# Gravitation

From Wikipedia, the free encyclopedia

This article is about
the natural phenomenon. For other uses, see Gravitation
(disambiguation).

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

"Law of Gravity"
and "Laws of Gravity" redirect here. For other uses, see
Law
of Gravity (disambiguation).

Hammer and feather drop: Apollo
15 astronaut
David Scott on
the Moon recreating Galileo's famous gravity experiment. (1.38 MB,
ogg/Theora
format).

**Gravitation** or **gravity** is a natural
phenomenon by which all physical
bodies attract each other. Gravity gives weight
to physical objects and causes them to fall
toward one another.

In modern physics,
gravitation is most accurately described by the general
theory of relativity (proposed by Einstein)
which describes gravitation as a consequence of the curvature of
spacetime. For
most situations gravity is well approximated by Newton's
law of universal gravitation, which postulates that the
gravitational force
of two bodies of mass is directly proportional
to the product of their masses and inversely
proportional to the square
of the distance
between them.

In pursuit of a theory
of everything, the merging of general relativity and quantum
mechanics (or quantum field theory) into a more general theory of
quantum
gravity has become an area of active research. It is hypothesised
that the gravitational force is mediated by a massless spin-2
particle called the graviton,
and that gravity would have separated from the electronuclear
force during the grand
unification epoch.

Gravity is the weakest of the four fundamental
forces of nature. The gravitational force is approximately 10^{−38}
times the strength of the strong force (i.e. gravity is 38 orders of
magnitude weaker), 10^{−36} times the strength of the
electromagnetic force, and 10^{−29} times the strength
of the weak force. As a consequence, gravity has a negligible
influence on the behavior of sub-atomic particles, and plays no role
in determining the internal properties of everyday matter. On the
other hand, gravity is the dominant force at the macroscopic scale,
that is the cause of the formation, shape, and trajectory (orbit) of
astronomical bodies, including those of asteroids,
comets, planets,
stars, and galaxies.
It is responsible for causing the Earth and the other planets to
orbit the Sun; for
causing the Moon to
orbit the Earth; for the formation of tides;
for natural convection,
by which fluid flow occurs under the influence of a density
gradient and gravity; for heating the interiors of forming stars
and planets to very high temperatures; for solar
system, galaxy,
stellar
formation and evolution; and for various other phenomena observed on
Earth and throughout the universe. This is the case for several
reasons: gravity is the only force acting on all particles; it has an
infinite range; it is always attractive and never repulsive; and it
cannot be absorbed, transformed, or shielded against. Even though
electromagnetism is far stronger than gravity, electromagnetism is
not relevant to astronomical objects, since such bodies have an equal
number of protons and electrons that cancel out (i.e., a net electric
charge of zero).

## History
of gravitational theory

Main article: History
of gravitational theory

### Scientific
revolution

Modern
work on gravitational theory began with the work of Galileo
Galilei in the late 16th and early 17th centuries. In his famous
(though possibly apocryphal[1])
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 accelerate faster.[2]
Galileo postulated air
resistance as the reason that lighter objects may fall slower in
an atmosphere. Galileo's work set the stage for the formulation of
Newton's theory of gravity.

### Newton's
theory of gravitation

Main article: Newton's
law of universal gravitation

Sir Isaac
Newton, an English physicist who lived from 1642 to 1727

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."[3]
The equation is the following:

Where *F* is the force, *m*_{1} and *m*_{2}
are the masses of the objects interacting, *r* is the distance
between the centers of the masses and *G* is the gravitational
constant.

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 for by the actions of the other planets.
Calculations by both John
Couch Adams and Urbain
Le Verrier predicted the general position of the planet, and Le
Verrier's calculations are what led Johann
Gottfried Galle to the discovery of Neptune.

A discrepancy in Mercury's
orbit pointed out flaws in Newton's theory. By the end of the 19th
century, it was known that its orbit showed slight perturbations that
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 theory of general
relativity, which accounted for the small 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 involving sufficiently small masses, speeds and
energies.

### Equivalence
principle

The equivalence
principle, explored by a succession of researchers including
Galileo, Loránd
Eötvös, and Einstein, expresses the idea that all
objects fall in the same way. The simplest way to test the weak
equivalence principle is to drop two objects of different masses
or compositions in a vacuum and see whether they hit the ground at
the same time. Such experiments demonstrate that all objects fall at
the same rate when friction (including air resistance) is negligible.
More sophisticated tests use a torsion balance of a type invented by
Eötvös. Satellite experiments, for example STEP,
are planned for more accurate experiments in space.[4]

Formulations of the equivalence principle include:

The
weak equivalence principle: *The trajectory of a point mass in a
gravitational
field depends only on its initial position and velocity, and is
independent of its composition.*[5]

The Einsteinian equivalence principle: *The outcome of any local
non-gravitational experiment in a freely falling laboratory is
independent of the velocity of the laboratory and its location in
spacetime.*[6]

The strong equivalence principle requiring both of the above.

### General
relativity

See also: Introduction
to general relativity

Two-dimensional analogy of spacetime
distortion generated by the mass of an object. Matter changes the
geometry of spacetime, this (curved) geometry being interpreted as
gravity. White
lines do not represent the curvature of space but instead represent
the coordinate
system imposed on the curved spacetime, which would be
rectilinear
in a flat spacetime.

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 and
describes free-falling inertial objects as being accelerated relative
to non-inertial observers on the ground.[7][8]
In Newtonian
physics, however, no such acceleration can occur unless at least
one of the objects is being operated on by a force.

Einstein proposed that spacetime is curved by matter, and that
free-falling objects are moving along locally straight paths in
curved spacetime. These straight paths are called geodesics.
Like Newton's first law of motion, Einstein's theory states that if a
force is applied on an object, it would deviate from a geodesic. For
instance, we are no longer following geodesics while standing because
the mechanical resistance of the Earth exerts an upward force on us,
and we are non-inertial on the ground as a result. This explains why
moving along the geodesics in spacetime is considered inertial.

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 tests
of general relativity included the following:[9]

General
relativity accounts for the anomalous perihelion
precession of Mercury.[10]

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
Stanley Eddington from his observations during the Solar
eclipse of May 29, 1919.[11][12]
Eddington measured starlight deflections twice those predicted by
Newtonian corpuscular theory, in accordance with the predictions of
general relativity. However, his interpretation of the results was
later disputed.[13]
More recent tests using radio interferometric measurements of
quasars passing
behind the Sun have
more accurately and consistently confirmed the deflection of light
to the degree predicted by general relativity.[14]
See also gravitational
lens.

The time
delay of light passing close to a massive object was first
identified by Irwin
I. Shapiro in 1964 in interplanetary spacecraft signals.

Gravitational
radiation has been indirectly confirmed through studies of
binary pulsars.

Alexander
Friedmann in 1922 found that Einstein equations have
non-stationary solutions (even in the presence of the cosmological
constant). In 1927 Georges
Lemaître showed that static solutions of the Einstein
equations, which are possible in the presence of the cosmological
constant, are unstable, and therefore the static universe envisioned
by Einstein could not exist. Later, in 1931, Einstein himself agreed
with the results of Friedmann and Lemaître. Thus general
relativity predicted that the Universe had to be non-static—it
had to either expand or contract. The expansion of the universe
discovered by Edwin
Hubble in 1929 confirmed this prediction.[15]

The
theory's prediction of frame
dragging was consistent with the recent Gravity
Probe B results.[16]

General relativity predicts that
light should lose its energy when travelling away from the massive
bodies. The group of Radek Wojtak of the Niels Bohr Institute at the
University of Copenhagen collected data from 8000 galaxy clusters
and found that the light coming from the cluster centers tended to
be red-shifted compared to the cluster edges, confirming the energy
loss due to gravity.[17]

### Gravity
and quantum mechanics

Main articles: Graviton
and Quantum
gravity

In the decades after the discovery of general relativity it was
realized that general relativity is incompatible with quantum
mechanics.[18]
It is possible to describe gravity in the framework of quantum
field theory like the other fundamental
forces, such that 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.[19][20]
This reproduces general relativity in the classical
limit. However, this approach fails at short distances of the
order of the Planck
length,[18]
where a more complete theory of quantum
gravity (or a new approach to quantum mechanics) is required.

## 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 all
objects. Assuming a spherically symmetrical planet, 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 expressed below as the standard
average. According to the International
Bureau of Weights and Measures, under the International
System of Units (SI), the Earth's standard acceleration due to
gravity is:

*g* = 9.80665 m/s^{2} (32.1740 ft/s^{2}).[21][22]
This means that, ignoring air resistance, an object falling freely
near the Earth's surface increases its velocity by 9.80665 m/s
(32.1740 ft/s or 22 mph) for each second of its descent.
Thus, an object starting from rest will attain a velocity of
9.80665 m/s (32.1740 ft/s) after one second, approximately
19.62 m/s (64.4 ft/s) after two seconds, and so on, adding
9.80665 m/s (32.1740 ft/s) to each resulting velocity.
Also, again ignoring air resistance, any and all objects, when
dropped from the same height, will hit the ground at the same time.
It is relevant to note that Earth's gravity doesn't have the exact
same value in all regions. There are slight variations in different
parts of the globe due to latitude, surface features such as
mountains and ridges, and perhaps unusually high or low sub-surface
densities.[23]

If an object with comparable mass to that of the Earth were to
fall towards it, then the corresponding acceleration of the Earth
would be observable.

According to Newton's
3rd Law, the Earth itself experiences a force
equal in magnitude and opposite in direction to that which it exerts
on a falling object. This means that the Earth also accelerates
towards the object until they collide. Because the mass of the Earth
is huge, however, the acceleration imparted to the Earth by this
opposite force is negligible in comparison to the object's. If the
object doesn't bounce after it has collided with the Earth, each of
them then exerts a repulsive contact
force on the other which effectively balances the attractive
force of gravity and prevents further acceleration.

The force of gravity on Earth is the resultant (vector sum) of two
forces: (a) The gravitational attraction in accordance with Newton's
universal law of gravitation, and (b) the centrifugal force, which
results from the choice of an earthbound, rotating frame of
reference. At the equator, the force of gravity is the weakest due to
the centrifugal force caused by the Earth's rotation. The force of
gravity varies with latitude and increases from about 9.780 m/s^{2}
at the Equator to about 9.832 m/s^{2} at the poles.

The standard value of 9.80665 m/s^{2} is the one
originally adopted by the International Committee on Weights and
Measures in 1901 for 45° latitude, even though it has been shown
to be too high by about five parts in ten thousand.[24]
This value has persisted in meteorology and in some standard
atmospheres as the value for 45° latitude even though it applies
more precisely to latitude of 45°32'33".[25]

###
Equations for a falling body near the surface of the Earth

Ball falling freely under gravity. See
text for description.

Main article: Equations
for a falling body

Under an assumption of constant gravity, Newton's
law of universal 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/s^{2}. 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}⁄_{20}
of a second the ball drops one unit of distance (here, a unit is
about 12 mm); by ^{2}⁄_{20} it has dropped
at total of 4 units; by ^{3}⁄_{20}, 9 units and
so on.

Under the same constant gravity assumptions, the potential
energy, *E*_{p}, of a body at height *h*
is given by *E*_{p} = *mgh* (or *E*_{p}
= *Wh*, with *W* meaning weight). This expression is valid
only over small distances *h* from the surface of the Earth.
Similarly, the expression
for the maximum height reached by a vertically projected body with
initial velocity *v* is useful for small heights and small
initial velocities only.

### 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 exerted on one object by another is directly
proportional to the product of those objects' masses and inversely
proportional to the square of the distance between them.

### Gravitational
radiation

Main article: Gravitational
wave

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
B1913+16. It is believed that neutron
star mergers and black
hole formation may create detectable amounts of gravitational
radiation. Gravitational radiation observatories such as the Laser
Interferometer Gravitational Wave Observatory (LIGO)
have been created to study the problem. No confirmed detections have
been made of this hypothetical radiation.

### Speed of gravity

Main article: Speed
of gravity

In December
2012, a research team in China announced that it had produced
measurements of the phase lag of Earth
tides during full and new moons which seem to prove that the
speed of gravity is equal to the speed of light.[26]
It means that if the Sun suddenly disappeared, the Earth would keep
orbiting it normally for 8 minutes, which is the time light takes to
travel that distance. The team's findings were released in the
Chinese
Science Bulletin in February 2013.[27]

## 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.

Rotation curve of a typical spiral galaxy: predicted (**A**)
and observed (**B**). The discrepancy between the curves is
attributed to dark
matter.

**Accelerating
expansion**: The metric
expansion of space 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 are reinterpreted to
take this into account, the expansion is not speeding up after
all,[28]
however this conclusion is disputed.[29]

**Extra energetic
photons**: Photons travelling through galaxy clusters should gain
energy and then lose it again on the way out. The accelerating
expansion of the universe should stop the photons returning all the
energy, but even taking this into account photons from the cosmic
microwave background radiation gain twice as much energy as
expected. This may indicate that gravity falls off *faster*
than inverse-squared at certain distance scales.[30]

**Extra massive
hydrogen clouds**: The spectral lines of the Lyman-alpha
forest suggest that hydrogen clouds are more clumped together at
certain scales than expected and, like dark
flow, may indicate that gravity falls off *slower* than
inverse-squared at certain distance scales.[30]

## Alternative
theories

Main article: Alternatives
to general relativity

### Historical
alternative theories

### Recent
alternative theories

## See also