Sphere Of Influence (astrodynamics)
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Sphere Of Influence (astrodynamics)
A sphere of influence (SOI) in astrodynamics and astronomy is the oblate spheroid, oblate-spheroid-shaped region around a celestial body where the primary gravity, gravitational influence on an orbiting object is that body. This is usually used to describe the areas in the Solar System where planets dominate the orbits of surrounding objects such as natural satellite, moons, despite the presence of the much more massive but distant Sun. In the patched conic approximation, used in estimating the trajectories of bodies moving between the neighbourhoods of different masses using a two body approximation, ellipses and hyperbolae, the SOI is taken as the boundary where the trajectory switches which mass field it is influenced by. The general equation describing the radius of the sphere r_ of a planet: : r_ \approx a\left(\frac\right)^ where : a is the semimajor axis of the smaller object's (usually a planet's) orbit around the larger body (usually the Sun). : m and M are the masses of ...
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Astrodynamics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the Newton's law of universal gravitation, law of universal gravitation. Orbital mechanics is a core discipline within space exploration, space-mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical object, astronomical bodies such as star systems, planets, Natural satellite, moons, and comets. Orbital mechanics focuses on spacecraft trajectory, trajectories, including orbital maneuvers, orbital plane (astronomy), orbital plane changes, and interplanetary transfers, and is used by mission planners to predict the results of spacecraft propulsion, propulsive maneuvers. General relativity is a more exact ...
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Mercury (planet)
Mercury is the smallest planet in the Solar System and the closest to the Sun. Its orbit around the Sun takes 87.97 Earth days, the shortest of all the Sun's planets. It is named after the Roman god ' ( Mercury), god of commerce, messenger of the gods, and mediator between gods and mortals, corresponding to the Greek god Hermes (). Like Venus, Mercury orbits the Sun within Earth's orbit as an inferior planet, and its apparent distance from the Sun as viewed from Earth never exceeds 28°. This proximity to the Sun means the planet can only be seen near the western horizon after sunset or the eastern horizon before sunrise, usually in twilight. At this time, it may appear as a bright star-like object, but is more difficult to observe than Venus. From Earth, the planet telescopically displays the complete range of phases, similar to Venus and the Moon, which recurs over its synodic period of approximately 116 days. The synodic proximity of Mercury to Earth makes Mercury most ...
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Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker. It primarily reissues books that are out of print from their original publishers. These are often, but not always, books in the public domain. The original published editions may be scarce or historically significant. Dover republishes these books, making them available at a significantly reduced cost. Classic reprints Dover reprints classic works of literature, classical sheet music, and public-domain images from the 18th and 19th centuries. Dover also publishes an extensive collection of mathematical, scientific, and engineering texts. It often targets its reprints at a niche market, such as woodworking. Starting in 2015, the company branched out into graphic novel reprints, overseen by Dover acquisitions editor and former comics writer and editor Drew Ford. Most Dover reprints are photo facsimiles of the originals, retaining the original pagination and ...
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Sphere Of Influence (black Hole)
The sphere of influence is a region around a supermassive black hole in which the gravitational potential of the black hole dominates the gravitational potential of the host galaxy. The radius of the sphere of influence is called the "(gravitational) influence radius". There are two definitions in common use for the radius of the sphere of influence. The first is given by r_h = \frac where MBH is the mass of the black hole, ''σ'' is the stellar velocity dispersion of the host bulge, and ''G'' is the gravitational constant. The second definition is the radius at which the enclosed mass in stars equals twice MBH, i.e. M_\star(r. Which definition is most appropriate depends on the physical question that is being addressed. The first definition takes into account the bulge's overall effect on the motion of a star, since \sigma is determined in part by stars that have moved far from the black hole. The second definition compares the force from t ...
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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 ...
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Hill Sphere And SOI
A hill is a landform that extends above the surrounding terrain. It often has a distinct Summit (topography), summit. Terminology The distinction between a hill and a mountain is unclear and largely subjective, but a hill is universally considered to be not as tall, or as Grade (slope), steep as a mountain. Geographers historically regarded mountains as hills greater than above sea level, which formed the basis of the plot of the 1995 film ''The Englishman who Went up a Hill but Came down a Mountain''. In contrast, hillwalkers have tended to regard mountains as peaks above sea level. The ''Oxford English Dictionary'' also suggests a limit of and Whittow states "Some authorities regard eminences above as mountains, those below being referred to as hills." Today, a mountain is usually defined in the UK and Ireland as any summit at least high, while the official UK government's definition of a mountain is a summit of or higher. Some definitions include a topographical pro ...
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Neptune
Neptune is the eighth planet from the Sun and the farthest known planet in the Solar System. It is the fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 times the mass of Earth, and slightly more massive than its near-twin Uranus. Neptune is denser and physically smaller than Uranus because its greater mass causes more gravitational compression of its atmosphere. It is referred to as one of the solar system's two ice giant planets (the other one being Uranus). Being composed primarily of gases and liquids, it has no well-defined "solid surface". The planet orbits the Sun once every 164.8 julian year (astronomy), years at an average distance of . It is named after the Neptune (mythology), Roman god of the sea and has the astronomical symbol , representing Neptune's trident. Neptune is not visible to the unaided eye and is the only planet in the Solar System found by mathematical prediction ...
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Uranus
Uranus is the seventh planet from the Sun. Its name is a reference to the Greek god of the sky, Uranus (mythology), Uranus (Caelus), who, according to Greek mythology, was the great-grandfather of Ares (Mars (mythology), Mars), grandfather of Zeus (Jupiter (mythology), Jupiter) and father of Cronus (Saturn (mythology), Saturn). It has the third-largest planetary radius and fourth-largest planetary mass in the Solar System. Uranus is similar in composition to Neptune, and both have bulk chemical compositions which differ from that of the larger gas giants Jupiter and Saturn. For this reason, scientists often classify Uranus and Neptune as "ice giants" to distinguish them from the other giant planets. As with gas giants, ice giants also lack a well defined "solid surface." Uranus's Atmosphere#Others, atmosphere is similar to Jupiter's and Saturn's in its primary composition of hydrogen and helium, but it contains more "volatiles, ices" such as water, ammonia, and methane, al ...
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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 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 outer atmosphere is g ...
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Jupiter
Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandth the mass of the Sun. Jupiter is the List of brightest natural objects in the sky, third brightest natural object in the Earth's night sky after the Moon and Venus, and it has been observed since Pre-history, prehistoric times. It was named after the Jupiter (mythology), Roman god Jupiter, the king of the gods. Jupiter is primarily composed of hydrogen, but helium constitutes one-quarter of its mass and one-tenth of its volume. It probably has a rocky core of heavier elements, but, like the other giant planets in the Solar System, it lacks a well-defined solid surface. The ongoing contraction of Jupiter's interior generates more heat than it receives from the Sun. Because of its rapid rotation, the planet' ...
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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 (planet), Mercury. In the English language, Mars is named for the Mars (mythology), 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 (moon), Phobos and Deimos (moon), Deimos. Some of the most notable surface features on Mars include Olympus Mons, the largest volcano and List of tallest mountains in the Solar System, highest known mountain in the Solar System and Valles Marineris, one of the largest canyons in the Solar System. The North Polar Basin (Mars), Borealis basin in the Northern Hemisphere covers approximately 40% of the planet and may be a la ...
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