Laplace Sphere
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Laplace Sphere
In astronomy and orbital mechanics, the Laplace sphere concerns a specific kind of Three-body problem with orbits. The prototype idea is to study the Sun-Earth-Moon system, and determine if it would be possible for the Sun to steal away the Moon from Earth orbit, into solar orbit. More generally, it is applied to any satellite of a body (often called the 'planet') that is, in turn, orbiting a much more massive body (often called the 'star'). Besides the moon, the satellite is usually a small planetoid, exoplanet, or a spacecraft that is orbiting the earth. The Laplace sphere is a region around a planet where a satellite would maintain a stable orbit around the planet, rather than being pulled off toward the star, with its greater gravitational force, despite its larger distance. The 'sphere' region is actually an ellipsoid, specifically a prolate spheroid with its long axis perpendicular to the star-planet orbit. This results in the fact that the satellite with an eccentric or ...
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Astronomy
Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest include planets, natural satellite, moons, stars, nebulae, galaxy, galaxies, meteoroids, asteroids, and comets. Relevant phenomena include supernova explosions, gamma ray bursts, quasars, blazars, pulsars, and cosmic microwave background radiation. More generally, astronomy studies everything that originates beyond atmosphere of Earth, Earth's atmosphere. Cosmology is a branch of astronomy that studies the universe as a whole. Astronomy is one of the oldest natural sciences. The early civilizations in recorded history made methodical observations of the night sky. These include the Egyptian astronomy, Egyptians, Babylonian astronomy, Babylonians, Greek astronomy, Greeks, Indian astronomy, Indians, Chinese astronomy, Chinese, Maya civilization, M ...
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Orbital Mechanics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation. Astrodynamics is a core discipline within 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 bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbital plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton's laws for calculating orbits, and it is sometimes necessary to use it for greater accuracy or in high-gravity situations (e.g. orbits near the Sun). History Until th ...
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Three-body Problem
In physics, specifically classical mechanics, the three-body problem is to take the initial positions and velocities (or momenta) of three point masses orbiting each other in space and then calculate their subsequent trajectories using Newton's laws of motion and Newton's law of universal gravitation. Unlike the two-body problem, the three-body problem has no general closed-form solution, meaning there is no equation that always solves it. When three bodies orbit each other, the resulting dynamical system is chaotic for most initial conditions. Because there are no solvable equations for most three-body systems, the only way to predict the motions of the bodies is to estimate them using numerical methods. The three-body problem is a special case of the -body problem. Historically, the first specific three-body problem to receive extended study was the one involving the Earth, the Moon, and the Sun. In an extended modern sense, a three-body problem is any problem in cl ...
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Earth
Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all of Earth's water is contained in its global ocean, covering Water distribution on Earth, 70.8% of Earth's crust. The remaining 29.2% of Earth's crust is land, most of which is located in the form of continental landmasses within Earth's land hemisphere. Most of Earth's land is at least somewhat humid and covered by vegetation, while large Ice sheet, sheets of ice at Polar regions of Earth, Earth's polar polar desert, deserts retain more water than Earth's groundwater, lakes, rivers, and Water vapor#In Earth's atmosphere, atmospheric water combined. Earth's crust consists of slowly moving tectonic plates, which interact to produce mountain ranges, volcanoes, and earthquakes. Earth's outer core, Earth has a liquid outer core that generates a ...
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Moon
The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar day) that is synchronized to its orbital period (Lunar month#Synodic month, lunar month) of 29.5 Earth days. This is the product of Earth's gravitation having tidal forces, tidally pulled on the Moon until one part of it stopped rotating away from the near side of the Moon, near side, making always the same lunar surface face Earth. Conversley, the gravitational pull of the Moon, on Earth, is the main driver of Earth's tides. In geophysical definition of planet, geophysical terms, the Moon is a planetary-mass object or satellite planet. Its mass is 1.2% that of the Earth, and its diameter is , roughly one-quarter of Earth's (about as wide as the contiguous United States). Within the Solar System, it is the List of Solar System objects by ...
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Satellite
A satellite or an artificial satellite is an object, typically a spacecraft, placed into orbit around a celestial body. They have a variety of uses, including communication relay, weather forecasting, navigation ( GPS), broadcasting, scientific research, and Earth observation. Additional military uses are reconnaissance, early warning, signals intelligence and, potentially, weapon delivery. Other satellites include the final rocket stages that place satellites in orbit and formerly useful satellites that later become defunct. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisotope thermoelectric generators (RTGs). Most satellites also have a method of communication to ground stations, called transponders. Many satellites use a standardized bus to save cost and work, the most popular of which are small CubeSats. Similar satellites can work together as groups, forming constellatio ...
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Planetoid
According to the International Astronomical Union (IAU), a minor planet is an astronomical object in direct orbit around the Sun that is exclusively classified as neither a planet nor a comet. Before 2006, the IAU officially used the term ''minor planet'', but that year's meeting reclassified minor planets and comets into dwarf planets and small Solar System bodies (SSSBs).Press release, IAU 2006 General Assembly: Result of the IAU Resolution votes
International Astronomical Union, August 24, 2006. Accessed May 5, 2008.
In contrast to the eight official planets of the , all minor planets fail to
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Exoplanet
An exoplanet or extrasolar planet is a planet outside the Solar System. The first confirmed detection of an exoplanet was in 1992 around a pulsar, and the first detection around a main-sequence star was in 1995. A different planet, first detected in 1988, was confirmed in 2003. In 2016, it was recognized that the first possible evidence of an exoplanet had been noted in 1917. In collaboration with ground-based and other space-based observatories the James Webb Space Telescope (JWST) is expected to give more insight into exoplanet traits, such as their composition, environmental conditions, and potential for life. There are many methods of detecting exoplanets. Transit photometry and Doppler spectroscopy have found the most, but these methods suffer from a clear observational bias favoring the detection of planets near the star; thus, 85% of the exoplanets detected are inside the tidal locking zone. In several cases, multiple planets have been observed around a star ...
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Gravitational Force
Newton's law of universal gravitation describes gravity as a force by stating that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass. Separated objects attract and are attracted as if all their mass were concentrated at their centers. The publication of the law has become known as the " first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors. This is a general physical law derived from empirical observations by what Isaac Newton called ''inductive reasoning''. It is a part of classical mechanics and was formulated in Newton's work ''Philosophiæ Naturalis Principia Mathematica'' (Latin for 'Mathematical Principles of Natural Philosophy' (the ''Principia'')), first published on 5 July 1687. The equation for universal gravitation ...
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Ellipsoid
An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface;  that is, a Surface (mathematics), surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is characterized by either of the two following properties. Every planar Cross section (geometry), cross section is either an ellipse, or is empty, or is reduced to a single point (this explains the name, meaning "ellipse-like"). It is Bounded set, bounded, which means that it may be enclosed in a sufficiently large sphere. An ellipsoid has three pairwise perpendicular Rotational symmetry, axes of symmetry which intersect at a Central symmetry, center of symmetry, called the center of the ellipsoid. The line segments that are delimited on the axes of symmetry by the ellipsoid are called the ''principal ax ...
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Prolate Spheroid
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a ''prolate spheroid'', elongated like a rugby ball. The American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an ''oblate spheroid'', flattened like a lentil or a plain M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography and geodesy the Earth is often approximated by an oblate spheroid, known as the reference ellipsoid, instead of a sp ...
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Apsis
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides pertaining to orbits around different bodies have distinct names to differentiate themselves from other apsides. Apsides pertaining to geocentric orbits, orbits around the Earth, are at the farthest point called the ''apogee'', and at the nearest point the ''perigee'', like with orbits of satellites and the Moon around Earth. Apsides pertaining to orbits around the Sun are named ''aphelion'' for the farthest and ''perihelion'' for the nearest point in a heliocentric orbit. Earth's two apsides are the farthest point, ''aphelion'', and the nearest point, ''perihelion'', of its orbit around the host Sun. The terms ''aphelion'' and ''perihelion'' apply in the same way to the orbits of Jupiter and the other planets, the comets, and the asteroids of t ...
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