Gravity (from Latin gravitas, meaning 'weight'),
or gravitation, is a natural phenomenon by
which all things with mass or energy—including
planets, stars, galaxies, and even light—are
brought toward (or gravitate toward) one another.
On Earth, gravity gives weight to physical
objects, and the Moon's gravity causes the
ocean tides. The gravitational attraction
of the original gaseous matter present in
the Universe caused it to begin coalescing,
forming stars – and for the stars to group
together into galaxies – so gravity is responsible
for many of the large-scale structures in
the Universe. Gravity has an infinite range,
although its effects become increasingly weaker
on farther objects.
Gravity is most accurately described by the
general theory of relativity (proposed by
Albert Einstein in 1915) which describes gravity
not as a force, but as a consequence of the
curvature of spacetime caused by the uneven
distribution of mass. The most extreme example
of this curvature of spacetime is a black
hole, from which nothing—not even light—can
escape once past the black hole's event horizon.
However, for most applications, gravity is
well approximated by Newton's law of universal
gravitation, which describes gravity as a
force which causes any two bodies to be attracted
to each other, with the force proportional
to the product of their masses and inversely
proportional to the square of the distance
between them.
Gravity is the weakest of the four fundamental
forces of physics, approximately 1038 times
weaker than the strong force, 1036 times weaker
than the electromagnetic force and 1029 times
weaker than the weak force. As a consequence,
it has no significant influence at the level
of subatomic particles. In contrast, it is
the dominant force at the macroscopic scale,
and is the cause of the formation, shape and
trajectory (orbit) of astronomical bodies.
For example, gravity causes the Earth and
the other planets to orbit the Sun, it also
causes the Moon to orbit the Earth, and causes
the formation of tides, the formation and
evolution of the Solar System, stars and galaxies.
The earliest instance of gravity in the Universe,
possibly in the form of quantum gravity, supergravity
or a gravitational singularity, along with
ordinary space and time, developed during
the Planck epoch (up to 10−43 seconds after
the birth of the Universe), possibly from
a primeval state, such as a false vacuum,
quantum vacuum or virtual particle, in a currently
unknown manner. Attempts to develop a theory
of gravity consistent with quantum mechanics,
a quantum gravity theory, which would allow
gravity to be united in a common mathematical
framework (a theory of everything) with the
other three forces of physics, are a current
area of research.
== History of gravitational theory ==
=== Ancient India ===
Aryabhata first identified the force to explain
why objects do not fall when the earth rotates,
Brahmagupta described gravity as an attractive
force and used the term "gruhtvaakarshan"
for gravity.
=== 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) experiment dropping
balls from the Tower of Pisa, and later with
careful measurements of balls rolling down
inclines, Galileo showed that gravitational
acceleration is the same for all objects.
This was a major departure from Aristotle's
belief that heavier objects have a higher
gravitational acceleration. Galileo postulated
air resistance as the reason that objects
with less mass 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." The equation
is the following:
F
=
G
m
1
m
2
r
2
{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}\
}
Where F is the force, m1 and m2 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.
This discrepancy was the advance in the perihelion
of Mercury of 42.98 arcseconds per century.Although
Newton's theory has been superseded by Einstein's
general relativity, most modern non-relativistic
gravitational calculations are still made
using Newton's theory because it is simpler
to work with and it 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, and
that the effects of gravity are indistinguishable
from certain aspects of acceleration and deceleration.
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 other forces (such
as air resistance and electromagnetic effects)
are 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.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.
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.
The strong equivalence principle requiring
both of the above.
=== 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 and
describes free-falling inertial objects as
being accelerated relative to non-inertial
observers on the ground. 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.
==== Solutions ====
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 double 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 Friedmann-Lemaître-Robertson-Walker
solution, which predicts the expansion of
the Universe.
==== Tests ====
The tests of general relativity included the
following:
General relativity accounts for the anomalous
perihelion precession of Mercury.
The prediction that time runs slower at lower
potentials (gravitational time dilation) has
been confirmed by the Pound–Rebka experiment
(1959), 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 29 May 1919. 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. 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. 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.
On 11 February 2016, the LIGO and Virgo collaborations
announced the first observation of a gravitational
wave.
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.
The theory's prediction of frame dragging
was consistent with the recent Gravity Probe
B results.
General relativity predicts that light should
lose its energy when traveling away from massive
bodies through gravitational redshift. This
was verified on earth and in the solar system
around 1960.
=== Gravity and quantum mechanics ===
In the decades after the publication of the
theory 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,
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. 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.
== Specifics ==
=== 
Earth's gravity ===
Every planetary body (including the Earth)
is surrounded by its own gravitational field,
which can be conceptualized with Newtonian
physics as exerting an attractive force on
all objects. Assuming a spherically symmetrical
planet, the strength of this field at any
given point above the surface 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. The rate of acceleration
of falling objects near the Earth's surface
varies very slightly depending on latitude,
surface features such as mountains and ridges,
and perhaps unusually high or low sub-surface
densities. For purposes of weights and measures,
a standard gravity value is defined by the
International Bureau of Weights and Measures,
under the International System of Units (SI).
That value, denoted g, is g = 9.80665 m/s2
(32.1740 ft/s2).The standard value of 9.80665
m/s2 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. 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".Assuming
the standardized value for g and ignoring
air resistance, this means that 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.
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. The
force of gravity is the weakest at the equator
because of the centrifugal force caused by
the Earth's rotation and because points on
the equator are furthest from the center of
the Earth. The force of gravity varies with
latitude and increases from about 9.780 m/s2
at the Equator to about 9.832 m/s2 at the
poles.
=== Equations for a falling body near the
surface of the Earth ===
Under an assumption of constant gravitational
attraction, 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/s2 on Earth.
This resulting force is the object's weight.
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, 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
=
v
2
2
g
{\displaystyle h={\tfrac {v^{2}}{2g}}}
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 application of Newton's law of gravity
has enabled the acquisition of much of the
detailed information we have about the planets
in the Solar System, the mass of the Sun,
and details of quasars; even the existence
of dark matter is inferred using Newton's
law of gravity. 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.
The earliest gravity (possibly in the form
of quantum gravity, supergravity or a gravitational
singularity), along with ordinary space and
time, developed during the Planck epoch (up
to 10−43 seconds after the birth of the
Universe), possibly from a primeval state
(such as a false vacuum, quantum vacuum or
virtual particle), in a currently unknown
manner.
=== Gravitational radiation ===
According to 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. In February 2016, the
Advanced LIGO team announced that they had
detected gravitational waves from a black
hole collision. On 14 September 2015, LIGO
registered gravitational waves for the first
time, as a result of the collision of two
black holes 1.3 billion light-years from Earth.
This observation confirms the theoretical
predictions of Einstein and others that such
waves exist. The event confirms that binary
black holes exist. It also opens the way for
practical observation and understanding of
the nature of gravity and events in the Universe
including the Big Bang and what happened after
it.
=== 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. This 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.In October 2017,
the LIGO and Virgo detectors received gravitational
wave signals within 2 seconds of gamma ray
satellites and optical telescopes seeing signals
from the same direction. This confirmed that
the speed of gravitational waves was the same
as the speed of light.
== 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.
Extra-fast stars: Stars in galaxies follow
a distribution of velocities where stars on
the outskirts are moving faster than they
should according to the observed distributions
of normal matter. Galaxies within galaxy clusters
show a similar pattern. Dark matter, which
would interact through gravitation but not
electromagnetically, would account for the
discrepancy. Various modifications to Newtonian
dynamics have also been proposed.
Flyby anomaly: Various spacecraft have experienced
greater acceleration than expected during
gravity assist maneuvers.
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, however this conclusion
is disputed.
Anomalous increase of the astronomical unit:
Recent measurements indicate that planetary
orbits are widening faster than if this were
solely through the Sun losing mass by radiating
energy.
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.
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.
== 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.
Ritz's theory of gravitation, Ann. Chem. Phys.
13, 145, (1908) pp. 267–71, Weber-Gauss
electrodynamics applied to gravitation. Classical
advancement of perihelia.
Nordström's theory of gravitation (1912,
1913), an early competitor of general relativity.
Kaluza Klein theory (1921)
Whitehead's theory of gravitation (1922),
another early competitor of general relativity.
=== Modern 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
ƒ(R) gravity (1970)
Horndeski theory (1974)
Supergravity (1976)
String theory
In the modified Newtonian dynamics (MOND)
(1981), Mordehai Milgrom proposes a modification
of Newton's second law of motion for small
accelerations
The self-creation cosmology theory of gravity
(1982) by G.A. Barber in which the Brans-Dicke
theory is modified to allow mass creation
Loop quantum gravity (1988) by Carlo Rovelli,
Lee Smolin, and Abhay Ashtekar
Nonsymmetric gravitational theory (NGT) (1994)
by John Moffat
Conformal gravity
Tensor–vector–scalar gravity (TeVeS) (2004),
a relativistic modification of MOND by Jacob
Bekenstein
Gravity as an entropic force, gravity arising
as an emergent phenomenon from the thermodynamic
concept of entropy.
In the superfluid vacuum theory the gravity
and curved space-time arise as a collective
excitation mode of non-relativistic background
superfluid.
Chameleon theory (2004) by Justin Khoury and
Amanda Weltman.
Pressuron theory (2013) by Olivier Minazzoli
and Aurélien Hees.
== See also ==
== Footnotes
