Tidal Circularization
Tidal circularization is an effect of the tidal forces between an orbiting body and the primary object that it orbits, whereby the eccentricity of the orbit is reduced over time so that the orbit becomes less and less elliptical. In figure 1 let’s start by assuming body 1 is a star and body 2 is another star or maybe a Jupiter like planet. Initially think of body2 as a point mass. The gravity from Body 2 applied to Body 1 produces tidal bulges (see Tidal Force). Let’s assume the orbital period is slower than the rotation of Body 1 (ωΩ, the lag angle will be in the other direction. For a star we can think of inelasticity as viscocity. The main cause of inelasticity in a star seems to be convection forces inside the star. When the lag angle is non zero as in figure 1 you can see that the forces F1 and F2 combine to torque body 1 clockwise because F1 is stronger. At the same time they torque the orbital motion counter clockwise: if you ignore the portion of F1 and F2 that ...
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Tidal Force
The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomena, including tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within the Roche limit, and in extreme cases, spaghettification of objects. It arises because the gravitational field exerted on one body by another is not constant across its parts: the nearest side is attracted more strongly than the farthest side. It is this difference that causes a body to get stretched. Thus, the tidal force is also known as the differential force, as well as a secondary effect of the gravitational field. In celestial mechanics, the expression ''tidal force'' can refer to a situation in which a body or material (for example, tidal water) is mainly under the gravitational influence of a second body (for example, the Eart ...
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Orbital Eccentricity
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 *
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Tidal Circularization Figure1
Tidal is the adjectival form of tide. Tidal may also refer to: * ''Tidal'' (album), a 1996 album by Fiona Apple * Tidal (king), a king involved in the Battle of the Vale of Siddim * TidalCycles, a live coding environment for music * Tidal (service), a music streaming service * Tidal, Manitoba, Canada ** Tidal station, Tidal, Manitoba See also * Tidal flow (traffic), the flow of traffic thought of as an analogy with the flow of tides * Tidal force, a secondary effect of the force of gravity and is responsible for the tides * Tide (other) A tide is the rise and fall of a sea level caused by the Moon's gravity and other factors. Tide may also refer to: Media * The Tide (Nigeria), ''The Tide'' (Nigeria), a newspaper *Tide (TV series), ''Tide'' (TV series), 2019 Irish/Welsh/Scottish ...

Tidal Force
The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomena, including tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within the Roche limit, and in extreme cases, spaghettification of objects. It arises because the gravitational field exerted on one body by another is not constant across its parts: the nearest side is attracted more strongly than the farthest side. It is this difference that causes a body to get stretched. Thus, the tidal force is also known as the differential force, as well as a secondary effect of the gravitational field. In celestial mechanics, the expression ''tidal force'' can refer to a situation in which a body or material (for example, tidal water) is mainly under the gravitational influence of a second body (for example, the Eart ...
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Tidal Circularization Figure2
Tidal is the adjectival form of tide. Tidal may also refer to: * ''Tidal'' (album), a 1996 album by Fiona Apple * Tidal (king), a king involved in the Battle of the Vale of Siddim * TidalCycles, a live coding environment for music * Tidal (service), a music streaming service * Tidal, Manitoba, Canada ** Tidal station, Tidal, Manitoba See also * Tidal flow (traffic), the flow of traffic thought of as an analogy with the flow of tides * Tidal force, a secondary effect of the force of gravity and is responsible for the tides * Tide (other) A tide is the rise and fall of a sea level caused by the Moon's gravity and other factors. Tide may also refer to: Media * The Tide (Nigeria), ''The Tide'' (Nigeria), a newspaper *Tide (TV series), ''Tide'' (TV series), 2019 Irish/Welsh/Scottish ...

Apsis
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., f ...
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Orbital Mechanics
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 law of universal gravitation. Orbital mechanics 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 ne ...
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Tidal Lock
Tidal locking between a pair of co-orbiting astronomical bodies occurs when one of the objects reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit. In the case where a tidally locked body possesses synchronous rotation, the object takes just as long to rotate around its own axis as it does to revolve around its partner. For example, the same side of the Moon always faces the Earth, although there is some variability because the Moon's orbit is not perfectly circular. Usually, only the satellite is tidally locked to the larger body. However, if both the difference in mass between the two bodies and the distance between them are relatively small, each may be tidally locked to the other; this is the case for Pluto and Charon. Alternative names for the tidal locking process are gravitational locking, captured rotation, and spin–orbit locking. The effect arises between two bodies when their gravitational interaction slow ...
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Tidal Locking
Tidal locking between a pair of co-orbiting astronomical bodies occurs when one of the objects reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit. In the case where a tidally locked body possesses synchronous rotation, the object takes just as long to rotate around its own axis as it does to revolve around its partner. For example, the same side of the Moon always faces the Earth, although there is some variability because the Moon's orbit is not perfectly circular. Usually, only the satellite is tidally locked to the larger body. However, if both the difference in mass between the two bodies and the distance between them are relatively small, each may be tidally locked to the other; this is the case for Pluto and Charon. Alternative names for the tidal locking process are gravitational locking, captured rotation, and spin–orbit locking. The effect arises between two bodies when their gravitational interaction sl ...
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Tidal Acceleration
Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite (e.g. the Moon) and the primary planet that it orbits (e.g. Earth). The acceleration causes a gradual recession of a satellite in a prograde orbit away from the primary, and a corresponding slowdown of the primary's rotation. The process eventually leads to tidal locking, usually of the smaller body first, and later the larger body (e.g. theoretically with Earth in 50 billion years). The Earth–Moon system is the best-studied case. The similar process of tidal deceleration occurs for satellites that have an orbital period that is shorter than the primary's rotational period, or that orbit in a retrograde direction. The naming is somewhat confusing, because the average speed of the satellite relative to the body it orbits is ''decreased'' as a result of tidal acceleration, and ''increased'' as a result of tidal deceleration. This conundrum occurs because a positive acceleration at one instan ...
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Tides
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables can be used for any given locale to find the predicted times and amplitude (or "tidal range"). The predictions are influenced by many factors including the alignment of the Sun and Moon, the phase and amplitude of the tide (pattern of tides in the deep ocean), the amphidromic systems of the oceans, and the shape of the coastline and near-shore bathymetry (see '' Timing''). They are however only predictions, the actual time and height of the tide is affected by wind and atmospheric pressure. Many shorelines experience semi-diurnal tides—two nearly equal high and low tides each day. Other locations have a diurnal tide—one high and low tide each day. A "mixed tide"—two uneven magnitude tides a day—is a third regular category. Tides va ...
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