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Gravity

For other uses, see Gravitation (disambiguation), Gravity (disambiguation).

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In physics, gravitation or gravity is the universal force of attraction between objects with mass. Gravitation may also be defined as the tendency of objects with mass to accelerate toward each other. The gravitational force is one of the four fundamental forces in nature, the other three being the electromagnetic force, the weak nuclear force, and the strong nuclear force. The gravitational force is the weakest of the four forces, but acts over great distances. The particle that is postulated as the carrier of the gravitational force is the graviton.

The gravitational attraction of the earth endows objects with weight and causes them to fall to the ground when dropped. Moreover, gravity is the reason for the very existence of the earth, the sun and other celestial bodies; without it matter would not have coalesced into these bodies and life as we know it would not exist. Gravity is also responsible for keeping the earth and the other planets in their orbits around the sun, the moon in its orbit around the earth, for the tides, and for various other natural phenomena that we observe.

The force of gravitation keeps the planets in orbit about the sun

Contents 1 History of gravitational theory 2 Newton's law of universal gravitation 3 Einstein's theory of gravitation 4 Earth's gravity 5 Equations for a falling body 6 Gravity and astronomy 7 Gravity vs. Gravitation 8 Gravity and the fundamental forces 8.1 Electromagnetic force 8.2 Quantum mechanics 9 Applications 10 Alternative theories 11 See also 12 Notes 13 References 14 External links

History of gravitational theory

Main article: History of gravitational theory

There have been numerous theories of gravitation starting with the ideas 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. In 626, the Indian astronomer Brahmagupta, following 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', phonetically similar to the English 'gravity', had roughly the same meaning as "attraction".

Building on these foundations, in 1687 English mathematician Isaac Newton published the famous Principia, which postulated the first-ever law of gravitation. In is 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 force of gravity at the surface of the Earth; and found them pretty nearly. Most modern-day, non-relativistic, gravitational calculations are based on Newton's work.

Newton's law of universal gravitation

Main article: Newton's law of universal gravitation

In 1687 Newton published his work on the universal law of gravity in his Mathematical Principles of Natural Philosophy. Newtons law of gravitation states that: every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. If the particles have masses m₁ and m₂ and are separated by a distance r, the magnitude of this gravitational force is:

where G is a universal constant called the gravitational constant.

Einstein's theory of gravitation

Main article: Einstein's theory of gravitation

Newtons conception and quantification of gravitation held until the beginning of the 20th century, when the notion of instantaneous action at a distance, which it entailed, was recognized as unintelligible, particularly from the viewpoint of relativity. In his general theory of relativity, American (German-born) physicist Albert Einstein developed a wholly new concept of gravitation. Einstein proposed that the four-dimensional space-time continuum is curved by the presence of matter, producing a universe in which bodies travel in geodesics (shortest paths) that are the curved orbits interpreted by Newton as the result of some attractive force.

Earth's gravity

Main article: Gravity (earth)

Every planetary body, including the earth, has its own unique characteristic force of gravity, typically measured at surface level. The acceleration due to gravity at the Earth's surface, denoted g, is approximately 9.8 m/s² (metres per second squared) or 32 ft/sec². This means that, ignoring air resistance, an object falling freely near the earth's surface increases in speed by 9.8 m/s (around 22 mph) for each second of its descent. Thus, an object starting from rest will attain a speed of 9.8 m/s after one second, 19.6 m/s after two seconds, and so on. The earth itself experiences an equal and opposite force to that of the falling object, meaning that the earth also accelerates towards the object. However, because of the immense mass of the earth this acceleration is vanishingly small.

Equations for a falling body

Main article: Equations for a falling body

Under normal earth-bound conditions, when objects move owing to a constant gravitational force a set of dynamical equations describe the resultant trajectories. For example, Newtons law of gravitation simplifies to F = mg, where m is the mass of the body. This assumption is reasonable for objects falling to earth over the relatively short vertical distances of our everyday experience, but is very much untrue over larger distances, such as spacecraft trajectories.

Gravity and astronomy

Main article: Gravity (astronomy)

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 and even the theory of dark matter. Although we haven't traveled to all the planets nor to the sun, we know their mass. This is through the study of the law of gravity. In space everything is in an orbit around some massive object. They maintain orbit because of the force of gravity between them. Planets orbit stars, stars orbit galactic centers, galaxys orbit a center of mass in clusters, and clusters orbit in superclusters.

Gravity vs. Gravitation

It is important to note, in some contexts, that gravitation is not gravity, per se. Gravitation describes a phenomenon independent of any particular cause. It is possible for gravitation to exist without a force, and according to general relativity, that is indeed the case. In common usage "gravity" and "gravitation" are either used interchangeably, or the distinction is sometimes made that "gravity" is specifically the attractive force of the earth, while "gravitation" is the general property of mutual attraction between bodies of matter. In technical usage, "gravitation" is the tendency of bodies to accelerate towards one another, and "gravity" is the force that some theories use to explain this acceleration.

Gravity was rather poorly understood until Isaac Newton formulated his law of gravitation in the 17th century. Newton's theory is still widely used for many practical purposes, though for more advanced work it has been supplanted by Einstein's general relativity. While a great deal is now known about the properties of gravity, the ultimate cause of the gravitational force remains an open question and gravity remains an important topic of scientific research.

Gravity and the fundamental forces

Electromagnetic force

The gravitational attraction between protons is approximately a factor of 10³⁶ weaker than the electromagnetic repulsion. This factor is independent of distance, because both interactions are inversely proportional to the square of the distance. Therefore on an atomic scale mutual gravity is negligible. Hence, the main interaction between everyday objects and the Earth and between celestial bodies is gravity; at this scale matter is electrically neutral.

Essentially, there is an equal number of positively charged particles in the universe to negatively charged particles. For example, there aren't any positively charged planets that zoom into negatively charged planets. Thus, gravity dominates the universe even though it is the weaker force. However, to show the delicate balance of gravity over the electromagnetic force, given two bodies if even there were a surplus or deficit of only one electron for every 10¹⁸ protons and neutrons this would already be enough to cancel gravity or in the case of a surplus in one and a deficit in the other, double the force of attraction.

Though the force of gravity dominates the visible macro universe, the main interactions such as fusion between the charged particles in cosmic plasma, of which the sun is composed and which make up over 99% of the universe by volume, are due to the nuclear forces. In terms of Planck units, the charge of a proton is 0.085, while the mass is only 8 × 10²⁰. From that point of view, the gravitational force is not small as such, but because masses are small.

The relative weakness of gravity can be demonstrated with a small magnet picking up pieces of iron. The small magnet is able to overwhelm the gravitational effect of the entire Earth. Even though gravity is relatively weak, the small gravitational interaction exerted by bodies of ordinary size can fairly easily be detected through experiments such as the Cavendish torsion bar experiment.

Quantum mechanics

It is widely believed that three of the four fundamental forces, i.e. the strong nuclear force, the weak nuclear force, and the electromagnetic force, are manifestations of a single, more fundamental force. Combining gravity with these forces of quantum mechanics to create a theory of quantum gravity is currently an important topic of research amongst physicists.

General relativity is an essentially geometric theory that requires no exchange of particles in its explanation of gravity, whereas quantum mechanics relies on interactions between particles. Scientists have theorized about the graviton, a messenger particle that transmits the force of gravity, for years but have been frustrated in their attempts to find a consistent quantum theory to describe it. Many believe that string theory holds a great deal of promise to unify general relativity and quantum mechanics, but this promise has yet to be realized.

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.

Applications

Shot Tower, 1856 Dubuque, Iowa

A vast number of mechanical contrivances depend in some way on gravity for their operation. For example, a height difference can provide a useful pressure in a liquid, as in the case of an intravenous drip or a water tower. The gravitational potential energy of water supplies hydroelectricity can also be used to power a tramcar up an incline, using a system of water tanks and pulleys. An example is the Lynton & Lynmouth Cliff Railway in Devon, England. Also, a weight hanging from a cable over a pulley provides a constant tension in the cable, including the part on the other side of the pulley to the weight.

Examples are numerous, for example molten lead, when poured into the top of a shot tower, will coalesce into a rain of spherical lead shot, first separating into droplets, forming molten spheres, and finally freezing solid, undergoing many of the same effects as meteoritic tektites, which will cool into spherical, or near-spherical shapes in free-fall. Also, a fractionation tower can be used to manufacture some materials by separating out the material components based on their specific gravity. Weight-driven clocks are powered by gravitational potential energy, and pendulum clocks depend on gravity to regulate time. Artificial satellites are an application of gravitation which was mathematically described in Newton's Principia.

Alternative theories

Historical alternative theories

• Aristotelian theory of gravity
• Nikola Tesla challenged Albert Einstein's theory of relativity, announcing he was working on a Dynamic theory of gravity (which began between 1892 and 1894) and argued that a "field of force" was a better concept and focused on media with electromagnetic energy that fill all of space.
• Induced gravity: In 1967 Andrei Sakharov proposed something similar, if not essentially identical. His theory has been adopted and promoted by Messrs. Haisch, Rueda and Puthoff who, among other things, explain that gravitational and inertial mass are identical and that high speed rotation can reduce (relative) mass. Combining these notions with those of Thomas Townsend Brown, it is relatively easy to conceive how field propulsion vehicles such as "flying saucers" could be engineered given a suitable source of power.
• LeSage gravity, proposed by Georges-Louis LeSage, based on a fluid-based explanation where a light gas fills the entire universe.
• Nordström's theory of gravitation, an early competitor of general relativity.
• Whitehead's theory of gravitation, another early competitor of general relativity.

Recent alternative theories

• Brans-Dicke theory of gravity
• Rosen bi-metric theory of gravity
• In the modified Newtonian dynamics (MOND), 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 in which the Brans-Dicke theory is modified to allow mass creation.
• The satirical theory of Intelligent falling

See also

Artificial gravity Escape velocity General relativity Gravitation wave Gravitational binding energy Gravity Research Foundation Gravity and the divergence theorem Gravity field

Kepler's third law Newton's laws of motion n-body problem Pioneer anomaly Scalar Gravity Standard gravitational parameter Weight Weightlessness

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 3: 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

• Halliday, David; Robert Resnick; Kenneth S. Krane (2001). Physics v. 1, New York: John Wiley & Sons. ISBN 0471320579.
• Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers, 6th ed., Brooks/Cole. ISBN 0534408427.
• Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics, 5th ed., W. H. Freeman. ISBN 0716708094.
• Jefimenko, Oleg D., "Causality, electromagnetic induction, and gravitation : a different approach to the theory of electromagnetic and gravitational fields". Star City [West Virginia] : Electret Scientific Co., c1992. ISBN 0917406095
• Heaviside, Oliver, "A gravitational and electromagnetic analogy". The Electrician, 1893.

Categories: Gravity | Introductory physics | Celestial mechanics