# User Contributed Dictionary

### Verb

gravitated- past of gravitate

# Extensive Definition

Gravitation is a natural phenomenon by which all
objects with mass attract
each other, and is one of the fundamental
forces of physics. In everyday life, gravitation is most
commonly thought of as the agency that gives objects 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.

The terms gravitation and gravity are mostly
interchangeable in everyday use, but in scientific usage a
distinction may be made. "Gravitation" is a general term describing
the attractive influence that all objects with mass exert on each
other, while "gravity" specifically refers to a force that is supposed in some
theories (such as Newton's) to be the cause of this attraction. By
contrast, in general
relativity gravitation is due to spacetime curvatures that
cause inertially moving
objects to accelerate towards each other.

## History of gravitational theory

### Early history

Efforts to understand gravity began in ancient times. Philosophers in ancient India explained the phenomenon from the 8th century BC. According to Kanada, founder of the Vaisheshika school, "Weight causes falling; it is imperceptible and known by inference."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 (AD 628), responded to critics of the heliocentric system of
Aryabhata
(AD 476–550) 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 9th century, the eldest Banū
Mūsā brother,
Muhammad ibn Musa, in his Astral Motion and The Force of
Attraction, hypothesized that there was a force of attraction
between heavenly bodies, foreshadowing
Newton's law of universal gravitation. In the 1000s, the
Persian
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. All these early attempts
at trying to explain the force of gravity were philosophical in
nature and it would be Isaac Newton
that gave the first correct description of gravity.

### 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 still
made using Newton's theory because it is a much simpler theory to
work with than General
Relativity, and gives sufficiently 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:

- 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 Kerr-Newman solution for charged, 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 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 Alexander Friedmann) was confirmed by Edwin Hubble in 1929.

### Gravity and quantum mechanics

Several decades after the discovery of general
relativity it was realized that general relativity is incompatible
with quantum
mechanics. It is possible to describe gravity in the framework
of quantum
field theory like the other fundamental
forces, with 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 (or a new approach to quantum mechanics) is required.
Many believe the complete theory to be string
theory, or more currently M Theory.

## 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 center 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 expressed below as the standard
average.

g = 9.8 \frac = 32.2 \frac

This means that, ignoring air resistance, an
object falling freely near the earth's surface increases its
velocity with 9.8\tfrac (32.2\tfrac or 22 mph) for each second of
its descent. Thus, an object starting from rest will attain a
velocity of 9.8\tfrac (32.2\tfrac) after one second, 19.6\tfrac
(64\tfrac) after two seconds, and so on, adding 9.8\tfrac to each
resulting velocity. 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

The kinematical and dynamical equations describing the trajectories of falling bodies are considerably simpler if the gravitational force is assumed constant. This assumption is reasonable for objects falling to Earth over the relatively short vertical distances of our everyday experience, but does not hold over larger distances, such as spacecraft trajectories, since the acceleration due to Earth's gravity is much smaller at large distances.Under an assumption of constant gravity,
Newton’s law of gravitation simplifies to F = mg, where m is
the mass of the body and g
is a constant vector with an average magnitude of
9.81 m/s². The acceleration due to gravity is equal to
this g. 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.

Under the same constant gravity assumptions, the
potential
energy, Ep, of a body at height h is given by Ep = mgh (or Ep =
Wh, with W meaning weight). This expression is valid only over
small distances h from the surface of the Earth. Similarly, the
expression h = \tfrac for the maximum height reached by a
vertically projected body with velocity v 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, v=\sqrt, assuming
negligible air resistance.

### 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 mass of an object and inversely proportional to the square of the distance between the objects.### Gravitational radiation

In general relativity, gravitational radiation is
generated in situations where the curvature of spacetime is oscillating, such
as is the case with co-orbiting objects. The 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.

## Anomalies and discrepancies

There are some observations that are not
adequately accounted for, which may point to the need for better
theories of gravity or perhaps be explained in other ways.

- Stars on the outskirts of galaxies are moving faster than they should. Also galaxies within galaxy clusters are moving faster than they should. Dark Matter and MOND have both been proposed as explanations.

- The expansion of the universe seems to be speeding up. Dark Energy has been proposed to explain this. A recent alternative explanation is that the geometry of space is not homogeneous (due to clusters of galaxies) and that when the data is reinterpreted to take this into account, the expansion is not speeding up after all.

- The Pioneer spacecraft seem to be slowing down in a way which has yet to be explained.

- Various spacecraft have experienced greater accelerations during slingshot maneuvers than expected.

- An apparent frame dragging effect has been measured by Martin Tajmar and others which exceeds that predicted by General Relativity by many orders of magnitude.

## 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
- Tensor-vector-scalar gravity (TeVeS) (2004), a relativistic modification of MOND by Jacob Bekenstein

## See also

portal Gravitation- Anti-gravity, the idea of neutralizing or repelling gravity
- Artificial gravity
- Escape velocity, the minimum velocity needed to fly away from a massive space object
- General relativity
- g-force, a measure of acceleration
- Gravitational field
- Gravitational waves
- Gravitational binding energy
- Gravity Research Foundation
- Gauss's law for gravity
- Jovian-Plutonian gravitational effect
- 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
- Gravity assist

## Notes

- 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
- 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

- Physics v. 1
- Physics for Scientists and Engineers
- Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics

## External links

- Chapter 10. Gravity, from Light and Matter: educational materials for physics and astronomy
- Gravity Probe B Experiment The Official Einstein website from Stanford University
- Center for Gravity, Electrical, and Magnetic Studies
- Gravity for kids (flash)
- Ask a scientist, Physics Archive
- How stuff works:
- Alternative theory of gravity explains large structure formation -- without dark matter PhysOrg.com
- Do it yourself, gravitation experiment

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