Gravitation

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Gravitation is a phenomenon through which all objects attract each other. Modern physics describes gravitation using the general theory of relativity, but the much simpler Newton's law of universal gravitation provides an excellent approximation in many cases. Gravitation is the reason for the very existence of the Earth, the Sun, and most macroscopic objects in the universe; without it, matter would not have coalesced into large masses (stars and planets) and life, as we know it, would not exist. Gravitation 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 heating interiors of forming stars and planets to very high temperatures, for the formation of tides, for rising hot air or water (convection), and for various other natural phenomena that we observe.

The gravitational force keeps the planets in orbit about the Sun.
The gravitational force keeps the planets in orbit about the Sun.

Contents

[edit] History of gravitational theory

Main article: History of gravitational theory

[edit] Early history

Since the time of the Greek philosopher Aristotle in the 4th century BCE, there have been many attempts to understand and explain gravity. Aristotle believed that there was no effect without a cause, and therefore no motion without a force. He hypothesized that everything tried to move towards its proper place in the crystalline spheres of the heavens, and that physical bodies fell toward the center of the Earth in proportion to their weight.

Moreover,Brahmasphuta Siddhanta (628 CE), responded to critics of the heliocentric system of Aryabhata (perhaps 476-550 CE) 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."[1][2]

Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th century and early 17th century. In his famous experiment dropping balls at the Tower of Pisa and later with careful measurements of balls rolling down inclines, Galileo showed that gravitation accelerates all objects at the same rate. This was a major departure from Aristotle's belief that heavier objects are accelerated faster. (Galileo correctly postulated air resistance as the reason that lighter objects fall more slowly.) Galileo's work set the stage for the formulation of Newton's theory of gravity.

[edit] Newton's theory of gravitation

Main article: Law of universal 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.

[edit] General relativity

Main article: Introduction to 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 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:

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:

[edit] Gravity and quantum mechanics

Main articles: Graviton and Quantum gravity

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.[3] 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.[4][5] This reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length,[6] where a more complete theory of quantum gravity is required. Many believe the complete theory to be string theory.[7]

[edit] Specifics

[edit] Earth's gravity

Main article: Earth's gravity

Every planetary body, including the Earth, is surrounded by its own gravitational field, which exerts an attractive force on any object. This field is proportional to the body's mass and varies inversely with the square of distance from the body. 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 approximately 9.8 m/s². This means that, ignoring air resistance, an object falling freely near the earth's surface increases in speed by 9.807 m/s (32.174 ft/s or 22 mi/h) for each second of its descent. Thus, an object starting from rest will attain a speed of 9.807 m/s (32.17 ft/s) after one second, 19.614 m/s (64.34 ft/s) after two seconds, and so on. 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 measurable acceleration of the Earth by this same force is negligible, when measured relative to the system's center of mass.

[edit] 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 kinematical and dynamical equations describe the resultant trajectories. For example, Newton’s 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 does not necessarily hold over larger distances, such as spacecraft trajectories, because the acceleration far from the surface of the Earth will not in general be g. A further example is the expression that we use for the calculation of potential energy P.E. of a body at height h ( P.E. = mgh). This expression can be used only over small distances h from the Earth. Similarly the expression for the maximum height reached by a vertically projected body, h = u2 / 2g 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.

[edit] 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, quasars and even the theory of dark matter. Although we have not traveled to all the planets nor to the Sun, we know their mass. The mass is 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 centers, galaxies orbit a center of mass in clusters, and clusters orbit in superclusters.

[edit] Gravity versus gravitation

In scientific terminology gravitation and gravity are distinct. Gravitation is the attractive influence that all objects exert on each other, while "gravity" specifically refers to a force which all massive objects are theorized to exert on each other to cause gravitation. Although these terms are used interchangeably in everyday use, in theories other than Newton's, gravitation is caused by factors other than gravity. For example in general relativity, gravitation is due to spacetime curvatures which causes inertially moving objects to tend to accelerate towards each other. Another (but discredited) example is Le Sage's theory of gravitation, in which massive objects are effectively pushed towards each other.

[edit] Alternative theories

Main article: Alternatives to general relativity

[edit] Historical alternative theories

[edit] Recent alternative theories

[edit] See also

Portal:Gravitation
 Gravitation Portal

[edit] 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.)

[edit] References

  1. ^ Brahmagupta (628 CE). Brahmasphuta Siddhanta ("The Opening of the Universe").
  2. ^ Al-Biruni (1030 CE). Ta'rikh al-Hind ("Chronicles of India").
  3. ^ Randall, Lisa (2005). Warped Passages: Unraveling the Universe's Hidden Dimensions. Ecco. ISBN 0-06-053108-8. 
  4. ^ Feynman, R. P.; Morinigo, F. B., Wagner, W. G., & Hatfield, B. (1995). Feynman lectures on gravitation. Addison-Wesley. ISBN 0201627345. 
  5. ^ Zee, A. (2003). Quantum Field Theory in a Nutshell. Princeton University Press. ISBN 0-691-01019-6. 
  6. ^ Randall, Lisa (2005). Warped Passages: Unraveling the Universe's Hidden Dimensions. Ecco. ISBN 0-06-053108-8. 
  7. ^ 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. 

[edit] External links

v • d • e
The Four Fundamental Interactions of Physics

Strong interaction · Electromagnetism · Weak interaction · Gravitation

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