History of gravitational theory

History of gravitational theory

In physics, theories of gravitation postulate mechanisms of interaction governing the movements of bodies with mass. There have been numerous theories of gravitation since ancient times.


In the 4th century BC, the Greek philosopher Aristotle believed that there is no effect or motion without a cause. The cause of the downward motion of heavy bodies, such as the element earth, was related to their nature, which caused them to move downward toward the center of the universe, which was their natural place. Conversely, light bodies such as the element fire, move by their nature upward toward the inner surface of the sphere of the Moon. Thus in Aristotle's system heavy bodies are not attracted to the earth by an external force of gravity, but tend toward the center of the universe because of an inner "gravitas" or heaviness. [Edward Grant, "The Foundations of Modern Science in the Middle Ages", (Cambridge: Cambridge Univ. Pr., 1996), pp. 60-1.] [Olaf Pedersen, "Early Physics and Astronomy", (Cambridge: Cambridge Univ. Pr., 1993), p. 130]

Middle Ages

The Indian astronomer Brahmagupta, in his "Brahmasphuta Siddhanta" ("The Opening of the Universe") (628), recognized gravity as a force of attraction. Brahmagupta followed the heliocentric solar system of gravitation, earlier developed by Aryabhata in 499, and understood that there was a force of attraction between the Sun and the Earth. The 11th century Persian astronomer Abu al-Rayhan al-Biruni, in his "Ta'rikh al-Hind", later translated into Latin as "Indica", commented on their works and wrote that critics refuting Aryabhata's heliocentric system argued:

quote|"If such were the case, stones would and trees would fall from the earth."
Al-Biruni (1030), "Ta'rikh al-Hind" ("Indica")

According to Biruni, Brahmagupta responded to these criticisms with the following argument:

quote|"On the contrary, if that were the case, the earth would not vie in keeping an even and uniform pace with the minutes of heaven, the pranas of the times. [...] All heavy things are attracted towards the center of the earth. [...] The earth on all its sides is the same; all people on earth stand upright, and 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."
Brahmagupta, in Al-Biruni (1030), "Ta'rikh al-Hind" ("Indica")

The Sanskrit term Brahmagupta used for gravity, "gruhtvaakarshan", phonetically similar to the English 'gravity', had roughly the same meaning as "attraction".

Al-Biruni himself described the Earth's gravitation as: [http://muslimheritage.com/topics/default.cfm?ArticleID=482 Khwarizm] , Foundation for Science Technology and Civilisation.]

In the 9th century, the eldest Banū Mūsā brother, Muhammad ibn Musa, in his "Astral Motion" and "The Force of Attraction", hypothesized that there was a force of attraction between heavenly bodies, [K. A. Waheed (1978). "Islam and The Origins of Modern Science", p. 27. Islamic Publication Ltd., Lahore.] foreshadowing Newton's law of universal gravitation. [Robert Briffault (1938). "The Making of Humanity", p. 191.]

In the 1000s, Ibn al-Haytham (Alhacen), a contemporary of Biruni, discussed the theory of attraction between masses, and it seems that he was aware of the magnitude of acceleration due to gravity. [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.]

In 1121, Al-Khazini, in "The Book of the Balance of Wisdom", differentiated between force, mass, and weight, [Donald Routledge Hill (1993), "Islamic Science and Engineering", p. 61, Edinburgh University Press. (cf. Salah Zaimeche PhD (2005), [http://www.muslimheritage.com/uploads/Merv.pdf Merv] , p. 5, Foundation for Science Technology and Civilization.)] and claimed that gravity varies with the distance from the centre of the Earth,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.] though he believed that the weight of heavy bodies increased as they moved farther from the centre of the Earth.

quote|"The weight of any heavy body, of known weight at a particular distance from the centre of the world, varies according to the variation of its distance therefrom; so that, as often as it is removed from the centre, it becomes heavier, and when brought nearer to it, is lighter. On this account, the relation of gravity to gravity is as the relation of distance to distance from the centre." [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.] [Alternative translation:
M. Rozhanskaya and I. S. Levinova, "Statics", in R. Rashed (1996), "Encyclopaedia of Arabic Science", Vol. 2, p. 622. (cf. Salah Zaimeche PhD (2005). [http://www.muslimheritage.com/uploads/Merv.pdf Merv] , p. 7. Foundation for Science Technology and Civilization.)quote|"For each heavy body of a known weight positioned at a certain distance from the centre of the universe, its gravity depends on the remoteness from the centre of the universe. For that reason, the gravities of bodies relate as their distances from the centre of the universe."
These early attempts at explaining gravity were largely philisophical concepts and were neither given proper scientific treatment nor regularly verified by experimentation. It would not be until Isaac Newton that the force of gravity was given proper scientific treatment and an accurate mathemartical expression upon which a correct description of gravity can be deduced.

Modern Era

Before 1543 in De revolutionibus orbium coelestium Copernicus wrote :"...inter centrum gravitatis terrae, & centrum magnitudis..."

During the 17th century, Galileo found that, counter to Aristotle's teachings, all objects accelerated equally when falling.

In the 1660s, influenced by the ideas of Alkindus, Robert Hooke explained his law of celestial gravity:Asghar Qadir (1989). "Relativity: An Introduction to the Special Theory", p. 6-11. World Scientific, Singapore.]

In the late 17th century, as a result of Robert Hooke's suggestion that there is a gravitational force which depends on the inverse square of the distance, Isaac Newton was able to mathematically derive Kepler's three kinematic laws of planetary motion, including the elliptical orbits for the seven known planets:

quote|"I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centres 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 to answer pretty nearly."
Isaac Newton, 1666

So Newton's original formula was:

:{ m Force,of,gravity} propto frac{ m mass,of,object,1, imes,mass,of,object,2}{ m distance,from,centers^2}

where the symbol propto means "is proportional to".

To make this into an equal-sided formula or equation, there needed to be a multiplying factor or constant that would give the correct force of gravity no matter the value of the masses or distance between them. This gravitational constant was first measured in 1797 by Henry Cavendish.

In 1907 Albert Einstein, in what was described by him as "the happiest thought of my life", realized that an observer who is falling from the roof of a house experiences no gravitational field. In other words, gravitation was exactly equivalent to acceleration. Between 1911 and 1915 this idea, initially stated as the Equivalence principle, was formally developed into Einstein's theory of general relativity.

Newton's theory of gravitation

In 1687, English mathematician Sir Isaac Newton published "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.”

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 by the actions of the other planets. Calculations by John Couch Adams and Urbain Le Verrier both predicted the general position of the planet, and Le Verrier's calculations are what led Johann Gottfried Galle to the discovery of Neptune.

Ironically, it was another discrepancy in a planet's orbit that helped to doom Newton's theory. By the end of the 19th century, it was known that the orbit of Mercury could not be accounted for entirely under Newton's theory, and all searches for another perturbing body (such as a planet orbiting the Sun even closer than Mercury) have been fruitless. This issue was resolved in 1915 by Albert Einstein's new general relativity theory. This theory accounted for the discrepancy in Mercury's orbit.

Although Newton's theory has been superseded, most modern non-relativistic gravitational calculations are based on Newton's work because it is a much easier theory to work with and sufficient for most applications.

Mechanical explanations of gravitation

The mechanical theories or explanations of the gravitation are attempts to explain the law of gravity by aid of basic mechanical processes, such as pushes, and without the use of any action at a distance. These theories were developed from the 16th until the 19th century in connection with the aether theories. [Citation | author=Taylor, W. B. | title =Kinetic Theories of Gravitation | journal = Smithsonian repplace | year =1876 | pages =205-282]

René Descartes (1644) and Christiaan Huygens (1690) used vortices to explain gravitation.
Robert Hooke (1671) and James Challis (1869) assumed, that every body emits waves which lead to an attraction of other bodies.
Nicolas Fatio de Duillier (1690) and Georges-Louis Le Sage (1748) proposed a corpuscular model, using some sort of screening or shadowing mechanism. Later a similar model was created by Hendrik Lorentz, who used electromagnetic radiation instead of the corpuscles.
Isaac Newton (1675) and Bernhard Riemann (1853) argued that aether streams carry all bodies to each other.Newton (1717) and Leonhard Euler (1760) proposed a model, in which the aether loses density near the masses, leading to a net force directing to the bodies.
Lord Kelvin (1871) proposed that every body pulsates, which might be an explanations of gravitation and the electric charges.

However, those models were overthrown because most of them lead to an unacceptable amount of drag, which is not observed. Other models are violating the energy conservation law and are incompatible with modern thermodynamics. [Citation | author=Zenneck, J. | author-link =Jonathan Zenneck| title = [http://dz-srv1.sub.uni-goettingen.de/sub/digbib/loader?did=D189514 Gravitation] | journal =Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen | volume =5 | Issue =1 | pages =25-67 | year =1903 | place=Leipzig]

General relativity

In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of to a force. The starting point for general relativity is the equivalence principle, which equates free fall with inertial motion. The issue that this creates is that free-falling objects can accelerate with respect to each other. In Newtonian physics, no such acceleration can occur unless at least one of the objects is being operated on by a force (and therefore is not moving inertially).

To deal with this difficulty, Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. (This type of path is called a geodesic). More specifically, Einstein and Hilbert 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, non-linear, 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 Schwarzschild solution, which describes spacetime surrounding a spherically symmetric non-rotating uncharged massive object. For compact enough objects, this solution generated a black 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.
* 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 cosmological Robertson-Walker solution, which predicts the expansion of the universe.

General relativity has enjoyed much success because of how its predictions of phenomena which are not called for by the theory of gravity have been regularly confirmed. For example:
* General relativity accounts for the anomalous perihelion precession 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.

Gravity and quantum mechanics

Several decades after the discovery of general relativity it was realized that it cannot be the complete theory of gravity because it is incompatible with quantum mechanics. [cite book | author=Randall, Lisa | title=Warped Passages: Unraveling the Universe's Hidden Dimensions | publisher=Ecco | year=2005 | id=ISBN] 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. [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=0201627345 ] [cite book | author=Zee, A. |title=Quantum Field Theory in a Nutshell | publisher = Princeton University Press | year=2003 | id=ISBN] This reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length, [cite book | author=Randall, Lisa | title=Warped Passages: Unraveling the Universe's Hidden Dimensions | publisher=Ecco | year=2005 | id=ISBN] where a more complete theory of quantum gravity is required. Many believe the complete theory to be string theory. [cite book | author=Greene, Brian | title=The elegant universe: superstrings, hidden dimensions, and the quest for the ultimate theory | publisher=Vintage Books |location = New York| year=2000 | id=ISBN]

It is notable that in general relativity, gravitational radiation, which under the rules of quantum mechanics must be composed of gravitons, is created only in situations where the curvature of spacetime is oscillating, such as is the case with co-orbiting objects. The amount of 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 1913+16. It is believed that neutron star mergers and black hole formation may create detectable amounts of gravitational radiation. Gravitational radiation observatories such as 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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