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*i.e.,*an object with mass). The terms are mostly interchangeable in everyday use. In general relativity, gravitation is due to spacetime curvatures which causes inertially moving objects to tend to accelerate towards each other. Another (discredited) example is Le Sage's theory of gravitation, in which massive objects are effectively pushed towards each other.

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History of gravitational theory

### Early history

^{[1]}According to Kanada, founder of the Vaisheshika school, "Weight causes falling; it is imperceptible and known by inference."

^{[2]}

*Brahmasphuta Siddhanta*(628 AD), responded to critics of the heliocentric system of Aryabhata (476–550 AD) stating that "all heavy things are attracted towards the center of the earth" and that "all heavy things fall down to the earth by a law of nature, for it is the nature of the earth to attract and to keep things, as it is the nature of water to flow, that of fire to burn, and that of wind to set in motion... The earth is the only low thing, and seeds always return to it, in whatever direction you may throw them away, and never rise upwards from the earth."

^{[3]}

^{[4]}

*Astral Motion*and

*The Force of Attraction*, discovered that there was a force of attraction between heavenly bodies,

^{[5]}foreshadowing Newton's law of universal gravitation.

^{[6]}In the 1000s, the Iraqi scientist Ibn al-Haytham (Alhacen), in the

*Mizan al-Hikmah*, discussed the theory of attraction between masses, and it seems that he was aware of the magnitude of acceleration due to gravity.

^{[7]}In 1121, Al-Khazini, in

*The Book of the Balance of Wisdom*, differentiated between force, mass, and weight,

^{[8]}and discovered that gravity varies with the distance from the centre of the Earth,

^{[9]}though he believed that the weight of heavy bodies increase as they are farther from the centre of the Earth.

^{[10]}

###

Newton's theory of gravitation

*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.”

General relativity

The Schwarzschild solution, which describes spacetime surrounding a spherically symmetric non-rotatingblack hole with a central 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. uncharged massive object. For compact enough objects, this solution generated a

The 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 horizons.

The Kerr solution for rotating massive objects. This solution also produces black holes with multiple event horizons.

The Kerr-Newman solution for charged, rotating massive objects. This solution also produces black holes with multiple event horizons.

The cosmological Robertson-Walker solution, which predicts the expansion of the universe.

General relativity accounts for the anomalous perihelionprecession of the planet Mercury.

The prediction that time runs slower at lower potentials has been confirmed by the Pound-Rebka experiment, the Hafele-Keating experiment, and the GPS.

The prediction of the deflection of light was first confirmed by Arthur Eddington in 1919, and has more recently been strongly confirmed through the use of a quasar which passes behind the Sun as seen from the Earth. See also gravitational lensing.

The time delay of light passing close to a massive object was first identified by Irwin Shapiro in 1964 in interplanetary spacecraft signals.

Gravitational radiation has been indirectly confirmed through studies of binary pulsars.

The expansion of the universe (predicted by the Robertson-Walker metric) was confirmed by Edwin Hubble in 1929.

^{[11]}Later it was understood that it is possible to describe gravity in the framework of quantum field theory like the other fundamental forces. In this framework 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.

^{[12]}

^{[13]}This reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length,

^{[14]}where a more complete theory of quantum gravity is required. Many believe the complete theory to be string theory,

^{[15]}or more currently M Theory.

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Specifics

###

Earth's gravity

*g*, is approximately 9.81 m/s² as the standard average. This means that, ignoring air resistance, an object falling freely near the earth's surface increases its velocity with 9.81 m/s (32 ft/s or 22 mi/h) for each second of its descent. Thus, an object starting from rest will attain a velocity of 9.81 m/s (32 ft/s) after one second, 19.6 m/s (64 ft/s) after two seconds, and so on, adding 9.8 m/s to each resulting velocity. According to Newton's 3rd Law, the Earth itself experiences an equal and opposite force to that acting on the falling object, meaning that the Earth also accelerates towards the object. However, because the mass of the Earth is huge, the acceleration of the Earth by this same force is negligible, when measured relative to the system's center of mass.

###

Equations for a falling body

*F*=

*mg*, where

*m*is the mass

*g*is a constant vector with an average magnitude of 9.81 m/s². 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 1/20th of a second the ball drops one unit of distance (here, a unit is about 12 mm); by 2/20ths it has dropped at total of 4 units; by 3/20ths, 9 units and so on. of the body and

*E*, of a body at height

_{p}*h*is given by

*E*(or

_{p}mgh*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

*h*=

*v*

^{2}/ 2

*g*for the maximum height reached by a vertically projected body with velocity

*v*is useful for small heights and small initial velocities only. In case of large initial velocities we have to use the principle of conservation of energy to find the maximum height reached. This same expression can be solved for

*v*to determine the velocity of an object dropped from a height

*h*immediately before hitting the ground,

, assuming negligible air resistance. =

###

Gravity and astronomy

###

Gravitational radiation

##

Alternative theories

###

Historical alternative theories

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.

Nordström's theory of gravitation (1912, 1913), an early competitor of general relativity.

Whitehead's theory of gravitation (1922), another early competitor of general relativity.

###

Recent alternative theories

Brans-Dicke theory of gravity (1961)

Induced gravity (1967), a proposal by Andrei Sakharovgeneral relativity might arise from quantum field theories of matter. according to which

Rosen bi-metric theory of gravity

In the modified Newtonian dynamics (MOND) (1981), Mordehai Milgrom proposes a modification of Newton's Second Law of motion for small accelerations.

The new and highly controversial Process Physics theory attempts to address gravity

The self-creation cosmology theory of gravity (1982) by G.A. Barber in which the Brans-Dicke theory is modified to allow mass creation.

Nonsymmetric gravitational theory (NGT) (1994) by John Moffat

The satirical theory of Intelligent falling (2002, in its first incarnation as "Intelligent grappling")

Tensor-vector-scalar gravity (TeVeS) (2004), a relativistic modification of MOND by Jacob Bekenstein

##

See also

Anti-gravity, the idea of neutralizing or repelling gravity

Escape velocity, the minimum velocity needed to fly away from a massive space object

g-force, a measure of acceleration

##

Notes

Note 1: 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

Note 2: 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.)

##

References

^ Dick Teresi (2002),*Lost Discoveries: The Ancient Roots of Modern Science - from the Babylonians to the Maya*, Simon & Schuster, New York, ISBN 0-684-83718-8:

"Two hundred years before Pythagoras, philosophers in northern India had understood that gravitation held the solar system together, and that therefore the sun, the most massive object, had to be at its centre."

^ S. Kak (2003). Indian Physics: Outline of Early History, p. 22. arXiv*. Louisiana State University.*

^ Brahmagupta (628 AD).*Brahmasphuta SiddhantaThe Opening of the Universe*"). ("

^ K. A. Waheed (1978).*Islam and The Origins of Modern Science*, p. 27. Islamic Publication Ltd., Lahore.

^ Robert Briffault (1938).*The Making of Humanity*, p. 191.

^ Dr. Nader El-Bizri, "Ibn al-Haytham or Alhazen", in Josef W. Meri (2006),*Medieval Islamic Civilization: An Encyclopaedia*, Vol. II, p. 343-345, Routledge, New York, London.

^ Donald Routledge Hill (1993),*Islamic Science and Engineering*, p. 61, Edinburgh University Press. (cf.Merv, p. 5, Foundation for Science Technology and Civilization.) Salah Zaimeche PhD (2005),

^ Professor Mohammed Abattouy (2002). "The Arabic Science of weights: A Report on an Ongoing Research Project",*The Bulletin of the Royal Institute for Inter-Faith Studies*4, p. 109-130.

^ N. Khanikoff, ed. and trans. (1858-1860), "Analysis and Extracts of ... Book of the Balance of Wisdom, An Arabic Work on the Water-Balance, Written by 'Al-Khâzinî in the Twelfth Century", chap. 5, sect. 3.1,*Journal of the American Oriental Society*6, p. 36.

^ Randall, Lisa (2005).*Warped Passages: Unraveling the Universe's Hidden Dimensions*. Ecco. ISBN 0-06-053108-8.

^ Feynman, R. P.; Morinigo, F. B., Wagner, W. G., & Hatfield, B. (1995).*Feynman lectures on gravitation*. Addison-Wesley. ISBN 0201627345.

^ Zee, A. (2003).*Quantum Field Theory in a Nutshell*. Princeton University Press. ISBN 0-691-01019-6.

^ Randall, Lisa (2005).*Warped Passages: Unraveling the Universe's Hidden Dimensions*. Ecco. ISBN 0-06-053108-8.

^ Greene, Brian (2000).*The elegant universe: superstrings, hidden dimensions, and the quest for the ultimate theory*. New York: Vintage Books. ISBN 0375708111.

Halliday, David; Robert Resnick; Kenneth S. Krane (2001).*Physics v. 1*. New York: John Wiley & Sons. ISBN 0-471-32057-9.

Serway, Raymond A.; Jewett, John W. (2004).*Physics for Scientists and Engineers*, 6th ed., Brooks/Cole. ISBN 0-534-40842-7.

Tipler, Paul (2004).*Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics*, 5th ed., W. H. Freeman. ISBN 0-7167-0809-4.

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External links

Chapter 10. Gravity, from Light and Matter: educational materials for physics and astronomy

Gravity Probe B Experiment The Official Einstein website from Stanford University

Gravity for kids (flash)

Ask a scientist, Physics Archive

How stuff works: How does gravity work?