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Gravity (), or gravitation, is a by which all things with or —including s, s, , and even —are attracted to (or ''gravitate'' toward) one another. , gravity gives to s, and the causes the s of the oceans. The gravitational attraction of the original gaseous matter present in the caused it to begin 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 (proposed by in 1915), which describes gravity not as a force, but as a consequence of masses moving along lines in a curved 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 . However, for most applications, gravity is well approximated by , which describes gravity as a causing any two bodies to be attracted toward each other, with magnitude to the product of their masses and to the of the between them. Gravity is the weakest of the four s of physics, approximately 1038 times weaker than the , 1036 times weaker than the and 1029 times weaker than the . As a consequence, it has no significant influence at the level of subatomic particles. In contrast, it is the dominant interaction at the , and is the cause of the formation, shape and () of . Current models of imply that the earliest instance of gravity in the Universe, possibly in the form of , or a , along with ordinary and , developed during the (up to 10−43 seconds after the of the Universe), possibly from a primeval state, such as a , or , in a currently unknown manner. – discusses "" and "" at the of the Universe Attempts to develop a theory of gravity consistent with , a theory, which would allow gravity to be united in a common mathematical framework (a ) with the other three fundamental interactions of physics, are a current area of research.

# History of gravitational theory

## Ancient world

The ancient Greek philosopher discovered the 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 in ' postulated that gravity of an object did not depend on weight but its "nature". The Indian mathematician-astronomer first identified gravity to explain why objects do not spin out when the Earth rotates, and described gravity as an attractive force and used the term ' for gravity.

## Scientific revolution

In the mid-16th century, various Europeans experimentally disproved the notion that heavier objects at a faster rate. The mid-16th century Italian physicist published papers claiming that, due to , objects of the same material but different weights would fall at the same speed. With the 1586 the physicist 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, demonstrated (perhaps as a ) 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 is the reason that objects with a low density and high fall more slowly in an atmosphere. In 1604, Galileo correctly hypothesized that the distance of a falling object is proportional to the 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 and between 1640 and 1650. They also made a calculation of by recording the oscillations of a pendulum.

## Newton's theory of gravitation

In 1679, wrote to English mathematician of his hypothesis concerning orbital motion, which partly depends on an force. In 1684, both Hooke and Newton told that they had proven the inverse-square law of planetary motion. Hooke refused to produce his proofs, but Newton produced ' ('On the motion of bodies in an orbit'), in which he derives . Halley supported Newton's expansion of his work into the ' (''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: $F = G \frac,$ 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 based on motions of that could not be accounted for by the actions of the other planets. Calculations by both and predicted the general position of the planet, and Le Verrier's calculations are what led to the discovery of Neptune. A discrepancy in '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 's new theory of , which accounted for the small discrepancy in Mercury's orbit. This discrepancy was the advance in the of Mercury of 42.98 arcseconds per century. Although Newton's theory has been superseded by Albert Einstein's general relativity, most modern gravitational calculations are still made using Newton's theory because it is simpler to work with and it gives sufficiently accurate results for most applications involving sufficiently small masses, speeds and energies.

## Equivalence principle

The , explored by a succession of researchers including Galileo, , 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 , 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 depends only on its initial position and velocity, and is independent of its composition.'' * The Einsteinian equivalence principle: ''The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.'' * The strong equivalence principle requiring both of the above.

## General relativity

In , the effects of gravitation are ascribed to instead of a force. The starting point for general relativity is the , 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 , 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 . 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 s of general relativity, which relate the presence of matter and the curvature of spacetime and are named after him. The are a set of 10 , , s. The solutions of the field equations are the components of the 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 , which describes spacetime surrounding a non- uncharged massive object. For compact enough objects, this solution generated a with a central . For radial distances from the center which are much greater than the , the accelerations predicted by the Schwarzschild solution are practically identical to those predicted by Newton's theory of gravity. * The , in which the central object has an electrical charge. For charges with a length which are less than the geometrized length of the mass of the object, this solution produces black holes with double s. * The for rotating massive objects. This solution also produces black holes with multiple event horizons. * The for charged, rotating massive objects. This solution also produces black holes with multiple event horizons. * The , which predicts the expansion of the Universe.

### Tests

The included the following: * General relativity accounts for the anomalous . * The prediction that time runs slower at lower potentials () has been confirmed by the (1959), the , and the . * The prediction of the deflection of light was first confirmed by from his observations during the . 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 s passing behind the Sun have more accurately and consistently confirmed the deflection of light to the degree predicted by general relativity. See also . * The passing close to a massive object was first identified by in 1964 in interplanetary spacecraft signals. * has been indirectly confirmed through studies of binary s. On 11 February 2016, the and collaborations announced the first observation of a gravitational wave. * in 1922 found that Einstein equations have non-stationary solutions (even in the presence of the ). In 1927 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 in 1929 confirmed this prediction.See W.Pauli, 1958, pp. 219–220 * The theory's prediction of was consistent with the recent results. * General relativity predicts that light should lose when traveling away from massive bodies through . 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 as . 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 , which has been successful to accurately describe the other s. The electromagnetic force arises from an exchange of virtual s, where the QFT description of gravity is that there is an exchange of s. This description reproduces general relativity in the . However, this approach fails at short distances of the order of the , where a more complete theory of (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 value is defined by the , under the (SI). That value, denoted ''g'', is ''g'' = 9.80665 m/s2 (32.1740 ft/s2). The standard value of 9.80665 m/s2 is the one originally adopted by the International Committee on Weights and Measures in 1901 for 45° latitude, even though it has been shown to be too high by about five parts in ten thousand.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 , the Earth itself experiences a 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 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 caused by the Earth's rotation and because points on the equator are furthest from the center of the Earth. The force of gravity varies with latitude and increases from about 9.780 m/s2 at the Equator to about 9.832 m/s2 at the poles.

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

Under an assumption of constant gravitational attraction, simplifies to ''F'' = ''mg'', where ''m'' is the of the body and ''g'' is a constant vector with an average magnitude of 9.81 m/s2 on Earth. This resulting force is the object's weight. The acceleration due to gravity is equal to this ''g''. An initially stationary object which is allowed to fall freely under gravity drops a distance which is proportional to the square of the elapsed time. The image on the right, spanning half a second, was captured with a stroboscopic flash at 20 flashes per second. During the first 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 , ''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 $h = \tfrac$ for the maximum height reached by a vertically projected body with initial velocity ''v'' is useful for small heights and small initial velocities only.

## Gravity and astronomy

The application of Newton's law of gravity has enabled the acquisition of much of the detailed information we have about the planets in the Solar System, the mass of the Sun, and details of s; even the existence of is inferred using Newton's law of gravity. Although we have not traveled to all the planets nor to the Sun, we know their masses. These masses are obtained by applying the laws of gravity to the measured characteristics of the orbit. In space an object maintains its because of the force of gravity acting upon it. Planets orbit stars, stars orbit , galaxies orbit a center of mass in clusters, and clusters orbit in 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. The earliest gravity (possibly in the form of quantum gravity, or a ), along with ordinary space and time, developed during the (up to 10−43 seconds after the of the Universe), possibly from a primeval state (such as a , or ), in a currently unknown manner.

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 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 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. 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 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 s 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 in February 2013. In October 2017, the 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 where stars on the outskirts are moving faster than they should according to the observed distributions of normal matter. Galaxies within show a similar pattern. , which would interact through gravitation but not electromagnetically, would account for the discrepancy. Various have also been proposed. * : Various spacecraft have experienced greater acceleration than expected during maneuvers. * Accelerating expansion: The seems to be speeding up. 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 : Recent measurements indicate that 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 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 suggest that hydrogen clouds are more clumped together at certain scales than expected and, like , may indicate that gravity falls off slower than inverse-squared at certain distance scales.

# Alternative theories

## Historical alternative theories

* * (1784) also called LeSage gravity but originally proposed by Fatio and further elaborated by , based on a fluid-based explanation where a light gas fills the entire Universe. * , ''Ann. Chem. Phys.'' 13, 145, (1908) pp. 267–271, Weber-Gauss electrodynamics applied to gravitation. Classical advancement of perihelia. * (1912, 1913), an early competitor of general relativity. * (1921) * (1922), another early competitor of general relativity.

## Modern alternative theories

* of gravity (1961) * (1967), a proposal by according to which might arise from of matter * (late 1960s) * (1970) * (1974) * (1976) * In the (MOND) (1981), proposes a modification of of motion for small accelerations * The theory of gravity (1982) by G.A. Barber in which the Brans-Dicke theory is modified to allow mass creation * (1988) by , , and * (NGT) (1994) by * (TeVeS) (2004), a relativistic modification of MOND by * (2004) by and . * (2013) by and . * *, gravity arising as an emergent phenomenon from the thermodynamic concept of entropy. *In the the gravity and curved space-time arise as a mode of non-relativistic background . *, a theory where gravitons and gravitational waves have a non-zero mass

* , the idea of neutralizing or repelling gravity * * * * * * , also called microgravity * * * * *

* * *