Gravity

For other uses, see Gravity (disambiguation).

"Gravity" redirects here. For other uses, see Gravity (disambiguation).

Gravitation is a natural phenomenon by which all objects attract each other. In everyday life, gravitation is most familiar as the agency that endows objects with weight. Gravitation is responsible for keeping the Earth and the other planets in their orbits around the Sun; for keeping the Moon in its orbit around the Earth; for the formation of tides; for convection (by which hot fluids rise); for heating the interiors of forming stars and planets to very high temperatures; and for various other phenomena that we observe. Gravitation is also 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 these large masses, and life, as we know it, would not exist.

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 most cases.

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 (objects with mass) are theorized to exert on each other to cause gravitation. Although these terms are interchangeable 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 (discredited) example is Le Sage's theory of gravitation, in which massive objects are effectively pushed towards each other.

Gravitation keeps the planets in orbit about the Sun.

History of gravitational theory

Main article: History of gravitational theory

Early history

Efforts to understand gravity began in ancient times. Philosophers in ancient India made attempts to explain the phenomenon from the 8th century BCE. According to Kanada, founder of the Vaisheshika school, "Weight causes falling; it is imperceptible and known by inference."

In the 4th century BCE, the Greek philosopher 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.

Brahmagupta, in the Brahmasphuta Siddhanta (628 CE), responded to critics of the heliocentric system of Aryabhata (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."

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. In 1121, Al-Khazini, in The Book of the Balance of Wisdom, differentiated between force, mass, and weight, and discovered that gravity varies with the distance from the centre of the Earth, though he believed that the weight of heavy bodies increase as they are farther from the centre of the Earth.

Scientific revolution

Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th century and early 17th century. In his famous (though probably apocryphal) 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 are perceived to fall more slowly.) Galileo's work set the stage for the formulation of Newton's theory of gravity.

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 point out flaws in 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, but all searches for another perturbing body (such as a planet orbiting the Sun even closer than Mercury) had been fruitless. The issue was resolved in 1915 by Albert Einstein's new General Theory of Relativity, which 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 gives fairly accurate results for most applications.

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:

• 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

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

Specifics

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.

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 and g is a constant vector with a magnitude of about 9.8 m/s². The acceleration due to gravity is equal to this g. 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 E_p of a body at height h (namely E_p = mgh or E_p = Wh, with W meaning weight). 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, $h=u^{2}/2g$ 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.

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.

Gravitational radiation

Main article: Gravitational wave

In general relativity, gravitational radiation is created 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.

Alternative theories

Main article: Alternatives to general relativity

Historical alternative theories

• Aristotelian theory of gravity
• 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 Sakharov according to which general relativity might arise from quantum field theories of matter.
• 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

• Artificial gravity
• Escape velocity
• General relativity
• g-force
• Gravitational waves
• Gravitational binding energy
• Gravity Research Foundation
• Gravity and the divergence theorem
• Kepler's third law of planetary motion
• Newton's laws of motion
• n-body problem
• The Pioneer spacecraft anomaly
• Scalar Gravity
• Speed of gravity
• Standard gravitational parameter
• Standard gravity
• Weight
• Weightlessness
• Lagrange Points

Notes

• Template:Fnb 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
• Template:Fnb 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 (2001). Physics v. 1. New York: John Wiley & Sons. ISBN 0-471-32057-9. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
• Serway, Raymond A. (2004). Physics for Scientists and Engineers (6th ed. ed.). Brooks/Cole. ISBN 0-534-40842-7. {{cite book}}: |edition= has extra text (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
• Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed. ed.). W. H. Freeman. ISBN 0-7167-0809-4. {{cite book}}: |edition= has extra text (help)

External links

• Gravity - a chapter from an online textbook
• Template:PDFlink on Project PHYSNET
• Gravity Probe B Experiment The Official Einstein website from Stanford University
• Center for Gravity, Electrical, and Magnetic Studies
• / Gravity for kids
• Alternative theory of gravity explains large structure formation -- without dark matter PhysOrg.com