Gravitation is a natural phenomenon by which all objects with mass attract each other. In everyday life, gravitation is most familiar as the agency that endows objects with
weight. It 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. (Not to scale)
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 BC.[1]
According to Kanada, founder of the Vaisheshika school,
"Weight causes falling; it is imperceptible and known by inference."[2]
In the 4th century BC, 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 AD), responded to critics of the heliocentric system of
Aryabhata (476–550 AD) 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."[3][4]
In the 9th century, the eldest Banū Mūsā brother, Muhammad ibn Musa, in his Astral Motion and The Force of Attraction,
discovered that there was a force of attraction between heavenly bodies,[5] foreshadowing Newton's law of universal
gravitation.[6] 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.[7] In
1121, Al-Khazini, in The Book of the Balance of Wisdom, differentiated between
force, mass, and weight,[8] and discovered that gravity varies with the distance from the
centre of the Earth,[9] though he believed
that the weight of heavy bodies increase as they are farther from the centre of the Earth.[10]
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 from 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 may fall more slowly in an atmosphere.) Galileo's work set the stage for the formulation of
Newton's theory of gravity.
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 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
-
In general relativity, the effects of gravitation are ascribed to
spacetime curvature instead of 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:
Gravity and quantum mechanics
-
Several decades after the discovery of general relativity it was realized that it (general relativity) cannot be the complete
theory of gravity because it is incompatible with quantum mechanics.[11] 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.[12][13]
This reproduces general relativity in the classical limit. However, this approach fails
at short distances of the order of the Planck length,[14] where a more complete theory of quantum
gravity is required. Many believe the complete theory to be string theory.[15]
Specifics
Earth's gravity
-
Every planetary body, including the Earth, is surrounded by its own gravitational field, which exerts an attractive force on
all objects. Assuming a spherically symmetrical planet (a reasonable approximation), the strength of this field at any given
point is proportional to the planetary body's mass and inversely proportional to the square of the distance from the centre of
the body.
The strength of 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 9.8 m/s (32 ft/s or 22 mi/h) for each second of its descent.
Thus, an object starting from rest will attain a speed of 9.8 m/s (32 ft/s) after one second, 19.6 m/s
(64 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 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
Ball falling freely under gravity. See text for description.
-
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 Ep of a body at height h (namely Ep = mgh or Ep
= 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 with velocity v, h = v2 / 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. This
same expression can be solved for v to determine the velocity of an object dropped from a height h immediately
before hitting the ground, 
, assuming negligible air resistance.
An initially-stationary object which is allowed to fall freely under gravity drops a distance which is proportional to the
square of the elapsed time. The image on the right, spanning half a second, was captured with a stroboscopic flash at 20 flashes
per second. During the first 1/20th of a second the ball drops one unit of distance (here, a unit is about 12 mm); by 2/20ths it
has dropped at total of 4 units; by 3/20ths, 9 units and so on.
Gravity and 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
masses. These masses are 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. The force of gravity is proportional
to the size of an object and inversely proportional to the square of the distance between the objects.
Gravitational radiation
-
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
-
Historical alternative theories
Recent alternative theories
See also
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
- ^ Dick Teresi (2002), Lost Discoveries: The Ancient Roots of Modern
Science - from the Babylonians to the Maya, Simon & Schuster, New York, ISBN 0-684-83718-8:
"Two hundred years before Pythagoras, philosophers in northern India had understood that
gravitation held the solar system together, and that therefore the sun, the most massive object, had to be at its centre."
- ^ S. Kak (2003). Indian Physics: Outline of Early History, p. 22.
arXiv. Louisiana State University.
- ^ Brahmagupta (628 AD).
Brahmasphuta Siddhanta ("The Opening of the Universe").
- ^ Al-Biruni (1030). Ta'rikh
al-Hind (Indica).
- ^ K. A. Waheed (1978). Islam and The Origins of Modern Science, p. 27.
Islamic Publication Ltd., Lahore.
- ^ Robert Briffault (1938). The
Making of Humanity, p. 191.
- ^ 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.
- ^ Donald Routledge Hill
(1993), Islamic Science and Engineering, p. 61, Edinburgh University
Press. (cf. Salah Zaimeche PhD (2005), Merv, p. 5, Foundation for Science
Technology and Civilization.)
- ^ 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.
- ^ 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.
- ^ Randall, Lisa (2005).
Warped Passages: Unraveling the Universe's Hidden Dimensions. Ecco. ISBN 0-06-053108-8.
- ^ Feynman, R. P.; Morinigo, F. B., Wagner, W. G., & Hatfield, B. (1995). Feynman lectures on
gravitation. Addison-Wesley. ISBN 0201627345.
- ^ Zee, A. (2003). Quantum
Field Theory in a Nutshell. Princeton University Press. ISBN 0-691-01019-6.
- ^ Randall, Lisa (2005).
Warped Passages: Unraveling the Universe's Hidden Dimensions. Ecco. ISBN 0-06-053108-8.
- ^ 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.
External links
nov:Gravitatione
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