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Existence of Libration Points in the Photogravitational Elliptic Restricted Three Body ProblemGravity
Gravity (or gravitation) is a natural phenomenon by which all things attract one another including stars, planets, galaxies and even light and subatomic particles. Gravity is responsible for the formation of the universe (e.g. creating spheres of hydrogen, igniting them under pressure to form stars and grouping them in to galaxies). Gravity is a cause of time dilation (time lapses more slowly in strong gravitation). Without gravity, the universe would be without thermal energy and composed only of equally spaced particles. On Earth, gravity gives weight to physical objects and causes the tides. Gravity has an infinite range, and it cannot be absorbed, transformed, or shielded against.
Gravity is most accurately described by the general theory of relativity (proposed by Albert Einstein in 1915) which describes gravity, not as a force, but as a consequence of the curvature of spacetime caused by the uneven distribution of mass/energy. For most applications, gravity is well approximated by Newton's law of universal gravitation, which postulates that the gravitational force of two bodies of mass is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Gravity is the weakest of the four fundamental interactions of nature. The gravitational force is approximately 10^{−38} times the strength of the strong force (i.e. gravity is 38 orders of magnitude weaker), 10^{−36} times the strength of the electromagnetic force, and 10^{−29} times the strength of the weak force. As a consequence, gravity has a negligible influence on the behavior of subatomic particles, and plays no role in determining the internal properties of everyday matter. On the other hand, gravity is the dominant force at the macroscopic scale, that is the cause of the formation, shape, and trajectory (orbit) of astronomical bodies, including those of asteroids, comets, planets, stars, and galaxies. It is responsible for causing the Earth and the other planets to orbit the Sun; for causing the Moon to orbit the Earth; for the formation of tides; for natural convection, by which fluid flow occurs under the influence of a density gradient and gravity; for heating the interiors of forming stars and planets to very high temperatures; for solar system, galaxy, stellar formation and evolution; and for various other phenomena observed on Earth and throughout the universe.
In pursuit of a theory of everything, the merging of general relativity and quantum mechanics (or quantum field theory) into a more general theory of quantum gravity has become an area of research.
Contents
History of gravitational theory
Classical mechanics  

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Core topics  
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Scientific revolutionModern work on gravitational theory began with the work of Galileo Galilei in the late 16th and early 17th centuries. In his famous (though possibly apocryphal^{[1]}) experiment dropping balls from the Tower of Pisa, and later with careful measurements of balls rolling down inclines, Galileo showed that gravity accelerates all objects at the same rate. This was a major departure from Aristotle's belief that heavier objects accelerate faster.^{[2]} Galileo postulated air resistance as the reason that lighter objects may fall more slowly in an atmosphere. Galileo's work set the stage for the formulation of Newton's theory of gravity. Newton's theory of gravitationMain article: Newton's law of universal gravitation
In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inversesquare law of universal gravitation. In his own words, "I deduced that the forces which keep the planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly."^{[3]} The equation is the following: <math>F = G \frac{m_1 m_2}{r^2}\ </math> Where F is the force, m_{1} and m_{2} are the masses of the objects interacting, r is the distance between the centers of the masses and G is the gravitational constant. Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams and Urbain Le Verrier predicted the general position of the planet, and Le Verrier's calculations are what led Johann Gottfried Galle to the discovery of Neptune. A discrepancy in Mercury's orbit pointed out flaws in Newton's theory. By the end of the 19th century, it was known that its orbit showed slight perturbations that could not be accounted for entirely under Newton's theory, but all searches for another perturbing body (such as a planet orbiting the Sun even closer than Mercury) had been fruitless. The issue was resolved in 1915 by Albert Einstein's new theory of general relativity, which accounted for the small discrepancy in Mercury's orbit. Although Newton's theory has been superseded by the Einstein's general relativity, most modern nonrelativistic gravitational calculations are still made using the Newton's theory because it is simpler to work with and it gives sufficiently accurate results for most applications involving sufficiently small masses, speeds and energies. Equivalence principleThe equivalence principle, explored by a succession of researchers including Galileo, Loránd Eötvös, and Einstein, expresses the idea that all objects fall in the same way. The simplest way to test the weak equivalence principle is to drop two objects of different masses or compositions in a vacuum and see whether they hit the ground at the same time. Such experiments demonstrate that all objects fall at the same rate when other forces (such as air resistance and electromagnetic effects) are negligible. More sophisticated tests use a torsion balance of a type invented by Eötvös. Satellite experiments, for example STEP, are planned for more accurate experiments in space.^{[4]} Formulations of the equivalence principle include:
General relativitySee also: Introduction to general relativity
In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of a force. The starting point for general relativity is the equivalence principle, which equates free fall with inertial motion and describes freefalling inertial objects as being accelerated relative to noninertial observers on the ground.^{[7]}^{[8]} In Newtonian physics, however, no such acceleration can occur unless at least one of the objects is being operated on by a force. Einstein proposed that spacetime is curved by matter, and that freefalling objects are moving along locally straight paths in curved spacetime. These straight paths are called geodesics. Like Newton's first law of motion, Einstein's theory states that if a force is applied on an object, it would deviate from a geodesic. For instance, we are no longer following geodesics while standing because the mechanical resistance of the Earth exerts an upward force on us, and we are noninertial on the ground as a result. This explains why moving along the geodesics in spacetime is considered inertial. Einstein discovered the field equations of general relativity, which relate the presence of matter and the curvature of spacetime and are named after him. The Einstein field equations are a set of 10 simultaneous, nonlinear, differential equations. The solutions of the field equations are the components of the metric tensor of spacetime. A metric tensor describes a geometry of spacetime. The geodesic paths for a spacetime are calculated from the metric tensor. Notable solutions of the Einstein field equations include:
The tests of general relativity included the following:^{[9]}
Gravity and quantum mechanicsMain articles: Graviton and Quantum gravity
In the decades after the discovery of general relativity, it was realized that general relativity is incompatible with quantum mechanics.^{[18]} It is possible to describe gravity in the framework of quantum field theory like the other fundamental forces, such that the attractive force of gravity arises due to exchange of virtual gravitons, in the same way as the electromagnetic force arises from exchange of virtual photons.^{[19]}^{[20]} This reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length,^{[18]} where a more complete theory of quantum gravity (or a new approach to quantum mechanics) is required. SpecificsEarth's gravityMain article: Earth's gravity
Every planetary body (including the Earth) is surrounded by its own gravitational field, which exerts an attractive force on all objects. Assuming a spherically symmetrical planet, the strength of this field at any given point above the surface is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body. The strength of the gravitational field is numerically equal to the acceleration of objects under its influence.^{[citation needed]} The rate of acceleration of falling objects near the Earth's surface varies very slightly depending on elevation, latitude, and other factors. For purposes of weights and measures, a standard gravity value is defined by the International Bureau of Weights and Measures, under the International System of Units (SI). That value, denoted g, is g = 9.80665 m/s^{2} (32.1740 ft/s^{2}).^{[21]}^{[22]} The standard value of 9.80665 m/s^{2} is the one originally adopted by the International Committee on Weights and Measures in 1901 for 45° latitude, even though it has been shown to be too high by about five parts in ten thousand.^{[23]} This value has persisted in meteorology and in some standard atmospheres as the value for 45° latitude even though it applies more precisely to latitude of 45°32'33".^{[24]} Assuming the standardized value for g and ignoring air resistance, this means that an object falling freely near the Earth's surface increases its velocity by 9.80665 m/s (32.1740 ft/s or 22 mph) for each second of its descent. Thus, an object starting from rest will attain a velocity of 9.80665 m/s (32.1740 ft/s) after one second, approximately 19.62 m/s (64.4 ft/s) after two seconds, and so on, adding 9.80665 m/s (32.1740 ft/s) to each resulting velocity. Also, again ignoring air resistance, any and all objects, when dropped from the same height, will hit the ground at the same time. It is relevant to note that Earth's gravity doesn't have exactly the same value in all regions. There are slight variations in different parts of the globe due to latitude, surface features such as mountains and ridges, and perhaps unusually high or low subsurface densities.^{[25]} According to Newton's 3rd Law, the Earth itself experiences a force equal in magnitude and opposite in direction to that which it exerts on a falling object. This means that the Earth also accelerates towards the object until they collide. Because the mass of the Earth is huge, however, the acceleration imparted to the Earth by this opposite force is negligible in comparison to the object's. If the object doesn't bounce after it has collided with the Earth, each of them then exerts a repulsive contact force on the other which effectively balances the attractive force of gravity and prevents further acceleration. The force of gravity on Earth is the resultant (vector sum) of two forces:^{[dubious – discuss]}^{[citation needed]} (a) The gravitational attraction in accordance with Newton's universal law of gravitation, and (b) the centrifugal force^{[dubious – discuss]}^{[citation needed]}, which results from the choice of an earthbound, rotating frame of reference. At the equator, the force of gravity is the weakest due to the centrifugal force caused by the Earth's rotation. The force of gravity varies with latitude and increases from about 9.780 m/s^{2} at the Equator to about 9.832 m/s^{2} at the poles. Equations for a falling body near the surface of the EarthMain article: Equations for a falling body
Under an assumption of constant gravitational attraction, Newton's law of universal gravitation simplifies to F = mg, where m is the mass of the body and g is a constant vector with an average magnitude of 9.81 m/s^{2} on Earth. This resulting force is the object's weight. The acceleration due to gravity is equal to this g. An initially stationary object which is allowed to fall freely under gravity drops a distance which is proportional to the square of the elapsed time. The image on the right, spanning half a second, was captured with a stroboscopic flash at 20 flashes per second. During the first ^{1}⁄_{20} of a second the ball drops one unit of distance (here, a unit is about 12 mm); by ^{2}⁄_{20} it has dropped at total of 4 units; by ^{3}⁄_{20}, 9 units and so on. Under the same constant gravity assumptions, the potential energy, E_{p}, of a body at height h is given by E_{p} = mgh (or E_{p} = Wh, with W meaning weight). This expression is valid only over small distances h from the surface of the Earth. Similarly, the expression <math>h = \tfrac{v^2}{2g}</math> for the maximum height reached by a vertically projected body with initial velocity v is useful for small heights and small initial velocities only. Gravity and astronomyThe application of Newton's law of gravity has enabled the acquisition of much of the detailed information we have about the planets in our solar system, the mass of the Sun, and details of quasars; even the existence of dark matter is inferred using Newton's law of gravity. Although we have not traveled to all the planets nor to the Sun, we know their masses. These masses are obtained by applying the laws of gravity to the measured characteristics of the orbit. In space an object maintains its orbit because of the force of gravity acting upon it. Planets orbit stars, stars orbit Galactic Centers, galaxies orbit a center of mass in clusters, and clusters orbit in superclusters. The force of gravity exerted on one object by another is directly proportional to the product of those objects' masses and inversely proportional to the square of the distance between them. Gravitational radiationMain article: Gravitational wave
In general relativity, gravitational radiation is generated in situations where the curvature of spacetime is oscillating, such as is the case with coorbiting objects. The gravitational radiation emitted by the Solar System is far too small to measure. However, gravitational radiation has been indirectly observed as an energy loss over time in binary pulsar systems such as PSR B1913+16. It is believed that neutron star mergers and black hole formation may create detectable amounts of gravitational radiation. Gravitational radiation observatories such as the Laser Interferometer Gravitational Wave Observatory (LIGO) have been created to study the problem. No confirmed detections have been made of this hypothetical radiation. Speed of gravityMain article: Speed of gravity
In December 2012, a research team in China announced that it had produced measurements of the phase lag of Earth tides during full and new moons which seem to prove that the speed of gravity is equal to the speed of light.^{[27]} This means that if the Sun suddenly disappeared, the Earth would keep orbiting it normally for 8 minutes, which is the time light takes to travel that distance. The team's findings were released in the Chinese Science Bulletin in February 2013.^{[28]} Anomalies and discrepanciesThere are some observations that are not adequately accounted for, which may point to the need for better theories of gravity or perhaps be explained in other ways.
Alternative theoriesMain article: Alternatives to general relativity
Historical alternative theories
Recent alternative theories
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Footnotes
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