Gravitation, or gravity, is the natural phenomenon by which physical bodies appear to attract each other with a force proportional to their masses. It is most commonly experienced as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped. The phenomenon of gravitation itself, however, is a byproduct of a more fundamental phenomenon described by general relativity, which suggests that spacetime is curved according to the presence of matter through a yet-to-be discovered mechanism.
Gravitation is one of the four fundamental interactions of
nature, along with electromagnetism, and the nuclear strong force and weak
force. In modern physics, the phenomenon of gravitation is most accurately described
by the general theory of relativity by Einstein, in which the phenomenon itself
is a consequence of the curvature of spacetime governing the motion of inertial
objects. The simpler Newton's law of universal gravitation provides an accurate
approximation for most physical situations including calculations as critical
as spacecraft trajectory.
From a cosmological perspective, gravitation causes
dispersed matter to coalesce, and coalesced matter to remain intact, thus
accounting for the existence of planets, stars, galaxies and most of the
macroscopic objects in the universe. 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 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; and for various other phenomena observed on Earth and throughout
the universe.
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 correctly 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]
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 if they hit the ground at the same time.
These 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.
General relativity
Introduction
Mathematical formulation
Resources
Fundamental concepts[show]
Phenomena[show]
Equations[show]
Advanced theories[show]
Solutions[show]
Scientists[show]
Spacetime[show]
v t e
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 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 Friedmann-Lemaitre-Robertson-Walker
solution, which predicts the expansion of the universe.
The tests of general relativity included the following:[9]
General relativity accounts for the anomalous perihelion
precession of Mercury.2
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.[10][11] 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.[12] 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.[13] 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.[14]
The theory's prediction of frame dragging was consistent
with the recent Gravity Probe B results.[15]
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.[16]
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.[17] 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.[18][19] This
reproduces general relativity in the classical limit. However, this approach
fails at short distances of the order of the Planck length,[17] 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 approximately expressed below as the standard
average.
g = 9.81 m/s2 = 32.2 ft/s2
This means that, ignoring air resistance, an object falling
freely near the Earth's surface increases its velocity by 9.81 m/s (32.2 ft/s
or 22 mph) for each second of its descent. Thus, an object starting from rest
will attain a velocity of 9.81 m/s (32.2 ft/s) after one second, 19.62 m/s
(64.4 ft/s) after two seconds, and so on, adding 9.81 m/s (32.2 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.
If an object with comparable mass to that of the Earth were
to fall towards it, then the corresponding acceleration of the Earth really
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.
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/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 1⁄20 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
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, 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.
Speed of gravity
In December 2012, a research team in China announced that it
had produced findings which seem to prove that the speed of gravity is equal to
the speed of light. The team's findings were due to be released in a journal in
2013.[20]
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.
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
gravitationally 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,[21] however this
conclusion is disputed.[22]
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.[23]
Dark flow: Surveys of galaxy motions have detected a mystery
dark flow towards an unseen mass. Such a large mass is too large to have
accumulated since the Big Bang using current models and may indicate that
gravity falls off slower than inverse-squared at certain distance scales.[23]
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.[23]
Alternative theories
Main article: Alternatives to general relativity
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. 267–271, Weber-Gauss electrodynamics applied to gravitation. Classical
advancement of perihelia.
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
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
Nonsymmetric gravitational theory (NGT) (1994) by John
Moffat
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.
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