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Orbiting Body
In astrodynamics, an orbiting body is any physical body that orbits a more massive one, called the primary body. The orbiting body is properly referred to as the secondary body (m_2), which is less massive than the primary body (m_1). Thus, m_2 m_2. Under standard assumptions in astrodynamics, the barycenter of the two bodies is a focus of both orbits. An orbiting body may be a spacecraft (i.e. an artificial satellite) or a natural satellite, such as a planet, dwarf planet, moon, moonlet, asteroid, or comet. A system of two orbiting bodies is modeled by the Two-Body Problem and a system of three orbiting bodies is modeled by the Three-Body Problem. These problems can be generalized to an N-body problem. While there are a few analytical solutions to the n-body problem, it can be reduced to a 2-body system if the secondary body stays out of other bodies' Sphere of Influence and remains in the primary body's sphere of influence. See also *Barycenter * Double planet *Primary ...
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Astrodynamics
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 Newton's law of universal gravitation, law of universal gravitation. Astrodynamics 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 theory than Newton's laws for calculati ...
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Comet
A comet is an icy, small Solar System body that warms and begins to release gases when passing close to the Sun, a process called outgassing. This produces an extended, gravitationally unbound atmosphere or Coma (cometary), coma surrounding the nucleus, and sometimes a Comet tail, tail of gas and dust gas blown out from the coma. These phenomena are due to the effects of solar radiation and the outstreaming solar wind plasma acting upon the nucleus of the comet. Comet nuclei range from a few hundred meters to tens of kilometers across and are composed of loose collections of ice, dust, and small rocky particles. The coma may be up to 15 times Earth's diameter, while the tail may stretch beyond one astronomical unit. If sufficiently close and bright, a comet may be seen from Earth without the aid of a telescope and can Subtended angle, subtend an arc of up to 30° (60 Moons) across the sky. Comets have been observed and recorded since ancient times by many cultures and religion ...
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Orbits
In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an physical body, object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an satellite, artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the barycenter, center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion. For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains Newton's law of universal gravitation, gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits ...
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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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Two-body Problem
In classical mechanics, the two-body problem is to calculate and predict the motion of two massive bodies that are orbiting each other in space. The problem assumes that the two bodies are point particles that interact only with one another; the only force affecting each object arises from the other one, and all other objects are ignored. The most prominent example of the classical two-body problem is the gravitational case (see also Kepler problem), arising in astronomy for predicting the orbits (or escapes from orbit) of objects such as satellites, planets, and stars. A two-point-particle model of such a system nearly always describes its behavior well enough to provide useful insights and predictions. A simpler "one body" model, the " central-force problem", treats one object as the immobile source of a force acting on the other. One then seeks to predict the motion of the single remaining mobile object. Such an approximation can give useful results when one object is much ...
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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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Primary (astronomy)
A primary bodyalso called a central body, host body, gravitational primary, or simply primaryis the main physical body of a gravitationally bound, multi-object system. This object constitutes most of that system's mass and will generally be located near the system's barycenter. In the Solar System, the Sun is the primary for all objects that orbit the star. In the same way, the primary of all satellites (be they natural satellites (moons) or artificial ones) is the planet they orbit. The term ''primary'' is often used to avoid specifying whether the object near the barycenter is a planet, a star, or any other astronomical object. In this sense, the word ''primary'' is always used as a noun. The center of mass is the average position of all the objects weighed by mass. The Sun is so massive that the Solar System's barycenter frequently lies very near the Sun's center but owing to the mass and distance of the gas giant planets, the Solar System's barycenter occasionally lies ou ...
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Double Planet
In astronomy, a double planet (also binary planet) is a binary satellite system where both objects are planets, or planetary-mass objects, and whose barycenter is external to both planetary bodies. Although up to a third of the star systems in the Milky Way are binary, double planets are expected to be much rarer given the typical planet to satellite mass ratio is around 1:10,000, they are influenced heavily by the gravitational pull of the parent star and according to the giant-impact hypothesis are gravitationally stable only under particular circumstances. The Solar System does not have an official double planet, however the Earth–Moon system is sometimes considered to be one. In promotional materials advertising the SMART-1 mission, the European Space Agency referred to the Earth–Moon system as a double planet. Several dwarf planet candidates can be described as binary planets. At its 2006 General Assembly, the International Astronomical Union considered a proposal ...
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Barycenter
In astronomy, the barycenter (or barycentre; ) is the center of mass of two or more bodies that orbit one another and is the point about which the bodies orbit. A barycenter is a dynamical point, not a physical object. It is an important concept in fields such as astronomy and astrophysics. The distance from a body's center of mass to the barycenter can be calculated as a two-body problem. If one of the two orbiting bodies is much more massive than the other and the bodies are relatively close to one another, the barycenter will typically be located within the more massive object. In this case, rather than the two bodies appearing to orbit a point between them, the less massive body will appear to orbit about the more massive body, while the more massive body might be observed to wobble slightly. This is the case for the Earth–Moon system, whose barycenter is located on average from Earth's center, which is 74% of Earth's radius of . When the two bodies are of similar m ...
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Sphere Of Influence
In the field of international relations, a sphere of influence (SOI) is a spatial region or concept division over which a state or organization has a level of cultural, economic, military, or political exclusivity. While there may be a formal alliance or other treaty obligations between the influenced and influencer, such formal arrangements are not necessary and the influence can often be more of an example of soft power. Similarly, a formal alliance does not necessarily mean that one country lies within another's sphere of influence. High levels of exclusivity have historically been associated with higher levels of conflict. In more extreme cases, a country within the "sphere of influence" of another may become a subsidiary of that state and serve in effect as a satellite state or '' de facto'' colony. This was the case with the Soviet Union and its Eastern Bloc after World War II. The system of spheres of influence by which powerful nations intervene in the affairs of others ...
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N-body Problem
In physics, the -body problem is the problem of predicting the individual motions of a group of astronomical object, 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 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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