Gravitation
Overview

Gravitation, or gravity, is a natural phenomenon
Natural phenomenon
A natural phenomenon is a non-artificial event in the physical sense, and therefore not produced by humans, although it may affect humans . Common examples of natural phenomena include volcanic eruptions, weather, decay, gravity and erosion...

by which physical bodies
Physical body
In physics, a physical body or physical object is a collection of masses, taken to be one...

attract with a force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

proportional
Proportionality (mathematics)
In mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...

to their mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

. Gravitation is most familiar as the agent that gives weight
Weight
In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:...

to objects with mass and causes them to fall to the ground when dropped. Gravitation causes dispersed matter to coalesce, and coalesced matter to remain intact, thus accounting for the existence of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

, the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

, and most of the macroscopic objects in the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

.

Gravitation is responsible for keeping the Earth and the other planets in their orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...

s around the Sun; for keeping the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

in its orbit around the Earth; for the formation of tide
Tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the moon and the sun and the rotation of the Earth....

s; for natural convection
Convection
Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....

, by which fluid flow occurs under the influence of a density gradient
Density gradient is a spatial variation in density over an area. The term is used in the natural sciences to describe varying density of matter, but can apply to any quantity whose density can be measured...

and gravity; for heating the interiors of forming stars and planets to very high temperatures; and for various other phenomena observed on Earth.

Gravitation is one of the four fundamental interaction
Fundamental interaction
In particle physics, fundamental interactions are the ways that elementary particles interact with one another...

s of nature, along with electromagnetism, and the nuclear strong force
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...

and weak force
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...

.
Discussions
Encyclopedia
Gravitation, or gravity, is a natural phenomenon
Natural phenomenon
A natural phenomenon is a non-artificial event in the physical sense, and therefore not produced by humans, although it may affect humans . Common examples of natural phenomena include volcanic eruptions, weather, decay, gravity and erosion...

by which physical bodies
Physical body
In physics, a physical body or physical object is a collection of masses, taken to be one...

attract with a force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

proportional
Proportionality (mathematics)
In mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...

to their mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

. Gravitation is most familiar as the agent that gives weight
Weight
In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:...

to objects with mass and causes them to fall to the ground when dropped. Gravitation causes dispersed matter to coalesce, and coalesced matter to remain intact, thus accounting for the existence of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

, the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

, and most of the macroscopic objects in the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

.

Gravitation is responsible for keeping the Earth and the other planets in their orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...

s around the Sun; for keeping the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

in its orbit around the Earth; for the formation of tide
Tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the moon and the sun and the rotation of the Earth....

s; for natural convection
Convection
Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....

, by which fluid flow occurs under the influence of a density gradient
Density gradient is a spatial variation in density over an area. The term is used in the natural sciences to describe varying density of matter, but can apply to any quantity whose density can be measured...

and gravity; for heating the interiors of forming stars and planets to very high temperatures; and for various other phenomena observed on Earth.

Gravitation is one of the four fundamental interaction
Fundamental interaction
In particle physics, fundamental interactions are the ways that elementary particles interact with one another...

s of nature, along with electromagnetism, and the nuclear strong force
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...

and weak force
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...

. Modern physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

describes gravitation using the general theory of relativity by Einstein, in which it is a consequence of the curvature of spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

governing the motion of inertial objects. The simpler Newton's law of universal gravitation
Newton's law of universal gravitation
Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...

provides an accurate approximation for most physical situations.

### Scientific revolution

Modern work on gravitational theory began with the work of Galileo Galilei
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...

in the late 16th and early 17th centuries. In his famous (though possibly apocryphal) experiment dropping balls from the Tower of Pisa
Leaning Tower of Pisa
The Leaning Tower of Pisa or simply the Tower of Pisa is the campanile, or freestanding bell tower, of the cathedral of the Italian city of Pisa...

, and later with careful measurements of balls rolling down inclines
Inclined plane
The inclined plane is one of the original six simple machines; as the name suggests, it is a flat surface whose endpoints are at different heights. By moving an object up an inclined plane rather than completely vertical, the amount of force required is reduced, at the expense of increasing the...

, Galileo showed that gravitation accelerates all objects at the same rate. This was a major departure from Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

's belief that heavier objects accelerate 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
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

published Principia, which hypothesizes the inverse-square law
Inverse-square law
In physics, an inverse-square law is any physical law stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity....

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
Neptune
Neptune is the eighth and farthest planet from the Sun in the Solar System. Named for the Roman god of the sea, it is the fourth-largest planet by diameter and the third largest by mass. Neptune is 17 times the mass of Earth and is slightly more massive than its near-twin Uranus, which is 15 times...

based on motions of Uranus
Uranus
Uranus is the seventh planet from the Sun. It has the third-largest planetary radius and fourth-largest planetary mass in the Solar System. It is named after the ancient Greek deity of the sky Uranus , the father of Cronus and grandfather of Zeus...

that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams
John Couch Adams was a British mathematician and astronomer. Adams was born in Laneast, near Launceston, Cornwall, and died in Cambridge. The Cornish name Couch is pronounced "cooch"....

and Urbain Le Verrier predicted the general position of the planet, and Le Verrier's calculations are what led Johann Gottfried Galle
Johann Gottfried Galle
Johann Gottfried Galle was a German astronomer at the Berlin Observatory who, on 23 September 1846, with the assistance of student Heinrich Louis d'Arrest, was the first person to view the planet Neptune, and know what he was looking at...

to the discovery of Neptune.

A discrepancy in Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...

'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
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

even closer than Mercury) had been fruitless. The issue was resolved in 1915 by Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

's new theory of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, which accounted for the small discrepancy in Mercury's orbit.

Although Newton's theory has been superseded, most modern non-relativistic
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....

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
Equivalence principle
In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body is actually...

, explored by a succession of researchers including Galileo, Loránd Eötvös
Loránd Eötvös
Baron Loránd Eötvös de Vásárosnamény , more commonly called Baron Roland von Eötvös in English literature, was a Hungarian physicist. He is remembered today largely for his work on gravitation and surface tension.-Life:...

, 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 mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

es 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
STEP (satellite)
The Satellite Test of the Equivalence Principle is a proposed space science experiment to test the equivalence principle of general relativity...

, 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
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

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.

The equivalence principle can be used to make physical deductions about the gravitational constant
Gravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...

, the geometrical nature of gravity, the possibility of a fifth force
Fifth force
Occasionally, physicists have postulated the existence of a fifth force in addition to the four known fundamental forces. The force is generally believed to have roughly the strength of gravity Occasionally, physicists have postulated the existence of a fifth force in addition to the four known...

, and the validity of concepts such as general relativity and Brans-Dicke theory
Brans-Dicke theory
In theoretical physics, the Brans–Dicke theory of gravitation is a theoretical framework to explain gravitation. It is a well-known competitor of Einstein's more popular theory of general relativity...

.

### General relativity

In general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, the effects of gravitation are ascribed to spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

curvature
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...

instead of a force. The starting point for general relativity is the equivalence principle
Equivalence principle
In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body is actually...

, 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
Geodesic (general relativity)
In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational, force is a particular type of geodesic...

. 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 equation
Field equation
A field equation is an equation in a physical theory that describes how a fundamental force interacts with matter...

s of general relativity, which relate the presence of matter and the curvature of spacetime and are named after him. The Einstein field equations
Einstein field equations
The Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...

are a set of 10 simultaneous
Simultaneous equations
In mathematics, simultaneous equations are a set of equations containing multiple variables. This set is often referred to as a system of equations. A solution to a system of equations is a particular specification of the values of all variables that simultaneously satisfies all of the equations...

, non-linear, differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...

s. The solutions of the field equations are the components of the metric tensor
Metric tensor (general relativity)
In general relativity, the metric tensor is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational field familiar from Newtonian gravitation...

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
Circular symmetry
Circular symmetry in mathematical physics applies to a 2-dimensional field which can be expressed as a function of distance from a central point only. This means that all points on each circle take the same value....

non-rotating
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...

uncharged massive object. For compact enough objects, this solution generated a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

with a central singularity
Gravitational singularity
A gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...

. For radial distances from the center which are much greater than the Schwarzschild radius
The Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...

, 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 horizon
Event horizon
In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...

s.
• The Kerr solution
Kerr metric
The Kerr metric describes the geometry of empty spacetime around an uncharged axially-symmetric black-hole with an event horizon which is topologically a sphere. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which...

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
Physical cosmology
Physical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...

Friedmann-Lemaitre-Robertson-Walker solution, which predicts the expansion of the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

.

The tests of general relativity
Tests of general relativity
At its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's...

included the following:
• 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 Stanley Eddington
Arthur Stanley Eddington
Sir Arthur Stanley Eddington, OM, FRS was a British astrophysicist of the early 20th century. He was also a philosopher of science and a popularizer of science...

from his observations during the Solar eclipse of May 29, 1919
Solar eclipse of May 29, 1919
A total solar eclipse occurred on May 29, 1919. With a maximum duration of totality of 6 minutes 51 seconds, it was one of the longest solar eclipses of the 20th century. It was visible throughout most of South America and Africa as a partial eclipse...

. 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 quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...

s passing behind the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

have more accurately and consistently confirmed the deflection of light to the degree predicted by general relativity. See also gravitational lens
Gravitational lens
A gravitational lens refers to a distribution of matter between a distant source and an observer, that is capable of bending the light from the source, as it travels towards the observer...

.
• The time delay of light passing close to a massive object was first identified by Irwin I. Shapiro
Irwin I. Shapiro
Irwin I. Shapiro is an American astrophysicist. Since 1982, he has been a professor at Harvard University. Shapiro was director of the Harvard-Smithsonian Center for Astrophysics from 1982 to 2004.- Biography :Irwin Shapiro was born in New York City in 1929...

in 1964 in interplanetary spacecraft signals.
• Gravitational radiation has been indirectly confirmed through studies of binary pulsar
Pulsar
A pulsar is a highly magnetized, rotating neutron star that emits a beam of electromagnetic radiation. The radiation can only be observed when the beam of emission is pointing towards the Earth. This is called the lighthouse effect and gives rise to the pulsed nature that gives pulsars their name...

s.
• Alexander Friedmann in 1922 found that Einstein equations have non-stationary solutions (even in the presence of the cosmological constant
Cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...

). In 1927 Georges Lemaître
Georges Lemaître
Monsignor Georges Henri Joseph Édouard Lemaître was a Belgian priest, astronomer and professor of physics at the Catholic University of Louvain. He was the first person to propose the theory of the expansion of the Universe, widely misattributed to Edwin Hubble...

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
Edwin Hubble
Edwin Powell Hubble was an American astronomer who profoundly changed the understanding of the universe by confirming the existence of galaxies other than the Milky Way - our own galaxy...

in 1929 confirmed this prediction.
• The theory's prediction of frame dragging was consistent with the recent Gravity Probe B
Gravity Probe B
Gravity Probe B is a satellite-based mission which launched on 20 April 2004 on a Delta II rocket. The spaceflight phase lasted until 2005; its aim was to measure spacetime curvature near Earth, and thereby the stress–energy tensor in and near Earth...

results.
• General relativity predicts that the 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 the data from 8000 galaxy clusters and found that the light coming from the cluster centers tended to be redshifted compared to the cluster egdes, confirming the energy loss due to the gravity.

### Gravity and quantum mechanics

In the decades after the discovery of general relativity it was realized that general relativity is incompatible with quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

. It is possible to describe gravity in the framework of quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

like the other fundamental forces, such that the attractive force of gravity arises due to exchange of virtual
Virtual particle
In physics, a virtual particle is a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle...

gravitons, in the same way as the electromagnetic force arises from exchange of virtual photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s. This reproduces general relativity in the classical limit
Classical limit
The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters. The classical limit is used with physical theories that predict non-classical behavior...

. However, this approach fails at short distances of the order of the Planck length, where a more complete theory of quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

(or a new approach to quantum mechanics) is required. Many believe the complete theory to be string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

, or more currently M-theory
M-theory
In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...

, and, on the other hand, it may be a background independent theory such as loop quantum gravity
Loop quantum gravity
Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...

or causal dynamical triangulation.

### 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
Standard gravity
Standard gravity, or standard acceleration due to free fall, usually denoted by g0 or gn, is the nominal acceleration of an object in a vacuum near the surface of the Earth. It is defined as precisely , or about...

.

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, 19.6 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.
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
Contact force
In physics, a contact force is a force that acts at the point of contact between two objects, in contrast to body forces. Contact forces are described by Newton's laws of motion, as with all other forces in dynamics....

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

Under an assumption of constant gravity, Newton's law of universal gravitation
Newton's law of universal gravitation
Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...

simplifies to F = mg, where m is the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

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 of a second the ball drops one unit of distance (here, a unit is about 12 mm); by it has dropped at total of 4 units; by , 9 units and so on.

Under the same constant gravity assumptions, the potential energy
Potential energy
In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...

, 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 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, quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...

s and even the theory of dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...

. 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
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...

because of the force of gravity acting upon it. Planets orbit stars, stars orbit Galactic Center
Galactic Center
The Galactic Center is the rotational center of the Milky Way galaxy. It is located at a distance of 8.33±0.35 kpc from the Earth in the direction of the constellations Sagittarius, Ophiuchus, and Scorpius where the Milky Way appears brightest...

s, galaxies
Galaxy
A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...

orbit a center of mass in clusters, and clusters orbit in supercluster
Supercluster
Superclusters are large groups of smaller galaxy groups and clusters and are among the largest known structures of the cosmos. They are so large that they are not gravitationally bound and, consequently, partake in the Hubble expansion.-Existence:...

s. 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.

In general relativity, gravitational radiation is generated in situations where the curvature of spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

is oscillating, such as is the case with co-orbiting objects. The gravitational radiation emitted by the Solar System
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

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
Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

mergers and black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

formation may create detectable amounts of gravitational radiation. Gravitational radiation observatories such as LIGO
LIGO
LIGO, which stands for the Laser Interferometer Gravitational-Wave Observatory, is a large-scale physics experiment aiming to directly detect gravitational waves. Cofounded in 1992 by Kip Thorne and Ronald Drever of Caltech and Rainer Weiss of MIT, LIGO is a joint project between scientists at MIT,...

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.

• Extra fast stars: Stars in galaxies follow a distribution of velocities
Galaxy rotation curve
The rotation curve of a galaxy can be represented by a graph that plots the orbital velocity of the stars or gas in the galaxy on the y-axis against the distance from the center of the galaxy on the x-axis....

where stars on the outskirts are moving faster than they should according to the observed distributions of normal matter. Galaxies within galaxy clusters
Galaxy groups and clusters
Galaxy groups and clusters are the largest known gravitationally bound objects to have arisen thus far in the process of cosmic structure formation. They form the densest part of the large scale structure of the universe...

show a similar pattern. Dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...

, which would interact gravitationally but not electromagnetically, would account for the discrepancy. Various modifications to Newtonian dynamics
Modified Newtonian dynamics
In physics, Modified Newtonian dynamics is a hypothesis that proposes a modification of Newton's law of gravity to explain the galaxy rotation problem. When the uniform velocity of rotation of galaxies was first observed, it was unexpected because Newtonian theory of gravity predicts that objects...

have also been proposed.

• Flyby anomaly
Flyby anomaly
The flyby anomaly is an unexpected energy increase during Earth-flybys of spacecraft. This anomaly has been observed as shifts in the S-Band and X-Band Doppler and ranging telemetry. Taken together it causes a significant unaccounted velocity increase of over 13 mm/s during...

: Various spacecraft have experienced greater acceleration than expected during gravity assist maneuvers.

• Accelerating expansion: The metric expansion of space
Metric expansion of space
The metric expansion of space is the increase of distance between distant parts of the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...

seems to be speeding up. Dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...

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
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

: 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
In cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....

gain twice as much energy as expected. This may indicate that gravity falls off faster than inverse-squared at certain distance scales.

• Dark flow: Surveys of galaxy motions have detected a mystery dark flow
Dark flow
Dark flow is an astrophysical term describing a peculiar velocity of galaxy clusters. The actual measured velocity is the sum of the velocity predicted by Hubble's Law plus a small and unexplained velocity flowing in a common direction....

towards an unseen mass. Such a large mass is too large to have accumulated since the Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

using current models and may indicate that gravity falls off slower than inverse-squared at certain distance scales.

• Extra massive hydrogen clouds: The spectral lines of the Lyman-alpha forest
Lyman-alpha forest
In astronomical spectroscopy, the Lyman-alpha forest is the sum of absorption lines arising from the Lyman-alpha transition of the neutral hydrogen in the spectra of distant galaxies and quasars....

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.

### Historical alternative theories

• Aristotelian theory of gravity
• Le Sage's theory of gravitation
Le Sage's theory of gravitation
Le Sage's theory of gravitation is a kinetic theory of gravity originally proposed by Nicolas Fatio de Duillier in 1690 and later by Georges-Louis Le Sage in 1748. The theory proposed a mechanical explanation for Newton's gravitational force in terms of streams of tiny unseen particles impacting...

(1784) also called LeSage gravity, proposed by Georges-Louis Le Sage
Georges-Louis Le Sage
Georges-Louis Le Sage was a physicist and is most known for his theory of gravitation, for his invention of an electric telegraph and his anticipation of the kinetic theory of gases....

, based on a fluid-based explanation where a light gas fills the entire universe.
• Ritz's theory of gravitation
Ritz's Equation
In 1908, Walter Ritz published Recherches critiques sur l'Électrodynamique Générale, a lengthy criticism of Maxwell-Lorentz electromagnetic theory, in which he contended that the theory's connection with the luminiferous aether made it "essentially inappropriate to express the comprehensive laws...

, Ann. Chem. Phys. 13, 145, (1908) pp. 267-271, Weber-Gauss electrodynamics applied to gravitation. Classical advancement of perihelia.
• Nordström's theory of gravitation
Nordström's theory of gravitation
In theoretical physics, Nordström's theory of gravitation was a predecessor of general relativity. Strictly speaking, there were actually two distinct theories proposed by the Finnish theoretical physicist Gunnar Nordström, in 1912 and 1913 respectively...

(1912, 1913), an early competitor of general relativity.
In theoretical physics, Whitehead's theory of gravitation was introduced by the distinguished mathematician and philosopher Alfred North Whitehead in 1922.-Principal features of the theory:Whitehead's theory is said to feature a prior geometry...

(1922), another early competitor of general relativity.

### Recent alternative theories

• Brans–Dicke theory of gravity (1961)
• Induced gravity
Induced gravity
Induced gravity is an idea in quantum gravity that space-time background emerges asa mean field approximation of underlying microscopic degrees of freedom, similar to the fluid mechanics approximation of Bose–Einstein condensates...

(1967), a proposal by Andrei Sakharov
Andrei Sakharov
Andrei Dmitrievich Sakharov was a Soviet nuclear physicist, dissident and human rights activist. He earned renown as the designer of the Soviet Union's Third Idea, a codename for Soviet development of thermonuclear weapons. Sakharov was an advocate of civil liberties and civil reforms in the...

according to which general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

might arise from quantum field theories
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

of matter
• In the modified Newtonian dynamics
Modified Newtonian dynamics
In physics, Modified Newtonian dynamics is a hypothesis that proposes a modification of Newton's law of gravity to explain the galaxy rotation problem. When the uniform velocity of rotation of galaxies was first observed, it was unexpected because Newtonian theory of gravity predicts that objects...

(MOND) (1981), Mordehai Milgrom
Mordehai Milgrom
Mordehai Milgrom is an Israeli physicist and professor in the department of Condensed Matter Physics at the Weizmann Institute in Rehovot, Israel. He is most famous for his proposal of Modified Newtonian dynamics as an alternative to the dark matter and galaxy rotation curve problems, in 1981...

proposes a modification of Newton's Second Law of motion for small accelerations
• The self-creation cosmology
Self-creation cosmology
Self-creation cosmology theories are gravitational theories in which the mass of the universe is created out of its self-contained gravitational and scalar fields, as opposed to the theory of continuous creation cosmology or the steady state theory which depend on an extra 'creation'...

theory of gravity (1982) by G.A. Barber in which the Brans-Dicke theory is modified to allow mass creation
• Nonsymmetric gravitational theory
Nonsymmetric gravitational theory
In theoretical physics, the nonsymmetric gravitational theory of John Moffat is a classical theory of gravitation which tries to explain the observation of the flat rotation curves of galaxies....

(NGT) (1994) by John Moffat
• Tensor-vector-scalar gravity
Tensor-vector-scalar gravity
Tensor–vector–scalar gravity , developed by Jacob Bekenstein, is a relativistic generalization of Mordehai Milgrom's MOdified Newtonian Dynamics paradigm.The main features of TeVeS can be summarized as follows:...

(TeVeS) (2004), a relativistic modification of MOND by Jacob Bekenstein
Jacob Bekenstein
Jacob David Bekenstein is an Israeli theoretical physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation.-Biography:...

• Gravity as an entropic force
Gravity as an entropic force
Entropic gravity is a hypothesis in modern physics that describes gravity as an entropic force; not a fundamental interaction mediated by a particle, but a probabilistic consequence of physical systems' tendency to increase their entropy...

, gravity arising as an emergent phenomenon from the thermodynamic concept of entropy.