Gravity (), or gravitation, is a ^{38} times weaker than the ^{36} times weaker than the ^{29} times weaker than the ^{−43} seconds after the

^{2} (32.1740 ft/s^{2}).
The standard value of 9.80665 m/s^{2} is the one originally adopted by the International Committee on Weights and Measures in 1901 for 45° latitude, even though it has been shown to be too high by about five parts in ten thousand.List, R.J. editor, 1968, Acceleration of Gravity, ''Smithsonian Meteorological Tables'', Sixth Ed. Smithsonian Institution, Washington, DC, p. 68. 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".U.S. Standard Atmosphere

, 1976, U.S. Government Printing Office, Washington, D.C., 1976. (Linked file is very large.) 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, Newton's 3rd Law, the Earth itself experiences a Newtons, 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 does not 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 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/s^{2} at the Equator to about 9.832 m/s^{2} at the poles.

^{2} 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 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, ''E''_{p}, of a body at height ''h'' is given by ''E''_{p} = ''mgh'' (or ''E''_{p} = ''Wh'', with ''W'' meaning weight). This expression is valid only over small distances ''h'' from the surface of the Earth. Similarly, the expression $h\; =\; \backslash tfrac$ for the maximum height reached by a vertically projected body with initial velocity ''v'' is useful for small heights and small initial velocities only.

^{−43} seconds after the

natural phenomenon
Types of natural phenomena include:
Weather, fog, thunder, tornadoes; biological processes, decomposition, germination
seedlings, three days after germination.
Germination is the process by which an organism grows from a seed or similar s ...

by which all things with mass
Mass is the quantity
Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...

or energy
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regula ...

—including planet
A planet is an astronomical body orbiting a star or Stellar evolution#Stellar remnants, stellar remnant that is massive enough to be Hydrostatic equilibrium, rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and ...

s, star
A star is an astronomical object consisting of a luminous spheroid of plasma
Plasma or plasm may refer to:
Science
* Plasma (physics), one of the four fundamental states of matter
* Plasma (mineral) or heliotrope, a mineral aggregate
* Quark ...

s, galaxies
A galaxy is a gravitationally bound system of star
A star is an astronomical object consisting of a luminous spheroid of plasma (physics), plasma held together by its own gravity. The List of nearest stars and brown dwarfs, nearest star to ...

, and even light
Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nan ...

—are attracted to (or ''gravitate'' toward) one another. On Earth, gravity gives weight
In science
Science () is a systematic enterprise that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe."... modern science is a discovery as well as ...

to physical object
A bubble of exhaled gas in water
In common usage and classical mechanics, a physical object or physical body (or simply an object or body) is a collection of matter within a defined contiguous boundary in three-dimensional space
Three-dimen ...

s, and the Moon's gravity causes the tide
Tides are the rise and fall of sea level
Mean sea level (MSL) (often shortened to sea level) is an average
In colloquial, ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of ...

s of the oceans. The gravitational attraction of the original gaseous matter present in the Universe
The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxy, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development ...

caused it to begin coalescing and and caused 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 weaker as objects get farther away.
Gravity is most accurately described by the general theory of relativity
General relativity, also known as the general theory of relativity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern ph ...

(proposed by Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity
The theo ...

in 1915), which describes gravity not as a force, but as a consequence of masses moving along geodesic
In geometry
Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position o ...

lines in a curved spacetime
In physics, spacetime is any mathematical model which fuses the three-dimensional space, three dimensions of space and the one dimension of time into a single four-dimensional manifold. Minkowski diagram, Spacetime diagrams can be used to visuali ...

caused by the uneven distribution of mass. The most extreme example of this curvature of spacetime is a , from which nothing—not even light—can escape once past the black hole's event horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. The term was coined by in the 1950s.
In 1784, proposed that in the vicinity of compact massive objects, gravity can be strong enough that even light ...

. However, for most applications, gravity is well approximated by Newton's law of universal gravitation
Newton's law of universal gravitation is usually stated as that every particle
In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object to which can ...

, which describes gravity as a force
In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...

causing any two bodies to be attracted toward each other, with magnitude proportional
Proportionality, proportion or proportional may refer to:
Mathematics
* Proportionality (mathematics), the property of two variables being in a multiplicative relation to a constant
* Ratio, of one quantity to another, especially of a part compared ...

to the product of their masses and inversely proportional
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...

to the square
In Euclidean geometry
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematics , Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's method ...

of the distance
Distance is a numerical measurement
'
Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or eve ...

between them.
Gravity is the weakest of the four fundamental interaction
In physics
Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through Sp ...

s of physics, approximately 10strong interaction
In nuclear physics and particle physics, the strong interaction is one of the four known fundamental interactions, with the others being electromagnetism, the weak interaction, and gravitation. At the range of 10−15 m (slightly more tha ...

, 10electromagnetic force
Electromagnetism is a branch of physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related ...

and 10weak interaction
In nuclear physics
Nuclear physics is the field of physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and ...

. As a consequence, it has no significant influence at the level of subatomic particles. In contrast, it is the dominant interaction at the macroscopic scale
The macroscopic scale is the length scale
In physics
Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motio ...

, and is the cause of the formation, shape and trajectory
A trajectory or flight path is the path that an with in follows through as a function of time. In , a trajectory is defined by via ; hence, a complete trajectory is defined by position and momentum, simultaneously.
The mass might be a or ...

(orbit
In celestial mechanics, an orbit is the curved trajectory of an physical body, object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an satellite, artificial satellite around an object or po ...

) of astronomical bodies
In astronomy, an astronomical object or celestial object is a naturally occurring physical object, physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...

.
Current models of particle physics
Particle physics (also known as high energy physics) is a branch of physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which rel ...

imply that the earliest instance of gravity in the Universe, possibly in the form of quantum gravity
Quantum gravity (QG) is a field of theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, n ...

, supergravity
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry
In particle physics, supersymmetry (SUSY) is a conjectured relationship between two basic c ...

or a gravitational singularity
A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravity
Gravity (), or gravitation, is a by which all things with or —including s, s, , and even —are attracted to (or ''gravitate ...

, along with ordinary space
Space is the boundless three-dimensional
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter
A parameter (from the Ancient Greek language, Ancient Gre ...

and time
Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...

, developed during the Planck epoch
The chronology of the universe describes the history and Future of an expanding universe, future of the universe according to Big Bang cosmology.
The earliest stages of the universe's existence are estimated as taking place 13.8 billion years ag ...

(up to 10birth
Birth is the act or process of bearing or bringing forth offspring, also referred to in technical contexts as parturition. In mammals, the process is initiated by hormones which cause the muscular walls of the uterus to contract, expelling the fe ...

of the Universe), possibly from a primeval state, such as a false vacuum
In quantum field theory
In theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, natu ...

, quantum vacuum or virtual particle
In physics
Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior throug ...

, in a currently unknown manner. – discusses "Planck time
In particle physics
Particle physics (also known as high energy physics) is a branch of that studies the nature of the particles that constitute and . Although the word ' can refer to various types of very small objects (e.g. , gas particl ...

" and "Planck era
The chronology of the universe describes the history and Future of an expanding universe, future of the universe according to Big Bang cosmology.
The earliest stages of the universe's existence are estimated as taking place 13.8 billion years ...

" at the of the Universe Attempts to develop a theory of gravity consistent with quantum mechanics
Quantum mechanics is a fundamental theory
A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with ...

, a quantum gravity
Quantum gravity (QG) is a field of theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, n ...

theory, which would allow gravity to be united in a common mathematical framework (a theory of everything
A theory of everything (TOE or ToE), final theory, ultimate theory, or master theory is a hypothetical single, all-encompassing, coherent theoretical framework of physics that fully explains and links together all physical aspects of the univers ...

) with the other three fundamental interactions of physics, are a current area of research.
History of gravitational theory

Ancient world

The ancient Greek philosopherArchimedes
Archimedes of Syracuse (; grc, ; ; ) was a Greek#REDIRECT Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece
Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Eu ...

discovered the center of gravity
In physics, the center of mass of a distribution of mass
Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a measure (mathematics), measure of the body's ''inertia'', the resistance to acceleration (change ...

of a triangle. He also postulated that if two equal weights did not have the same center of gravity, the center of gravity of the two weights together would be in the middle of the line that joins their centers of gravity.
The Roman architect and engineer Vitruvius
Vitruvius (; c. 80–70 BC – after c. 15 BC) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work entitled ''De architectura
(''On architecture'', published as ''Ten Books on Architecture'') i ...

in ''De Architectura
(''On architecture'', published as ''Ten Books on Architecture'') is a treatise on architecture
upright=1.45, alt=Plan d'exécution du second étage de l'hôtel de Brionne (dessin) De Cotte 2503c – Gallica 2011 (adjusted), Plan of the ...

'' postulated that gravity of an object did not depend on weight but its "nature".
The Indian mathematician-astronomer Aryabhata
Aryabhata (, ISO: ) or Aryabhata I (476–550 CE) was the first of the major mathematician
A mathematician is someone who uses an extensive knowledge of mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such ...

first identified gravity to explain why objects do not spin out when the Earth rotates, and Brahmagupta
Brahmagupta ( – ) was an Indian mathematician
A mathematician is someone who uses an extensive knowledge of mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures ...

described gravity as an attractive force and used the term '' gurutvākarṣaṇ'' for gravity.
Scientific revolution

In the mid-16th century, various Europeans experimentally disproved theAristotelian
Aristotelian may refer to:
* Aristotle (384–322 BCE), Greek philosopher
* Aristotelianism, the philosophical tradition begun by Aristotle
* Aristotelian ethics
* Aristotelian logic, term logic
* Aristotelian physics, the natural sciences
* Aristot ...

notion that heavier objects fall
Autumn, also known as fall in American English and Canadian English, is one of the four temperate seasons. Outside the tropics, autumn marks the transition from summer to winter, in September (Northern Hemisphere) or March (Southern Hemisphe ...

at a faster rate. The mid-16th century Italian physicist Giambattista Benedetti published papers claiming that, due to specific gravity
Relative density, or specific gravity, is the ratio
In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemon ...

, objects of the same material but different weights would fall at the same speed. With the 1586 Delft tower experiment the Flemish
Flemish (''Vlaams'') is a Low Franconian
Low Franconian, Low Frankish, NetherlandicSarah Grey Thomason, Terrence Kaufman: ''Language Contact, Creolization, and Genetic Linguistics'', University of California Press, 1991, p. 321. (Calling it " ...

physicist Simon Stevin
Simon Stevin (; 1548–1620), sometimes called Stevinus, was a Flemish mathematician
A mathematician is someone who uses an extensive knowledge of mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as ...

demonstrated that, when dropped from a tower, two cannonballs of differing sizes and weights would in fact reach the ground at the same time. In the late 16th century, Galileo Galilei
Galileo di Vincenzo Bonaiuti de' Galilei (; 15 February 1564 – 8 January 1642) was an Italian astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the ...

demonstrated the premise (perhaps as a thought experiment
A thought experiment is a hypothetical situation in which a hypothesis
A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can t ...

) that two balls of different weights dropped from a tower would fall at the same rate. Combining this knowledge with careful measurements of balls rolling down , Galileo firmly established that gravitational acceleration is the same for all objects. Galileo postulated that air resistance
In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding f ...

is the reason that objects with a low density and high surface area
The surface area of a Solid geometry, solid object is a measure of the total area that the Surface (mathematics), surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more ...

fall more slowly in an atmosphere. In 1604, Galileo correctly hypothesized that the distance of a falling object is proportional to the square
In Euclidean geometry
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematics , Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's method ...

of the time elapsed.
The relation of the distance of objects in free fall to the square of the time taken was confirmed by Italian Jesuits
The Society of Jesus ( la, Societas Iesu; abbreviated SJ), also known as the Jesuits (; la, Iesuitæ), is a religious order (Catholic), religious order of the Catholic Church headquartered in Rome. It was founded by Ignatius of Loyola and six co ...

and between 1640 and 1650. They also made a calculation of Earth's gravity
The gravity of Earth, denoted by , is the that is imparted to objects due to the combined effect of (from within ) and the (from the ).
In this acceleration is measured in (in symbols, /2 or m·s−2) or equivalently in per (N/kg or N· ...

by recording the oscillations of a pendulum.
Newton's theory of gravitation

In 1679,Robert Hooke
Robert Hooke FRS
FRS may also refer to:
Government and politics
* Facility Registry System, a centrally managed Environmental Protection Agency database that identifies places of environmental interest in the United States
* Family Resources ...

wrote to English mathematician Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician
A mathematician is someone who uses an extensive knowledge of mathematics
Mathematics (from Greek: ) includes the study of such topics a ...

of his hypothesis concerning orbital motion, which partly depends on an inverse-square force. In 1684, both Hooke and Newton told Edmond Halley
Edmond (or Edmund) Halley (; – ) was an English astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such ...

that they had proven the inverse-square law of planetary motion. Hooke refused to produce his proofs, but Newton produced ''De motu corporum in gyrum
:''For other works by a similar name see De Motu (disambiguation)''.
''De motu corporum in gyrum'' ('On the motion of bodies in an orbit') is the presumed title of a manuscript by Isaac Newton
Sir Isaac Newton (25 December 1642 – ...

'' ('On the motion of bodies in an orbit'), in which he derives Kepler's laws of planetary motion
In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the Copernican heliocentrism, heliocentric theory of Nicolaus Copernicus, repl ...

. Halley supported Newton's expansion of his work into the ''Philosophiæ Naturalis Principia Mathematica
(from Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman Republic, it bec ...

'' (''Mathematical Principles of Natural Philosophy''), in which he hypothesizes the inverse-square law of universal gravitation.
According to Newton, he "deduced that the forces which keep the planets in their orbs must 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: $$F\; =\; G\; \backslash frac,$$ where is the force, and are the masses of the objects interacting, is the distance between the centers of the masses and is the .
Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune
Neptune is the eighth and farthest-known Solar planet from the Sun. In the Solar System, it is the fourth-largest planet by diameter, the third-most-massive planet, and the densest giant planet. It is 17 times the mass of Earth, slightly mo ...

based on motions of Uranus
Uranus is the seventh planet from the Sun. Its name is a reference to the Greek god of the sky, Uranus, who, according to Greek mythology
Greek mythology is the body of myths originally told by the Ancient Greece, ancient Greeks, and ...

that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams
Prof John Couch Adams FRSE Royal Astronomical Society, FRAS LLD (; 5 June 1819 – 21 January 1892) was a British mathematician and astronomer. He was born in Laneast, near Launceston, Cornwall, and died in Cambridge.
His most famous achievement ...

and Urbain Le Verrier
Urbain Jean Joseph Le Verrier FRS (FOR) HFRSE
Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and Literature, letters, judged ...

predicted the general position of the planet, and Le Verrier's calculations are what led Johann Gottfried Galle
200px, Memorial plaque in Wittenberg
Johann Gottfried Galle (9 June 1812 – 10 July 1910) was a German astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the ...

to the discovery of Neptune.
A discrepancy in Mercury
Mercury usually refers to:
* Mercury (planet)
Mercury is the smallest planet in the Solar System and the closest to the Sun. Its orbit around the Sun takes 87.97 Earth days, the shortest of all the Sun's planets. It is named after the Roman g ...

'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
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity
The theo ...

's new theory of general relativity
General relativity, also known as the general theory of relativity, is the geometric
Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...

, which accounted for the small discrepancy in Mercury's orbit. This discrepancy was the advance in the perihelion
upright=1.15, The two-body system of interacting primary body (yellow); both are in elliptic orbits around their center of mass">common center of mass (or barycenter), (red +). ∗Periapsis and apoapsis as distances: The smallest and largest ...

of Mercury of 42.98 arcseconds per century.
Although Newton's theory has been superseded by Albert 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

Theequivalence principle
In the theory
A theory is a rational
Rationality is the quality or state of being rational – that is, being based on or agreeable to reason
Reason is the capacity of consciously making sense of things, applying logic
Logic (fr ...

, 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
Step or Steps may refer to:
General
* Stairs
* Walking
* Dance move, the building block of many dances
* Military step, a regular, ordered and synchronized walking of military formations
** Marching, refers to the organized, uniformed, steady and ...

, 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
In physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...

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

Ingeneral relativity
General relativity, also known as the general theory of relativity, is the geometric
Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...

, the effects of gravitation are ascribed to spacetime
In physics, spacetime is any mathematical model which fuses the three-dimensional space, three dimensions of space and the one dimension of time into a single four-dimensional manifold. Minkowski diagram, Spacetime diagrams can be used to visuali ...

curvature
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities an ...

instead of a force. The starting point for general relativity is the equivalence principle
In the theory
A theory is a rational
Rationality is the quality or state of being rational – that is, being based on or agreeable to reason
Reason is the capacity of consciously making sense of things, applying logic
Logic (fr ...

, 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
In geometry
Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space t ...

. 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 equations, simultaneous, nonlinear system, non-linear, differential equations. The solutions of the field equations are the components of the metric tensor (general relativity), 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 Circular symmetry, spherically symmetric non-rotation, rotating uncharged massive object. For compact enough objects, this solution generated a with a central gravitational singularity, 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 metric, 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 doubleevent horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. The term was coined by in the 1950s.
In 1784, proposed that in the vicinity of compact massive objects, gravity can be strong enough that even light ...

s.
* The Kerr metric, Kerr solution for rotating massive objects. This solution also produces black holes with multiple event horizons.
* The Kerr–Newman metric, Kerr-Newman solution for charged, rotating massive objects. This solution also produces black holes with multiple event horizons.
* The physical cosmology, cosmological Friedmann–Lemaître–Robertson–Walker metric, 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#Predecessors, 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 interferometer, 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.See W.Pauli, 1958, pp. 219–220 * The theory's prediction of frame dragging was consistent with the recent Gravity Probe B results. * General relativity predicts that light should lose photon energy, 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

An open question is whether it is possible to describe the small-scale interactions of gravity with the same framework asquantum mechanics
Quantum mechanics is a fundamental theory
A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with ...

. General relativity describes large-scale bulk properties whereas quantum mechanics is the framework to describe the smallest scale interactions of matter. Without modifications these frameworks are incompatible.
One path is to describe gravity in the framework of quantum field theory, which has been successful to accurately describe the other fundamental interaction
In physics
Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through Sp ...

s. The electromagnetic force arises from an exchange of virtual photons, where the QFT description of gravity is that there is an exchange of virtual particle, virtual gravitons. This description 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
Quantum gravity (QG) is a field of theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, n ...

(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/s, 1976, U.S. Government Printing Office, Washington, D.C., 1976. (Linked file is very large.) 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, Newton's 3rd Law, the Earth itself experiences a Newtons, 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 does not 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 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/s

Equations for a falling body near the surface of the Earth

Under an assumption of constant gravitational attraction,Newton's law of universal gravitation
Newton's law of universal gravitation is usually stated as that every particle
In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object to which can ...

simplifies to ''F'' = ''mg'', where ''m'' is the mass
Mass is the quantity
Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...

of the body and ''g'' is a constant vector with an average magnitude of 9.81 m/sGravity 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 itsorbit
In celestial mechanics, an orbit is the curved trajectory of an physical body, object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an satellite, artificial satellite around an object or po ...

because of the force of gravity acting upon it. Planets orbit stars, stars orbit bulge (astronomy), 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
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry
In particle physics, supersymmetry (SUSY) is a conjectured relationship between two basic c ...

or a gravitational singularity
A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravity
Gravity (), or gravitation, is a by which all things with or —including s, s, , and even —are attracted to (or ''gravitate ...

), along with ordinary space and time, developed during the Timeline of the formation of the Universe#Planck Epoch, Planck epoch (up to 10birth
Birth is the act or process of bearing or bringing forth offspring, also referred to in technical contexts as parturition. In mammals, the process is initiated by hormones which cause the muscular walls of the uterus to contract, expelling the fe ...

of the Universe), possibly from a primeval state (such as a false vacuum
In quantum field theory
In theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, natu ...

, quantum vacuum or virtual particle
In physics
Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior throug ...

), in a currently unknown manner.
Gravitational radiation

General relativity predicts that energy can be transported out of a system through gravitational radiation. Any accelerating matter can create curvatures in the space-time metric, which is how the gravitational radiation is transported away from the system. Co-orbiting objects can generate curvatures in space-time such as the Earth-Sun system, pairs of neutron stars, and pairs of black holes. Another astrophysical system predicted to lose energy in the form of gravitational radiation are exploding supernovae. The first indirect evidence for gravitational radiation was through measurements of the Hulse–Taylor binary in 1973. This system consists of a pulsar and neutron star in orbit around one another. Its orbital period has decreased since its initial discovery due to a loss of energy, which is consistent for the amount of energy loss due to gravitational radiation. This research was awarded the Nobel Prize in Physics in 1993. The first direct evidence for gravitational radiation was measured on 14 September 2015 by the LIGO detectors. The gravitational waves emitted during the collision of two black holes 1.3 billion-light years from Earth were measured. This observation confirms the theoretical predictions of Einstein and others that such waves 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. Neutron star and formation also create detectable amounts of gravitational radiation. This research was awarded the Nobel Prize in physics in 2017. , the gravitational radiation emitted by the Solar System is far too small to measure with current technology.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 the vacant point 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 Galaxy rotation curve, 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 groups and clusters, galaxy clusters show a similar pattern. Dark matter, which would interact through gravitation but not electromagnetically, would account for the discrepancy. Various Modified Newtonian dynamics, 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 Astronomical unit#Developments, 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 but originally proposed by Fatio and further elaborated by Georges-Louis Le Sage, based on a fluid-based explanation where a light gas fills the entire Universe. * Ritz's Equation, 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. * Kaluza–Klein theory, 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 whichgeneral relativity
General relativity, also known as the general theory of relativity, is the geometric
Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...

might arise from quantum field theory, quantum field theories of matter
*String theory (late 1960s)
* F(R) gravity, ƒ(R) gravity (1970)
* Horndeski's theory, Horndeski theory (1974)
* Supergravity (1976)
* 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 (physicist), John Moffat
*Tensor–vector–scalar gravity (TeVeS) (2004), a relativistic modification of MOND by Jacob Bekenstein
*Chameleon particle, Chameleon theory (2004) by Justin Khoury and Amanda Weltman.
* Pressuron, Pressuron theory (2013) by Olivier Minazzoli and Aurélien Hees.
*Conformal gravity
*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.
*Massive gravity, a theory where gravitons and gravitational waves have a non-zero mass
See also

* Anti-gravity, the idea of neutralizing or repelling gravity * Artificial gravity * Gauss's law for gravity * Gravitational potential * Gravitational wave * Kepler's third law, Kepler's third law of planetary motion * Micro-g environment, also called microgravity * Newton's laws of motion * Standard gravitational parameter * Weightlessness *Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity
The theo ...

*Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician
A mathematician is someone who uses an extensive knowledge of mathematics
Mathematics (from Greek: ) includes the study of such topics a ...

Footnotes

References

* * *Further reading

* *External links

* * {{Authority control Gravity, Acceleration Articles containing video clips Empirical laws