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| {{about|the natural phenomenon}}
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| {{Redirect|Gravity}}
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| {{Redirect2|Law of Gravity|Laws of Gravity}}
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| [[File:Apollo 15 feather and hammer drop.ogg|right|thumb|Hammer and feather drop: [[Apollo 15]] [[astronaut]] [[David Scott]] on the Moon recreating Galileo's famous gravity experiment. (1.38 [[Megabyte|MB]], [[ogg]]/[[Theora]] format).]]
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| '''Gravitation''', or '''gravity''', is a [[natural phenomenon]] by which all [[physical body|physical bodies]] attract each other. It is most commonly recognized and experienced as the agent that gives [[weight]] to physical objects, and causes physical objects to [[free fall|fall]] toward the ground when dropped from a height.
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| It is hypothesized that the gravitational force is mediated by a massless [[Spin (physics)|spin-2]] particle called the [[graviton]]. Gravity is one of the four [[fundamental interaction|fundamental forces]] of nature, along with [[electromagnetism]], and the nuclear [[strong interaction|strong force]] and [[weak interaction|weak force]]. Colloquially, gravitation is a force of attraction that acts between and on all physical objects with matter (mass) or energy. In modern [[physics]], gravitation is most accurately described by the [[general theory of relativity]] proposed by Einstein, which asserts that the phenomenon of gravitation is a consequence of the curvature of [[spacetime]]. 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 active research. [[Newton's law of universal gravitation]] postulates that the gravitational [[force]] of two bodies of mass is directly [[proportionality (mathematics)|proportional]] to the product of their masses and [[inversely proportional]] to the [[square (algebra)|square]] of the [[distance]] between them. It provides an accurate approximation for most physical situations including [[orbital mechanics|spacecraft trajectory]]. [[Newton's laws of motion]] are also based on the influence of gravity, encompassing three physical laws that lay down the foundations for classical mechanics.
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| During the [[grand unification epoch]], gravity separated from the [[electronuclear force]]. Gravity is the weakest of the four fundamental forces, and appears to have unlimited range (unlike the strong or weak force). The gravitational force is approximately 10<sup>-38</sup> times the strength of the strong force (i.e., gravity is 38 orders of magnitude weaker), 10<sup>-36</sup> times the strength of the electromagnetic force, and 10<sup>-29</sup> times the strength of the weak force. As a consequence, gravity has a negligible influence on the behavior of sub-atomic 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 [[asteroid]]s, [[comet]]s, [[planet]]s, [[star]]s, and [[galaxy|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 [[tide]]s; 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 [[formation and evolution of the solar system|solar system]], [[galaxy formation and evolution|galaxy]], [[stellar evolution|stellar]] formation and evolution; and for various other phenomena observed on Earth and throughout the universe. This is the case for several reasons: gravity is the only force acting on all particles with mass; it has an infinite range; always attractive and never repulsive; and cannot be absorbed, transformed, or shielded against. Even though electromagnetism is far stronger than gravity, electromagnetism is not relevant to astronomical objects, since such bodies have an equal number of protons and electrons that cancel out (i.e., a net electric charge of zero).
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| ==History of gravitational theory==
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| {{main|History of gravitational theory}}
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| {{Classical mechanics}}
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| ===Scientific revolution===
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| Modern 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]]<ref name=Ball_Piza>{{cite journal |last=Ball |first=Phil |year=2005 |month=06 |title=Tall Tales |journal=Nature News |doi=10.1038/news050613-10 }}</ref>) experiment dropping balls from the [[Leaning Tower of Pisa|Tower of Pisa]], and later with careful measurements of balls rolling down [[Inclined plane|inclines]], Galileo showed that gravitation accelerates all objects at the same rate. This was a major departure from [[Aristotle]]'s belief that heavier objects accelerate faster.<ref>[[Galileo]] (1638), ''[[Two New Sciences]]'', [http://oll.libertyfund.org/?option=com_staticxt&staticfile=show.php%3Ftitle=753&chapter=109891&layout=html&Itemid=27 First Day] Salviati speaks: "If this were what Aristotle meant you would burden him with another error which would amount to a falsehood; because, since there is no such sheer height available on earth, it is clear that Aristotle could not have made the experiment; yet he wishes to give us the impression of his having performed it when he speaks of such an effect as one which we see."</ref> Galileo postulated air resistance as the reason that lighter objects may fall slower in an atmosphere. Galileo's work set the stage for the formulation of Newton's theory of gravity.
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| ===Newton's theory of gravitation===
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| {{main|Newton's law of universal gravitation}}
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| [[File:Sir Isaac Newton (1643-1727).jpg|thumb|250px|[[Isaac Newton|Sir Isaac Newton]], an English physicist who lived from 1642 to 1727]]
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| In 1687, English mathematician Sir [[Isaac Newton]] published ''[[Philosophiæ Naturalis Principia Mathematica|Principia]]'', which hypothesizes the [[inverse-square 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.”<ref>*{{cite book
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| | first= Subrahmanyan
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| | last= Chandrasekhar
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| | authorlink= Subrahmanyan Chandrasekhar
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| | title= Newton's Principia for the common reader
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| | year= 2003
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| | publisher= Oxford University Press
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| | location= Oxford}} (pp.1–2). The quotation comes from a memorandum thought to have been written about 1714. As early as 1645 [[Ismaël Bullialdus]] had argued that any force exerted by the Sun on distant objects would have to follow an inverse-square law. However, he also dismissed the idea that any such force did exist. See, for example,
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| {{cite book | title= From Eudoxus to Einstein—A History of Mathematical Astronomy
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| | author= Linton, Christopher M.
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| | publisher= Cambridge University Press
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| | year= 2004
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| | location= Cambridge
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| | page= 225
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| | isbn= 978-0-521-82750-8
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| | ref= Linton-2004}}
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| </ref>
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| 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.
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| A discrepancy in [[Mercury (planet)|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.
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| Although Newton's theory has been superseded, most modern [[Theory of relativity|non-relativistic]] gravitational calculations are still made using Newton's theory because it is a much simpler theory to work with than general relativity, and gives sufficiently accurate results for most applications involving sufficiently small masses, speeds and energies.
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| ===Equivalence principle===
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| The [[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 [[mass]]es or compositions in a vacuum, and see if they hit the ground at the same time. These experiments demonstrate that all objects fall at the same rate when friction (including air resistance) is negligible. More sophisticated tests use a torsion balance of a type invented by Eötvös. Satellite experiments, for example [[STEP (satellite)|STEP]], are planned for more accurate experiments in space.<ref>{{cite web |author=M.C.W.Sandford |publisher=[[Rutherford Appleton Laboratory]] |title=STEP: Satellite Test of the Equivalence Principle |url=http://www.sstd.rl.ac.uk/fundphys/step/ |year=2008 |accessdate=2011-10-14}}</ref>
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| Formulations of the equivalence principle include:
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| * The weak equivalence principle: ''The trajectory of a point mass in a [[gravitational field]] depends only on its initial position and velocity, and is independent of its composition.''<ref name=Wesson>{{cite book |title=Five-dimensional Physics |author= Paul S Wesson |page=82 |url=http://books.google.com/?id=dSv8ksxHR0oC&printsec=frontcover&dq=intitle:Five+intitle:Dimensional+intitle:Physics |isbn=981-256-661-9 |publisher=World Scientific |year=2006}}</ref>
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| * The Einsteinian equivalence principle: ''The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.''<ref name="Lāmmerzahl">{{cite book |last=Haugen | first=Mark P. | author= | authorlink= | coauthors=C. Lämmerzahl |title=Principles of Equivalence: Their Role in Gravitation Physics and Experiments that Test Them |year=2001 |publisher=Springer |isbn=978-3-540-41236-6 |arxiv=gr-qc/0103067}}</ref>
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| * The strong equivalence principle requiring both of the above.
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| ===General relativity===
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| {{see also|Introduction to general relativity}}
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| [[File:GPB circling earth.jpg|thumb|300px|right|Two-dimensional analogy of spacetime distortion generated by the mass of an object. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as [[gravity]]. White lines do not represent the curvature of space but instead represent the [[coordinate system]] imposed on the curved spacetime, which would be [[regular grid|rectilinear]] in a flat spacetime.]]
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| {{General relativity}}
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| 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 free-falling inertial objects as being accelerated relative to non-inertial observers on the ground.<ref>{{cite web|url=http://www.black-holes.org/relativity6.html |title=Gravity and Warped Spacetime |publisher=black-holes.org |date= |accessdate=2010-10-16}}</ref><ref>{{cite web |title=Lecture 20: Black Holes—The Einstein Equivalence Principle |author=Dmitri Pogosyan |url=http://www.ualberta.ca/~pogosyan/teaching/ASTRO_122/lect20/lecture20.html |publisher=University of Alberta |accessdate=2011-10-14}}</ref> In [[Newtonian physics]], however, no such acceleration can occur unless at least one of the objects is being operated on by a force.
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| Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. These straight paths are called [[geodesic (general relativity)|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 non-inertial on the ground as a result. This explains why moving along the geodesics in spacetime is considered inertial.
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| Einstein discovered the [[field equation]]s 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 equations|simultaneous]], [[nonlinear system|non-linear]], [[differential equation]]s. The solutions of the field equations are the components of the [[metric tensor (general relativity)|metric tensor]] of spacetime. A metric tensor describes a geometry of spacetime. The geodesic paths for a spacetime are calculated from the metric tensor.
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| Notable solutions of the Einstein field equations include:
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| * The [[Schwarzschild solution]], which describes spacetime surrounding a [[Circular symmetry|spherically symmetric]] non-[[rotation|rotating]] uncharged massive object. For compact enough objects, this solution generated a [[black hole]] with a central [[gravitational singularity|singularity]]. For radial distances from the center which are much greater than the [[Schwarzschild radius]], the accelerations predicted by the Schwarzschild solution are practically identical to those predicted by Newton's theory of gravity.
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| * The [[Reissner–Nordström metric|Reissner-Nordström solution]], in which the central object has an electrical charge. For charges with a [[geometrized]] length which are less than the geometrized length of the mass of the object, this solution produces black holes with two [[event horizon]]s.
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| * The [[Kerr metric|Kerr solution]] for rotating massive objects. This solution also produces black holes with multiple event horizons.
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| * The [[Kerr–Newman metric|Kerr-Newman solution]] for charged, rotating massive objects. This solution also produces black holes with multiple event horizons.
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| * The [[physical cosmology|cosmological]] [[Friedmann–Lemaître–Robertson–Walker metric|Friedmann-Lemaître-Robertson-Walker solution]], which predicts the expansion of the [[universe]].
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| The [[tests of general relativity]] included the following:<ref name=Pauli1958>{{cite book|last=Pauli|first=Wolfgang Ernst|title=Theory of Relativity|year=1958|isbn=978-0-486-64152-2|publisher=Courier Dover Publications|chapter=Part IV. General Theory of Relativity}}</ref>
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| * General relativity accounts for the anomalous [[perihelion precession of Mercury]].<ref>[[Max Born]] (1924), ''Einstein's Theory of Relativity'' (The 1962 Dover edition, page 348 lists a table documenting the observed and calculated values for the precession of the perihelion of Mercury, Venus, and Earth.)</ref>
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| * The prediction that time runs slower at lower potentials has been confirmed by the [[Pound–Rebka experiment]], the [[Hafele–Keating experiment]], and the [[GPS#Relativity|GPS]].
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| * The prediction of the deflection of light was first confirmed by [[Arthur Stanley Eddington]] from his observations during the [[Solar eclipse of May 29, 1919]].<ref>{{cite journal|last1=Dyson|first1=F.W.|authorlink1=Frank Watson Dyson|last2= Eddington|first2=A.S.|authorlink2=Arthur Eddington|last3=Davidson|first3=C.R. |year=1920 |title=A Determination of the Deflection of Light by the Sun's Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919|journal= [[Philosophical Transactions of the Royal Society A: Physical, Mathematical and Engineering Sciences|Phil. Trans. Roy. Soc. A]]|volume=220|issue=571–581|pages= 291–333|bibcode=1920RSPTA.220..291D|doi=10.1098/rsta.1920.0009}}. Quote, p. 332: "Thus the results of the expeditions to Sobral and Principe can leave little doubt that a deflection of light takes place in the neighbourhood of the sun and that it is of the amount demanded by Einstein's generalised theory of relativity, as attributable to the sun's gravitational field."</ref><ref>{{cite book|first=Steven|last=Weinberg|authorlink=Steven Weinberg|title=Gravitation and cosmology|publisher=John Wiley & Sons|year=1972}}. Quote, p. 192: "About a dozen stars in all were studied, and yielded values 1.98 ± 0.11" and 1.61 ± 0.31", in substantial agreement with Einstein's prediction θ<sub>☉</sub> = 1.75"."</ref> Eddington measured starlight deflections twice those predicted by Newtonian corpuscular theory, in accordance with the predictions of general relativity. However, his interpretation of the results was later disputed.<ref>{{cite journal| last1=Earman |first1=John |last2=Glymour |first2=Clark |title=Relativity and Eclipses: The British eclipse expeditions of 1919 and their predecessors |year=1980 |journal=Historical Studies in the Physical Sciences |volume=11 |pages=49–85| doi=10.2307/27757471}}</ref> More recent tests using radio interferometric measurements of [[quasar]]s passing behind the [[Sun]] have more accurately and consistently confirmed the deflection of light to the degree predicted by general relativity.<ref>{{cite book|first=Steven|last=Weinberg|authorlink=Steven Weinberg|title=Gravitation and cosmology|publisher=John Wiley & Sons|year=1972|page=194}}</ref> See also [[gravitational lens]].
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| * The [[time delay of light]] passing close to a massive object was first identified by [[Irwin I. Shapiro]] in 1964 in interplanetary spacecraft signals.
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| * [[Gravitational radiation]] has been indirectly confirmed through studies of binary [[pulsar]]s.
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| * [[Alexander Friedmann]] in 1922 found that Einstein equations have non-stationary solutions (even in the presence of the [[cosmological constant]]). In 1927 [[Georges Lemaître]] showed that static solutions of the Einstein equations, which are possible in the presence of the cosmological constant, are unstable, and therefore the static universe envisioned by Einstein could not exist. Later, in 1931, Einstein himself agreed with the results of Friedmann and Lemaître. Thus general relativity predicted that the Universe had to be non-static—it had to either expand or contract. The expansion of the universe discovered by [[Edwin Hubble]] in 1929 confirmed this prediction.<ref name=Pauli1>See W.Pauli, 1958, pp.219–220</ref>
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| *The theory's prediction of [[frame dragging]] was consistent with the recent [[Gravity Probe B]] results.<ref>{{cite web|url=http://www.nasa.gov/home/hqnews/2011/may/HQ_11-134_Gravity_Probe_B.html |title=NASA's Gravity Probe B Confirms Two Einstein Space-Time Theories |publisher=Nasa.gov |date= |accessdate=2013-07-23}}</ref>
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| *General relativity predicts that light should lose its energy when travelling away from the massive bodies. The group of Radek Wojtak of the Niels Bohr Institute at the University of Copenhagen collected data from 8000 galaxy clusters and found that the light coming from the cluster centers tended to be red-shifted compared to the cluster edges, confirming the energy loss due to gravity.<ref>{{cite web|last=Bhattacharjee |first=Yudhijit |url=http://news.sciencemag.org/sciencenow/2011/09/galaxy-clusters-validate-einstei.html |title=Galaxy Clusters Validate Einstein's Theory |publisher=News.sciencemag.org |date= |accessdate=2013-07-23}}</ref>
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| ===Gravity and quantum mechanics===
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| {{main|Graviton|Quantum gravity}}
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| In the decades after the discovery of general relativity it was realized that general relativity is incompatible with [[quantum mechanics]].<ref name="Randall, Lisa 2005">{{cite book | author=Randall, Lisa | title=Warped Passages: Unraveling the Universe's Hidden Dimensions | publisher=Ecco | year=2005 | isbn=0-06-053108-8}}</ref> 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 particle|virtual]] gravitons, in the same way as the electromagnetic force arises from exchange of virtual [[photon]]s.<ref>{{cite book |last= Feynman |first= R. P. |coauthors= Morinigo, F. B., Wagner, W. G., & Hatfield, B. |title= Feynman lectures on gravitation |publisher= Addison-Wesley |year= 1995 |isbn=0-201-62734-5 }}</ref><ref>{{cite book | author=Zee, A. |title=Quantum Field Theory in a Nutshell | publisher = Princeton University Press | year=2003 | isbn=0-691-01019-6}}</ref> This reproduces general relativity in the [[classical limit]]. However, this approach fails at short distances of the order of the [[Planck length]],<ref name="Randall, Lisa 2005"/> where a more complete theory of [[quantum gravity]] (or a new approach to quantum mechanics) is required.
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| ==Specifics==
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| ===Earth's gravity===
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| {{main|Earth's gravity}}
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| 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 is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body.
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| The strength of the gravitational field is numerically equal to the acceleration of objects under its influence, and its value at the Earth's surface, denoted ''g'', is expressed below as the [[Standard gravity|standard average]]. According to the Bureau International de Poids et Mesures, International Systems of Units (SI), the Earth's standard acceleration due to gravity is:
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| ''g'' = 9.80665 m/s<sup>2</sup> (32.1740 ft/s<sup>2</sup>).<ref>{{cite paper
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| |author=Bureau International des Poids et Mesures
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| |year=2006
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| |url=http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf
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| |title=The International System of Units (SI)
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| |version=8th ed.
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| |accessdate=2009-11-25
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| |chapter=Chapter 5
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| |quote=Unit names are normally printed in roman (upright) type ... Symbols for quantities are generally single letters set in an italic font, although they may be qualified by further information in subscripts or superscripts or in brackets.}}</ref><ref>{{cite web
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| |url=http://physics.nist.gov/cuu/Units/checklist.html
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| |quote=Variables and quantity symbols are in italic type. Unit symbols are in roman type.
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| |title=SI Unit rules and style conventions
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| |author=
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| |date=September 2004
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| |work=
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| |publisher=National Institute For Standards and Technology (USA)
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| |accessdate=2009-11-25}}</ref>
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| This means that, ignoring air resistance, 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.
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| [[Image:Gravity action-reaction.gif|thumb|If an object with comparable mass to that of the Earth were to fall towards it, then the corresponding acceleration of the Earth really would be observable.]]
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| According to [[Newton's 3rd law|Newton's 3rd Law]], the Earth itself experiences a [[Newtons|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.
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| The force of gravity on Earth is the resultant (vector sum) of two forces: (a) The gravitational attraction in accordance with Newton's universal law of gravitation, and (b) the centrifugal force, 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 becomes stronger as you increase in latitude toward the poles. The standard value of 9.80665 m/s<sup>2</sup> 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.<ref name=List> List, R. J. editor, 1968, Acceleration of Gravity, ''Smithsonian Meteorological Tables'', Sixth Ed. Smithsonian Institution, Washington, D.C., p. 68. </ref> 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".<ref name=USSA1976>[http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770009539_1977009539.pdf U.S. Standard Atmosphere], 1976, U.S. Government Printing Office, Washington, D.C., 1976. (Linked file is very large.)</ref>
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| ===Equations for a falling body near the surface of the Earth===
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| [[Image:Falling ball.jpg|thumb|100px|Ball falling freely under gravity. See text for description.]]
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| {{main|Equations for a falling body}}
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| Under an assumption of constant gravity, [[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<sup>2</sup>. 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 {{frac|20}} of a second the ball drops one unit of distance (here, a unit is about 12 mm); by {{frac|2|20}} it has dropped at total of 4 units; by {{frac|3|20}}, 9 units and so on.
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| Under the same constant gravity assumptions, the [[potential energy]], ''E<sub>p</sub>'', of a body at height ''h'' is given by ''E<sub>p</sub>'' = ''mgh'' (or ''E<sub>p</sub>'' = ''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.
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| ===Gravity and astronomy===
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| The discovery and application of Newton's law of gravity accounts for the detailed information we have about the planets in our solar system, the mass of the Sun, the distance to stars, [[quasar]]s and even the theory of [[dark matter]]. 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 Center]]s, [[galaxy|galaxies]] orbit a center of mass in clusters, and clusters orbit in [[supercluster]]s. 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.
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| ===Gravitational radiation===
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| {{main|Gravitational wave}}
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| In general relativity, gravitational radiation is generated in situations where the curvature of [[spacetime]] is oscillating, such as is the case with co-orbiting 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, but as the science behind LIGO is refined and as the instruments themselves are endowed with greater sensitivity over the next decade, this may change.
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| ===Speed of gravity===
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| {{main|Speed of gravity}}
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| In December 2012, a research team in China announced that it had produced measurements of the phase lag of [[Earth tide]]s during full and new moons which seem to prove that the speed of gravity is equal to the speed of light.<ref>[http://www.astrowatch.net/2012/12/chinese-scientists-find-evidence-for.html Chinese scientists find evidence for speed of gravity], astrowatch.com, 12/28/12.</ref> The team's findings were released in the [[Chinese Science Bulletin]] in February 2013.<ref>{{cite journal|last=TANG|first=Ke Yun|coauthors=HUA ChangCai, WEN Wu, CHI ShunLiang, YOU QingYu, YU Dan|title=Observational evidences for the speed of the gravity based on the Earth tide|journal=Chinese Science Bulletin|date=February 2013|volume=58|issue=4-5|pages=474–477|doi=10.1007/s11434-012-5603-3|url=http://link.springer.com/content/pdf/10.1007%2Fs11434-012-5603-3.pdf|accessdate=12 June 2013}}</ref>
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| ==Anomalies and discrepancies==
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| There 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.
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| [[Image:GalacticRotation2.svg|frame|right|Rotation curve of a typical spiral galaxy: predicted ('''A''') and observed ('''B'''). The discrepancy between the curves is attributed to [[dark matter]].]]
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| * '''Extra fast stars''': Stars in galaxies follow a [[Galaxy rotation curve|distribution of velocities]] where stars on the outskirts are moving faster than they should according to the observed distributions of normal matter. Galaxies within [[Galaxy groups and clusters|galaxy clusters]] show a similar pattern. [[Dark matter]], which would interact gravitationally but not electromagnetically, would account for the discrepancy. Various [[Modified Newtonian dynamics|modifications to Newtonian dynamics]] have also been proposed.
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| * '''[[Flyby anomaly]]''': Various spacecraft have experienced greater acceleration than expected during [[gravity assist]] maneuvers.
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| * '''Accelerating expansion''': The [[metric expansion of space]] seems to be speeding up. [[Dark energy]] has been proposed to explain this. A recent alternative explanation is that the geometry of space is not homogeneous (due to clusters of galaxies) and that when the data are reinterpreted to take this into account, the expansion is not speeding up after all,<ref>[http://space.newscientist.com/channel/astronomy/cosmology/mg19726461.600-dark-energy-may-just-be-a-cosmic-illusion.html Dark energy may just be a cosmic illusion], ''New Scientist'', issue 2646, 7th March 2008.</ref> however this conclusion is disputed.<ref>[http://space.newscientist.com/article/mg20026783.800-swisscheese-model-of-the-cosmos-is-full-of-holes.html Swiss-cheese model of the cosmos is full of holes], ''New Scientist'', issue 2678, 18th October 2008.</ref>
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| * '''Anomalous increase of the [[astronomical unit]]''': Recent measurements indicate that [[Astronomical unit#Developments|planetary orbits are widening]] faster than if this were solely through the sun losing mass by radiating energy.
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| * '''Extra energetic photons''': Photons travelling through galaxy clusters should gain energy and then lose it again on the way out. The accelerating expansion of the universe should stop the photons returning all the energy, but even taking this into account photons from the [[cosmic microwave background radiation]] gain twice as much energy as expected. This may indicate that gravity falls off ''faster'' than inverse-squared at certain distance scales.<ref name=newsci2699>{{cite web|last=Chown|first=Marcus|title=Gravity may venture where matter fears to tread|url=http://www.newscientist.com/article/mg20126990.400-gravity-may-venture-where-matter-fears-to-tread.html|work=New Scientist|accessdate=4 August 2013|date=16 March 2009|issue=2699}}</ref>
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| * '''Extra massive hydrogen clouds''': The spectral lines of the [[Lyman-alpha forest]] suggest that hydrogen clouds are more clumped together at certain scales than expected and, like [[dark flow]], may indicate that gravity falls off ''slower'' than inverse-squared at certain distance scales.<ref name=newsci2699/>
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| ==Alternative theories==
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| {{main|Alternatives to general relativity}}
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| ===Historical alternative theories===
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| * [[Aristotelian theory of gravity]]
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| * [[Le Sage's theory of gravitation]] (1784) also called LeSage gravity, proposed by [[Georges-Louis Le Sage]], based on a fluid-based explanation where a light gas fills the entire universe.
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| * [[Ritz's Equation|Ritz's theory of gravitation]], ''Ann. Chem. Phys.'' 13, 145, (1908) pp. 267–271, Weber-Gauss electrodynamics applied to gravitation. Classical advancement of perihelia.
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| * [[Nordström's theory of gravitation]] (1912, 1913), an early competitor of general relativity.
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| * [[Whitehead's theory of gravitation]] (1922), another early competitor of general relativity.
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| ===Recent alternative theories===
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| * [[Brans–Dicke theory]] of gravity (1961)
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| * [[Induced gravity]] (1967), a proposal by [[Andrei Sakharov]] according to which [[general relativity]] might arise from [[quantum field theory|quantum field theories]] of matter
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| * In the [[modified Newtonian dynamics]] (MOND) (1981), [[Mordehai Milgrom]] proposes a modification of [[Newton's Second Law]] of motion for small accelerations
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| * The [[self-creation cosmology]] theory of gravity (1982) by G.A. Barber in which the Brans-Dicke theory is modified to allow mass creation
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| * [[Nonsymmetric gravitational theory]] (NGT) (1994) by [[John Moffat (physicist)|John Moffat]]
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| * [[Tensor–vector–scalar gravity]] (TeVeS) (2004), a relativistic modification of MOND by [[Jacob Bekenstein]]
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| * [[Gravity as an entropic force]], gravity arising as an emergent phenomenon from the thermodynamic concept of entropy.
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| * In the [[superfluid vacuum theory]] the gravity and curved space-time arise as a [[collective excitation]] mode of non-relativistic background [[superfluid]].
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| ==See also==
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| {{portal|Gravitation}}
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| {{cmn|3|
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| * [[Angular momentum]]
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| * [[Anti-gravity]], the idea of neutralizing or repelling gravity
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| * [[Artificial gravity]]
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| * [[Birkeland current]]
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| * [[Einstein–Infeld–Hoffmann equations]]
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| * [[Escape velocity]], the minimum velocity needed to escape from a [[gravity well]]
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| * [[g-force]], a measure of [[acceleration]]
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| * [[Gauge gravitation theory]]
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| * [[Gauss's law for gravity]]
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| * [[Gravitational binding energy]]
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| * [[Gravity assist]]
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| * [[Gravity gradiometry]]
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| * [[Gravity Recovery and Climate Experiment]]
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| * [[Gravity Research Foundation]]
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| * [[Jovian-Plutonian gravitational effect]]
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| * [[Kepler's third law|Kepler's third law of planetary motion]]
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| * [[Lagrangian point]]
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| * [[Mixmaster dynamics]]
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| * [[n-body problem|''n''-body problem]]
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| * [[Newton's laws of motion]]
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| * [[Pioneer anomaly]]
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| * [[Scalar theories of gravitation]]
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| * [[Speed of gravity]]
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| * [[Standard gravitational parameter]]
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| * [[Standard gravity]]
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| * [[Weightlessness]]
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| }}
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| ==Footnotes==
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| {{reflist|colwidth=30em}}
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| ==References==
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| {{refbegin}}
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| *{{cite book | last = Halliday | first = David | coauthors = Robert Resnick; Kenneth S. Krane | title = Physics v. 1 | location = New York | publisher = John Wiley & Sons | year = 2001 | isbn = 0-471-32057-9 }}
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| *{{cite book | last = Serway | first = Raymond A. | coauthors = Jewett, John W. | title = Physics for Scientists and Engineers | edition = 6th | publisher = Brooks/Cole | year = 2004 | isbn = 0-534-40842-7 }}
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| *{{cite book | last = Tipler | first = Paul | title = Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics | edition = 5th | publisher = W. H. Freeman | year = 2004 | isbn = 0-7167-0809-4 }}
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| {{refend}}
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| <!--Unused ref: Proposition 75, Theorem 35: p. 956 - I.Bernard Cohen and Anne Whitman, translators: Isaac Newton, ''The Principia'': Mathematical Principles of Natural Philosophy. Preceded by ''A Guide to Newton's Principia'', by I. Bernard Cohen. University of California Press 1999 ISBN 0-520-08816-6 ISBN 0-520-08817-4 -->
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| ==Further reading==
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| * {{cite book |author=[[Kip Thorne|Thorne, Kip S.]]; Misner, Charles W.; Wheeler, John Archibald |title=Gravitation |publisher=W.H. Freeman |year=1973 |isbn=0-7167-0344-0}}
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| ==External links==
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| {{wiktionary}}
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| {{Commons category|Gravitation}}
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| * {{springer|title=Gravitation|id=p/g045040}}
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| * {{springer|title=Gravitation, theory of|id=p/g045050}}
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| {{Fundamental interactions}}
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| {{Theories of gravitation}}
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| [[Category:Gravitation| ]]
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| [[Category:Empirical laws]]
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| [[Category:Concepts in physics]]
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| [[Category:Acceleration]]
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