History of gravitational theory
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</div>In physics, theories of gravitation postulate mechanisms of interaction governing the movements of bodies with mass. There have been numerous theories of gravitation since the time of the Greek philosopher Aristotle in the 4th century BC. He believed that there is no effect without a cause, and therefore no motion without a force. He concluded that all things tried to move toward their proper place in the crystalline spheres of the heavens, and that bodies fell toward the center of the Earth in proportion to their weight.
Indian astronomer Brahmagupta, in his Brahmasphuta Siddhanta (628), was the first to recognize 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. In response to critics refuting Aryabhata's heliocentric system "by saying that, if such were the case, stones would and trees would fall from the earth", Brahmagupta stated "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."<ref>Brahmagupta (628). Brahmasphuta Siddhanta ("The Opening of the Universe").</ref><ref>Al-Biruni (1030). Ta'rikh al-Hind ("Chronicles of India").</ref> The Sanskrit term he used for gravity, gruhtvaakarshan, phonetically similar to the English 'gravity', had roughly the same meaning as "attraction".
During the 16th century, Galileo found that, counter to Aristotle's teachings, all objects accelerated equally when falling. In the late 17th century, as a result of a suggestion by Robert Hooke 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.
- "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:
- <math>{\rm Force\,of\,gravity} \propto \frac{\rm mass\,of\,object\,1\,\times\,mass\,of\,object\,2}{\rm distance\,from\,centers^2}</math>
where the symbol <math>\propto</math> 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 discovered 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 his theory of general relativity, which ascribed all gravitational effects to spacetime curvature, so that bodies forcelessly follow curved paths which are natural geodesics. There has been observational confirmation of Einstein's predictions, including the bending of light from distant stars as it passes near the Sun, the perihelion precession of Mercury's orbit, and the discovery of black holes.
The first mathematical formulation of gravity was Isaac Newton's law of universal gravitation, published in his 1687 work Principia Mathematica. Professor William Whewell of Cambridge University, author of History of the Inductive Sciences (1837) stated:
- "The law of gravitation is indisputably and incomparably the greatest scientific discovery ever made, whether we look at the advance which it involved, the extent of the truth disclosed, or the fundamental and satisfactory nature of this truth." [In A Treasury of Science ed. Harlow Shapley et al, Harper & Bros. NY: 1946]
The law of universal gravitation was first clearly and rigorously formulated by Isaac Newton, the phenomenon was observed and recorded by others. Even Ptolemy (c. 100-178) had a vague conception of a force tending toward the center of the Earth which not only kept bodies upon its surface, but in some way upheld the order of the universe. Indian astronomer Brahmagupta (598-668), who followed a heliocentric solar system, was the first to recognize gravity as a force of attraction. He explained that "bodies fall towards the Earth as it is in the nature of the Earth to attract bodies, just as it is in the nature of water to flow". The Sanskrit term he used for gravity, 'gruhtvaakarshan' [similar sounding to the English 'gravity' when pronounced correctly] had roughly the same meaning as "attraction". Johannes Kepler (1571–1630) inferred that the planets move in their orbits under some influence or force exerted by the Sun; but the laws of motion were not then sufficiently developed, nor were Kepler's ideas of force sufficiently clear, to make a precise statement of the nature of the force. Christiaan Huygens and Robert Hooke, contemporaries of Newton, saw that Kepler's third law implied a force which varied inversely as the square of the distance. Newton's conceptual advance was to understand that the same force that causes a thrown rock to fall back to the Earth keeps the planets in orbit around the Sun, and the Moon in orbit around the Earth.
Newton was not alone in making significant contributions to the understanding of gravity. Before Newton, Galileo Galilei corrected a common misconception, started by Aristotle, that objects with different mass fall at different rates. To Aristotle, it simply made sense that objects of different mass would fall at different rates, and the ancient Greeks relied more on philosophic thought experiments than experimentation. Galileo, however, used experiments that actually observed falling objects of different mass released simultaneously. Most of Galileo's work was done with objects on inclined planes. Aside from differences due to friction, Galileo observed that all masses accelerate at the same rate. Newton's equation, <math>F = m a</math>, (see Acceleration due to gravity) showed insight into gravity's proportionality to mass that was missing from Galileo's law of inertia. However, both the work of Johannes Kepler and Galileo influenced Isaac Newton's formulation of the law of gravity.
Newton's law remained the standard theory of gravity until it was replaced by Einstein's theory of gravitation (general relativity) in the early part of the 20th century. Motivated by the equivalence principle, this more accurate theory postulates that mass and energy curve space-time, resulting in the phenomenon known as gravity. However, because general relativity's influence on gravity calculations is minimal or even imperceptible at speeds much less than the speed of light, Newtonian gravity is sufficiently accurate for calculations involving weak gravitational fields (e.g., launching rockets, projectiles, pendulums, etc.), and Newton's formulae are generally still preferred where they are applicable.
A number of alternative theories of gravitation have been proposed over the years, but none has gained general acceptance. For example, Nordström's theory of gravitation was only disproven by Eddington's 1919 observation on Principe island. Current theoretical work largely focuses on the relationship between gravity and quantum mechanics.
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