# Gravity

In physics, **gravity** (from Latin * gravitas* 'weight'^{[1]}) is a fundamental interaction which causes all things with mass or energy to be attracted (or *gravitate*) toward one another. Gravity is by far the weakest of the four fundamental interactions, approximately 10^{38} times weaker than the strong interaction, 10^{36} times weaker than the electromagnetic force and 10^{29} times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles.^{[2]} However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light.

On Earth, gravity gives weight to physical objects, and the Moon's gravity causes tides in the oceans. Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing the circulation of fluids in multicellular organisms. Investigation into the effects of weightlessness has shown that gravity may play a role in immune system function and cell differentiation within the human body.

The gravitational attraction between the original gaseous matter in the Universe allowed it to coalesce and form stars which eventually condensed 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 (proposed by Albert Einstein in 1915), which describes gravity not as a force, but as the curvature of spacetime, caused by the uneven distribution of mass, and causing masses to move along geodesic lines. The most extreme example of this curvature of spacetime is a black hole, from which nothing—not even light—can escape once past the black hole's event horizon.^{[3]} However, for most applications, gravity is well approximated by Newton's law of universal gravitation, which describes gravity as a force causing any two bodies to be attracted toward each other, with magnitude proportional to the product of their masses and inversely proportional to the square of the distance between them.

Current models of particle physics imply that the earliest instance of gravity in the Universe, possibly in the form of quantum gravity, supergravity or a gravitational singularity, along with ordinary space and time, developed during the Planck epoch (up to 10^{−43} seconds after the birth of the Universe), possibly from a primeval state, such as a false vacuum, quantum vacuum or virtual particle, in a currently unknown manner.^{[4]} Scientists are currently working to develop a theory of gravity consistent with quantum mechanics, a quantum gravity theory, which would allow gravity to be united in a common mathematical framework (a theory of everything) with the other three fundamental interactions of physics.

The nature and mechanism of gravity was explored by a wide range of ancient scholars. In Greece, Aristotle believed that objects fell towards the Earth because the Earth was the center of the Universe and attracted all of the mass in the Universe towards it. He also thought that the speed of a falling object should increase with its weight, a conclusion which was later shown to be false.^{[5]} While Aristotle's view was widely accepted throughout Ancient Greece, there were other thinkers such as Plutarch who correctly predicted that the attraction of gravity was not unique to the Earth.^{[6]}

Although he didn't understand gravity as a force, the ancient Greek philosopher Archimedes discovered the center of gravity of a triangle.^{[7]} 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.^{[8]}

In India, the mathematician-astronomer Aryabhata first identified gravity to explain why objects are not driven away from the Earth by the centrifugal force of the planet's rotation. Later, in the seventh century CE, Brahmagupta proposed the idea that gravity is an attractive force which draws objects to the Earth and used the term *gurutvākarṣaṇ* to describe it.^{[9]}^{[10]}^{[11]} This research has led some people to claim that Brahmagupta, not Isaac Newton, was responsible for "discovering" gravity.^{[12]}^{[13]}

In the ancient Middle East, gravity was a topic of fierce debate. The Persian intellectual Al-Biruni believed that the force of gravity was not unique to the Earth, and he correctly assumed that other heavenly bodies should exert a gravitational attraction as well.^{[14]} In contrast, Al-Khazini held the same position as Aristotle that all matter in the Universe is attracted to the center of the Earth.^{[15]}

In the mid-16th century, various European scientists experimentally disproved the Aristotelian notion that heavier objects fall at a faster rate.^{[16]} In particular, the Spanish Dominican priest Domingo de Soto wrote in 1551 that bodies in free fall uniformly accelerate.^{[16]} De Soto may have been influenced by earlier experiments conducted by other Dominican priests in Italy, including those by Benedetto Varchi, Francesco Beato, Luca Ghini, and Giovan Bellaso which contradicted Aristotle's teachings on the fall of bodies.^{[16]} The mid-16th century Italian physicist Giambattista Benedetti published papers claiming that, due to specific gravity, objects made of the same material but with different masses would fall at the same speed.^{[17]} With the 1586 Delft tower experiment, the Flemish physicist Simon Stevin observed that two cannonballs of differing sizes and weights fell at the same rate when dropped from a tower.^{[18]} Finally, in the late 16th century, Galileo Galilei performed his famous Leaning Tower of Pisa experiment in order to show once again that balls of different weights would fall at the same speed.^{[19]} Combining this knowledge with careful measurements of balls rolling down inclines, Galileo firmly established that gravitational acceleration is the same for all objects.^{[20]} Galileo postulated that air resistance is the reason that objects with a low density and high surface area fall more slowly in an atmosphere.

In 1604, Galileo correctly hypothesized that the distance of a falling object is proportional to the square of the time elapsed.^{[21]} This was later confirmed by Italian scientists Jesuits Grimaldi and Riccioli between 1640 and 1650. They also calculated the magnitude of the Earth's gravity by measuring the oscillations of a pendulum.^{[22]}

In 1684, Newton sent a manuscript to Edmond Halley titled *De motu corporum in gyrum ('On the motion of bodies in an orbit')*, which provided a physical justification for Kepler's laws of planetary motion.^{[23]} Halley was impressed by the manuscript an urged Newton to expand on it, and a few years later Newton published a groundbreaking book called *Philosophiæ Naturalis Principia Mathematica* (*Mathematical Principles of Natural Philosophy*). In this book, Newton described gravitation as a universal force, and claimed 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." This statement was later condensed into the following inverse-square law:

Newton's *Principia* was well-received by the scientific community, and his law of gravitation quickly spread across the European world.^{[24]} More than a century later, in 1821, his theory of gravitation rose to even greater prominence when it was used to predict the existence of Neptune. In that year, the French astronomer Alexis Bouvard used this theory to create a table modeling the orbit of Uranus, which was shown to differ significantly from the planet's actual trajectory. In order to explain this discrepancy, many astronomers speculated that there might be a large object beyond the orbit of Uranus which was disrupting Neptune's orbit. In 1846, the astronomers John Couch Adams and Urbain Le Verrier independently used Newton's law to predict Neptune's location in the night sky, and the planet was discovered there within a day.^{[25]}

Eventually, astronomers noticed an eccentricity in the orbit of the planet Mercury which could not be explained by Newton's theory: the perihelion of the orbit was increasing by about 42.98 arcseconds per century. The most obvious explanation for this discrepancy was an as-yet-undiscovered celestial body (such as a planet orbiting the Sun even closer than Mercury), but all efforts to find such a body turned out to be fruitless. Finally, in 1915, Albert Einstein developed a theory of general relativity which was able to accurately model Mercury's orbit.^{[26]}

In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of a force. Einstein began to toy with this idea in the form of the equivalence principle, a discovery which he later described as "the happiest thought of my life."^{[27]} In this theory, free fall is considered to be equivalent to inertial motion, meaning that free-falling inertial objects are accelerated relative to non-inertial observers on the ground.^{[28]}^{[29]} In contrast to Newtonian physics, Einstein believed that it was possible for this acceleration to occur without any force being applied to the object.

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. As in Newton's first law of motion, Einstein believed that a force applied to an object would cause it to deviate from a geodesic. For instance, people standing on the surface of the Earth are prevented from following a geodesic path because the mechanical resistance of the Earth exerts an upward force on them. This explains why moving along the geodesics in spacetime is considered inertial.

Einstein's description of gravity was quickly accepted by the majority of physicists, as it was able to explain a wide variety of previously baffling experimental results.^{[30]} In the coming years, a wide range of experiments provided additional support for the idea of general relativity.^{[31]}^{[32]}^{[33]}^{[34]} Today, Einstein's theory of relativity is used for all gravitational calculations where absolute precision is desired, although Newton's inverse-square law continues to be a useful and fairly accurate approximation.^{[35]}

In modern physics, general relativity remains the framework for the understanding of gravity. Physicists continue to work to find solutions to the Einstein field equations that form the basis of general relativity, while some scientists have speculated that general relativity may not be applicable at all in certain scenarios.^{[35]}

Einstein discovered the field equations of general relativity, which relate the presence of matter and the curvature of spacetime and are named after him. The Einstein field equations are a set of 10 simultaneous, non-linear, differential equations. The solutions of the field equations are the components of the metric tensor of spacetime. A metric tensor describes a geometry of spacetime. The geodesic paths for a spacetime are calculated from the metric tensor.

An open question is whether it is possible to describe the small-scale interactions of gravity with the same framework as quantum mechanics. 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.^{[44]}

One path is to describe gravity in the framework of quantum field theory, which has been successful to accurately describe the other fundamental interactions. The electromagnetic force arises from an exchange of virtual photons, where the QFT description of gravity is that there is an exchange of virtual gravitons.^{[45]}^{[46]} This description reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length,^{[44]} where a more complete theory of quantum gravity (or a new approach to quantum mechanics) is required.

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.^{[47]} 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.^{[48]} 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).

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.^{[51]} 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".^{[52]}

Assuming the standardized value for g and ignoring air resistance, this means that an object falling freely near the Earth's surface increases its velocity by 9.80665 m/s (32.1740 ft/s or 22 mph) for each second of its descent. Thus, an object starting from rest will attain a velocity of 9.80665 m/s (32.1740 ft/s) after one second, approximately 19.62 m/s (64.4 ft/s) after two seconds, and so on, adding 9.80665 m/s (32.1740 ft/s) to each resulting velocity. Also, again ignoring air resistance, any and all objects, when dropped from the same height, will hit the ground at the same time.

According to Newton's 3rd Law, the Earth itself experiences a force equal in magnitude and opposite in direction to that which it exerts on a falling object. This means that the Earth also accelerates towards the object until they collide. Because the mass of the Earth is huge, however, the acceleration imparted to the Earth by this opposite force is negligible in comparison to the object's. If the object 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:^{[53]} (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.

Under an assumption of constant gravitational attraction, Newton's law of universal gravitation simplifies to *F* = *mg*, where *m* is the mass of the body and *g* is a constant vector with an average magnitude of 9.81 m/s^{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 1⁄20 of a second the ball drops one unit of distance (here, a unit is about 12 mm); by 2⁄20 it has dropped at total of 4 units; by 3⁄20, 9 units and so on.

The application of Newton's law of gravity has enabled the acquisition of much of the detailed information we have about the planets in the Solar System, the mass of the Sun, and details of quasars; even the existence of dark matter is inferred using Newton's law of gravity. Although we have not traveled to all the planets nor to the Sun, we know their masses. These masses are obtained by applying the laws of gravity to the measured characteristics of the orbit. In space an object maintains its orbit because of the force of gravity acting upon it. Planets orbit stars, stars orbit galactic centers, galaxies orbit a center of mass in clusters, and clusters orbit in superclusters. The force of gravity exerted on one object by another is directly proportional to the product of those objects' masses and inversely proportional to the square of the distance between them.

The earliest gravity (possibly in the form of quantum gravity, supergravity or a gravitational singularity), along with ordinary space and time, developed during the Planck epoch (up to 10^{−43} seconds after the birth of the Universe), possibly from a primeval state (such as a false vacuum, quantum vacuum or virtual particle), in a currently unknown manner.^{[4]}

General relativity predicts that energy can be transported out of a system through gravitational radiation. Any accelerating matter can create curvatures in the spacetime metric, which is how the gravitational radiation is transported away from the system. Co-orbiting objects can generate curvatures in spacetime 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.^{[55]}^{[56]} 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.^{[57]} Neutron star and black hole formation also create detectable amounts of gravitational radiation.^{[58]} This research was awarded the Nobel Prize in physics in 2017.^{[59]}

As of 2020, the gravitational radiation emitted by the Solar System is far too small to measure with current technology.

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.^{[60]} 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.^{[61]}

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.^{[62]}

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.