan asteroids. The asteroid belt is the smallest and innermost known circumstellar disc in the Solar System. About 60% of its mass is contained in the four largest asteroids: Ceres, Vesta, Pallas, and Hygiea. The total mass of the asteroid belt is calculated to be 3% that of the Moon. Ceres, the only object in the asteroid belt large enough to be a dwarf planet, is about 950 km in diameter, whereas Vesta, Pallas, and Hygiea have mean diameters less than 600 km. The remaining bodies range down to the size of a dust par ...
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Orbital Resonance
In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relationship is found between a pair of objects (binary resonance). The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, whereby the orbit and the swing both have a natural frequency, and the body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies (i.e., their ability to alter or constrain each other's orbits). In most cases, this results in an ''unstable'' interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be self-correcting and thus stable. Examples are the 1:2:4 resonance o ...
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Inclinations
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Earth directly above the Equator, the plane of the satellite's orbit is the same as the Earth's equatorial plane, and the satellite's orbital inclination is 0°. The general case for a circular orbit is that it is tilted, spending half an orbit over the northern hemisphere and half over the southern. If the orbit swung between 20° north latitude and 20° south latitude, then its orbital inclination would be 20°. Orbits The inclination is one of the six orbital elements describing the shape and orientation of a celestial orbit. It is the angle between the orbital plane and the plane of reference, normally stated in degrees. For a satellite orbiting a planet, the plane of reference is usually the plane containing the planet's equator. For pl ...
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Astronomical Unit
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits the Sun, from a maximum (aphelion) to a minimum (perihelion) and back again once each year. The astronomical unit was originally conceived as the average of Earth's aphelion and perihelion; however, since 2012 it has been defined as exactly (see below for several conversions). The astronomical unit is used primarily for measuring distances within the Solar System or around other stars. It is also a fundamental component in the definition of another unit of astronomical length, the parsec. History of symbol usage A variety of unit symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union (IAU) had used the symbol ''A'' to denote a length equal to the astronomic ...
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Mars
Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury. In the English language, Mars is named for the Roman god of war. Mars is a terrestrial planet with a thin atmosphere (less than 1% that of Earth's), and has a crust primarily composed of elements similar to Earth's crust, as well as a core made of iron and nickel. Mars has surface features such as impact craters, valleys, dunes and polar ice caps. It has two small and irregularly shaped moons, Phobos and Deimos. Some of the most notable surface features on Mars include Olympus Mons, the largest volcano and highest known mountain in the Solar System and Valles Marineris, one of the largest canyons in the Solar System. The Borealis basin in the Northern Hemisphere covers approximately 40% of the planet and may be a large impact feature. Days and seasons on Mars are comparable to those of Earth, as the planets have a similar rotation period ...
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Mars-crossing Asteroid
A Mars-crossing asteroid (MCA, also Mars-crosser, MC) is an asteroid whose orbit crosses that of Mars. Some Mars-crossers numbered below 100000 are listed here. They include the two numbered Mars trojans 5261 Eureka and . Many databases, for instance the JPL Small-Body Database (JPL SBDB), only list asteroids with a perihelion greater than 1.3 AU as Mars-crossers. An asteroid with a perihelion less than this is classed as a near-Earth object even though it is crossing the orbit of Mars as well as crossing (or coming near to) that of Earth. Nevertheless, these objects are listed on this page. A grazer is an object with a perihelion below the aphelion of Mars (1.67 AU) but above the Martian perihelion (1.38 AU). The JPL SBDB lists 13,500 Mars-crossing asteroids. Only 18 MCAs are brighter than absolute magnitude (H) 12.5, which typically makes these asteroids with H<12.5 more than 13 km in diameter depending on the

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Saturn
Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; however, with its larger volume, Saturn is over 95 times more massive. Saturn's interior is most likely composed of a core of iron–nickel alloy, iron–nickel and rock (silicon and oxygen compounds). Its core is surrounded by a deep layer of metallic hydrogen, an intermediate layer of liquid hydrogen and liquid helium, and finally, a gaseous outer layer. Saturn has a pale yellow hue due to ammonia crystals in its upper atmosphere. An electrical current within the metallic hydrogen layer is thought to give rise to Saturn's planetary magnetic field, which is weaker than Earth's, but which has a magnetic moment 580 times that of Earth due to Saturn's larger size. Saturn's magnetic field strength is around one-twentieth of Jupiter's. The out ...
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Asteroid
An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. Of the roughly one million known asteroids the greatest number are located between the orbits of Mars and Jupiter, approximately 2 to 4 AU from the Sun, in the main asteroid belt. Asteroids are generally classified to be of three types: C-type, M-type, and S-type. These were named after and are generally identified with carbonaceous, metallic, and silicaceous compositions, respectively. The size of asteroids varies greatly; the largest, Ceres, is almost across and qualifies as a dwarf planet. The total mass of all the asteroids combined is only 3% that of Earth's Moon. The majority of main belt asteroids follow slightly elliptical, stable orbits, revolving in the same direction as the Earth and taking from three to six years to co ...
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Inclination
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Earth directly above the Equator, the plane of the satellite's orbit is the same as the Earth's equatorial plane, and the satellite's orbital inclination is 0°. The general case for a circular orbit is that it is tilted, spending half an orbit over the northern hemisphere and half over the southern. If the orbit swung between 20° north latitude and 20° south latitude, then its orbital inclination would be 20°. Orbits The inclination is one of the six orbital elements describing the shape and orientation of a celestial orbit. It is the angle between the orbital plane and the plane of reference, normally stated in degrees. For a satellite orbiting a planet, the plane of reference is usually the plane containing the planet's equator. ...
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Eccentricity (orbit)
In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit (or capture orbit), and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the Galaxy. Definition In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit. The eccentricity of this Kepler orbit is a non-negative number that defines its shape. The eccentricity may take the following values: * circular orbit: ''e'' = 0 * elliptic orbit: 0 < ''e'' < 1 *