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Gravitation

2007 Schools Wikipedia Selection. Related subjects: General Physics

   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 other celestial bodies; without it, matter would not have coalesced
   into these bodies 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 the formation of tides, and for various other natural phenomena
   that we observe.
   The gravitational force keeps the planets in orbit about the Sun.
   Enlarge
   The gravitational force keeps the planets in orbit about the Sun.

History of gravitational theory

Early (pre-Newtonian) history

   Since the time of the Greek philosopher Aristotle in the 4th century
   BC, 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 their proper place in the crystalline spheres of
   the heavens, and that physical bodies fell toward the centre of the
   Earth in proportion to their weight. Another example of an attempted
   explanation is that of the Indian astronomer Brahmagupta who, in AD 628
   , wrote 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".

   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 appear to fall more slowly.) 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 the famous
   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 come up empty.
   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
   due its being a much simpler theory to work with.

General relativity

   In this theory Einstein proposed that inertial motion occurs when
   objects are in free-fall instead of when they are at rest with respect
   to a massive object such as the Earth (as is the case in classical
   mechanics). The problem is that in flat spacetimes such as those of
   classical mechanics and special relativity, there is no way that
   inertial observers can accelerate with respect to each other, as
   free-falling bodies can do as they are each accelerated towards the
   centre of a massive object.

   To deal with this difficulty, Einstein proposed that spacetime is
   curved by the presence of matter, and that free-falling objects are
   following the geodesics of the spacetime. More specifically, Einstein
   discovered the field equations of general relativity, which relate the
   presence of matter and the curvature of spacetime. The Einstein field
   equations are a set of 10 simultaneous, non-linear, differential
   equations whose solutions give the components of the metric tensor of
   spacetime. Metric tensors describe the geometry of spacetime. The
   geodesic paths for objects in inertial motion are calculated from a
   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 centre which are
       much greater then 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 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 have been regularly confirmed. For example:
     * General relativity accounts for the anomalous 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 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.

Specifics

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
   9.80665 m/s² or 32.17405 ft/s². This means that, ignoring air
   resistance, an object falling freely near the earth's surface increases
   in speed by 9.80665 m/s (around 22 mph) for each second of its descent.
   Thus, an object starting from rest will attain a speed of 9.80665 m/s
   (32.17405 ft/s) after one second, 19.6133 m/s (64.3481 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.

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
   is very much untrue 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 = 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

   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 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
   centre of mass in clusters, and clusters orbit in superclusters.

Gravity versus gravitation

   It is important to note that gravitation is not gravity. 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, it is important to note
   that 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 object 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.

Applications

   Shot Tower, 1856 Dubuque, Iowa
   Enlarge
   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 differential in a liquid, as in the case of an
   intravenous drip or a water tower. The gravitational potential energy
   of water can be used to generate hydroelectricity as well as to haul a
   tramcar up an incline, using a system of water tanks and pulleys; the
   Lynton and Lynmouth Cliff Railway in Devon, England employs just such a
   system. 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.

   Gravity is used in geophysical exploration to investigate density
   contrasts in the subsurface of the Earth. Sensitive gravimeters use a
   complicated spring and mass system (in most cases) to measure the
   strength of the "downward" component of the gravitational force at a
   point. Measuring many stations over an area reveals anomalies measured
   in mGal or microGal (1 gal is 1 cm/s^2. Average gravitational
   acceleration is about 981 gal, or 981,000 mGal.). After corrections for
   the obliqueness of the Earth, elevation, terrain, instrument drift,
   etc., these anomalies reveal areas of higher or lower density in the
   crust. This method is used extensively in mineral and petroleum
   exploration, as well as time-lapse groundwater modeling. The newest
   instruments are sensitive enough to read the gravitational pull of the
   operator standing over them.

Alternative theories

   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

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