Gravitational interaction
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In physics, gravity (), also known as gravitation or a gravitational interaction, is a
fundamental interaction In physics, the fundamental interactions or fundamental forces are interactions in nature that appear not to be reducible to more basic interactions. There are four fundamental interactions known to exist: * gravity * electromagnetism * weak int ...
, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force between objects and the Earth. This force is dominated by the combined gravitational interactions of particles but also includes effect of the Earth's rotation. Gravity gives
weight In science and engineering, the weight of an object is a quantity associated with the gravitational force exerted on the object by other objects in its environment, although there is some variation and debate as to the exact definition. Some sta ...
to
physical object In natural language and physical science, a physical object or material object (or simply an object or body) is a contiguous collection of matter, within a defined boundary (or surface), that exists in space and time. Usually contrasted with ...
s and is essential to understanding the mechanisms responsible for surface water
waves United States Naval Reserve (Women's Reserve), better known as the WAVES (for Women Accepted for Volunteer Emergency Service), was the women's branch of the United States Naval Reserve during World War II. It was established on July 21, 1942, ...
and lunar
tide Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables ...
s. Gravity also has many important biological functions, helping to guide the growth of plants through the process of
gravitropism Gravitropism (also known as geotropism) is a coordinated process of differential growth by a plant in response to gravity pulling on it. It also occurs in fungi. Gravity can be either "artificial gravity" or natural gravity. It is a general feat ...
and influencing the circulation of fluids in
multicellular organism A multicellular organism is an organism that consists of more than one cell (biology), cell, unlike unicellular organisms. All species of animals, Embryophyte, land plants and most fungi are multicellular, as are many algae, whereas a few organism ...
s. The gravitational attraction between primordial
hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
and clumps of
dark matter In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relat ...
in the early
universe The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from s ...
caused the hydrogen gas to coalesce, eventually condensing and fusing to form stars. At larger scales this results in galaxies and clusters, so gravity is a primary driver for the large-scale structures in the universe. Gravity has an infinite range, although its effects become weaker as objects get farther away. Gravity is accurately described by the
general theory of relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physi ...
, proposed by
Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
in 1915, which describes gravity in terms of the
curvature In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
of
spacetime In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...
, caused by the uneven distribution of mass. The most extreme example of this curvature of spacetime is a
black hole A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...
, 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 outside observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive c ...
. However, for most applications, gravity is well approximated by
Newton's law of universal gravitation Newton's law of universal gravitation describes gravity as a force by stating that every particle attracts every other particle in the universe with a force that is Proportionality (mathematics)#Direct proportionality, proportional to the product ...
, which describes gravity as a
force In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...
causing any two bodies to be attracted toward each other, with magnitude proportional to the product of their masses and
inversely proportional In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. The ratio is called ''coefficient of proportionality'' (or ''proportionality ...
to the
square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...
of the
distance Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two co ...
between them. Scientists are currently working to develop a theory of gravity consistent with
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
, a quantum gravity theory, which would allow gravity to be united in a common mathematical framework (a
theory of everything A theory of everything (TOE), final theory, ultimate theory, unified field theory, or master theory is a hypothetical singular, all-encompassing, coherent theoretical physics, theoretical framework of physics that fully explains and links togeth ...
) with the other three fundamental interactions of physics. Although experiments are now being conducted to prove (or disprove) whether gravity is quantum, it is not known with certainty.


Definitions

Gravity is the word used to describe both a fundamental physical interaction and the observed consequences of that interaction on macroscopic objects on Earth. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the
strong interaction In nuclear physics and particle physics, the strong interaction, also called the strong force or strong nuclear force, is one of the four known fundamental interaction, fundamental interactions. It confines Quark, quarks into proton, protons, n ...
, 1036 times weaker than the
electromagnetic force In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interac ...
, and 1029 times weaker than the
weak interaction In nuclear physics and particle physics, the weak interaction, weak force or the weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, and gravitation. It is th ...
. As a result, it has no significant influence at the level of
subatomic particle In physics, a subatomic particle is a particle smaller than an atom. According to the Standard Model of particle physics, a subatomic particle can be either a composite particle, which is composed of other particles (for example, a baryon, lik ...
s. However, gravity is the most significant interaction between objects at the
macroscopic scale The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. Overview When applied to physical phenom ...
, and it determines the motion of
planet A planet is a large, Hydrostatic equilibrium, rounded Astronomical object, astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets b ...
s,
star A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...
s,
galaxies A galaxy is a system of stars, stellar remnants, interstellar gas, dust, and dark matter bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar Sys ...
, and even
light Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...
. Gravity, as the gravitational attraction at the surface of a planet or other celestial body, may also include the
centrifugal force Centrifugal force is a fictitious force in Newtonian mechanics (also called an "inertial" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It appears to be directed radially away from the axi ...
resulting from the planet's rotation .


History


Ancient world

The nature and mechanism of gravity were explored by a wide range of ancient scholars. In
Greece Greece, officially the Hellenic Republic, is a country in Southeast Europe. Located on the southern tip of the Balkan peninsula, it shares land borders with Albania to the northwest, North Macedonia and Bulgaria to the north, and Turkey to th ...
,
Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
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 that was later shown to be false. While Aristotle's view was widely accepted throughout Ancient Greece, there were other thinkers such as
Plutarch Plutarch (; , ''Ploútarchos'', ; – 120s) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo (Delphi), Temple of Apollo in Delphi. He is known primarily for his ''Parallel Lives'', ...
who correctly predicted that the attraction of gravity was not unique to the Earth. Although he did not understand gravity as a force, the ancient Greek philosopher
Archimedes Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenis ...
discovered the
center of gravity In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. For ...
of a triangle. He 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. Two centuries later, the Roman engineer and architect
Vitruvius Vitruvius ( ; ; –70 BC – after ) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work titled . As the only treatise on architecture to survive from antiquity, it has been regarded since the Renaissan ...
contended in his ''
De architectura (''On architecture'', published as ''Ten Books on Architecture'') is a treatise on architecture written by the Ancient Rome, Roman architect and military engineer Vitruvius, Marcus Vitruvius Pollio and dedicated to his patron, the emperor Caesa ...
'' that gravity is not dependent on a substance's weight but rather on its "nature". In the 6th century CE, the
Byzantine The Byzantine Empire, also known as the Eastern Roman Empire, was the continuation of the Roman Empire centred on Constantinople during late antiquity and the Middle Ages. Having survived the events that caused the fall of the Western Roman E ...
Alexandrian scholar
John Philoponus John Philoponus ( Greek: ; , ''Ioánnis o Philóponos''; c. 490 – c. 570), also known as John the Grammarian or John of Alexandria, was a Coptic Miaphysite philologist, Aristotelian commentator and Christian theologian from Alexandria, Byza ...
proposed the theory of impetus, which modifies Aristotle's theory that "continuation of motion depends on continued action of a force" by incorporating a causative force that diminishes over time. In 628 CE, the
India India, officially the Republic of India, is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area; the List of countries by population (United Nations), most populous country since ...
n mathematician and astronomer
Brahmagupta Brahmagupta ( – ) was an Indian Indian mathematics, mathematician and Indian astronomy, astronomer. He is the author of two early works on mathematics and astronomy: the ''Brāhmasphuṭasiddhānta'' (BSS, "correctly established Siddhanta, do ...
proposed the idea that gravity is an attractive force that draws objects to the Earth and used the term '' gurutvākarṣaṇ'' to describe it. In the ancient
Middle East The Middle East (term originally coined in English language) is a geopolitical region encompassing the Arabian Peninsula, the Levant, Turkey, Egypt, Iran, and Iraq. The term came into widespread usage by the United Kingdom and western Eur ...
, gravity was a topic of fierce debate. The Persian intellectual
Al-Biruni Abu Rayhan Muhammad ibn Ahmad al-Biruni (; ; 973after 1050), known as al-Biruni, was a Khwarazmian Iranian scholar and polymath during the Islamic Golden Age. He has been called variously "Father of Comparative Religion", "Father of modern ...
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. In contrast,
Al-Khazini Abū al-Fath Abd al-Rahman Mansūr al-Khāzini or simply al-Khāzini (, flourished 1115–1130) was an Iranian astronomer, mechanician and physicist of Byzantine Greek origin who lived during the Seljuk Empire. His astronomical tables, written ...
held the same position as Aristotle that all matter in the
Universe The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from s ...
is attracted to the center of the Earth.


Scientific revolution

In the mid-16th century, various European scientists experimentally disproved the Aristotelian notion that heavier objects fall at a faster rate. In particular, the
Spanish Spanish might refer to: * Items from or related to Spain: **Spaniards are a nation and ethnic group indigenous to Spain **Spanish language, spoken in Spain and many countries in the Americas **Spanish cuisine **Spanish history **Spanish culture ...
Dominican priest Domingo de Soto wrote in 1551 that bodies in
free fall In classical mechanics, free fall is any motion of a physical object, body where gravity is the only force acting upon it. A freely falling object may not necessarily be falling down in the vertical direction. If the common definition of the word ...
uniformly accelerate. 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 Luca Ghini ( Casalfiumanese, 1490 – Bologna, 4 May 1556) was an Italian physician and botanist, notable as the creator of the first recorded herbarium, as well as the first botanical garden in Europe. Biography Ghini was born in Casalfiumanese ...
, and Giovan Bellaso which contradicted Aristotle's teachings on the fall of bodies. The mid-16th century Italian physicist
Giambattista Benedetti Giambattista (Gianbattista) Benedetti (14 August 1530 – 20 January 1590) was an Italian mathematician from Venice who was also interested in physics, mechanics, the construction of sundials, and the Music psychology, science of music. Sci ...
published papers claiming that, due to
specific gravity Relative density, also called specific gravity, is a dimensionless quantity defined as the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for solids and liquids is nea ...
, objects made of the same material but with different masses would fall at the same speed. With the 1586 Delft tower experiment, the Flemish physicist
Simon Stevin Simon Stevin (; 1548–1620), sometimes called Stevinus, was a County_of_Flanders, Flemish mathematician, scientist and music theorist. He made various contributions in many areas of science and engineering, both theoretical and practical. He a ...
observed that two cannonballs of differing sizes and weights fell at the same rate when dropped from a tower. In the late 16th century,
Galileo Galilei Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei ( , , ) or mononymously as Galileo, was an Italian astronomer, physicist and engineer, sometimes described as a poly ...
's careful measurements of balls rolling down inclines allowed him to firmly establish that gravitational acceleration is the same for all objects. Galileo postulated that
air resistance In fluid dynamics, drag, sometimes referred to as fluid resistance, is a force acting opposite to the direction of motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers, two solid surfaces, or b ...
is the reason that objects with a low density and high
surface area The surface area (symbol ''A'') of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the d ...
fall more slowly in an atmosphere. In his 1638 work ''
Two New Sciences The ''Discourses and Mathematical Demonstrations Relating to Two New Sciences'' ( ) published in 1638 was Galileo Galilei's final book and a scientific testament covering much of his work in physics over the preceding thirty years. It was writ ...
'' Galileo proved that that the distance traveled by a falling object is proportional to the
square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...
of the time elapsed. His method was a form of graphical numerical integration since concepts of algebra and calculus were unknown at the time. This was later confirmed by Italian scientists
Jesuits The Society of Jesus (; abbreviation: S.J. or SJ), also known as the Jesuit Order or the Jesuits ( ; ), is a religious order (Catholic), religious order of clerics regular of pontifical right for men in the Catholic Church headquartered in Rom ...
Grimaldi and Riccioli between 1640 and 1650. They also calculated the magnitude of the Earth's gravity by measuring the oscillations of a pendulum. Galileo also broke with incorrect ideas of Aristotelian philosophy by regarding
inertia Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics, and described by Isaac Newto ...
as persistence of motion, not a tendency to come to rest. By considering that the laws of physics appear identical on a moving ship to those on land, Galileo developed the concepts of
reference frame In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system, whose origin, orientation, and scale have been specified in physical space. It is based on a set of reference points, defined as geometric ...
and the
principle of relativity In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference. For example, in the framework of special relativity, the Maxwell equations ...
. These concepts would become central to Newton's mechanics, only to be transformed in Einstein's theory of gravity, the general theory of relativity.
Johannes Kepler Johannes Kepler (27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, Natural philosophy, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best know ...
, in his 1609 book Astronomia nova described gravity as a mutual attraction, claiming that if the Earth and Moon were not held apart by some force they would come together. He recognized that mechanical forces cause action, creating a kind of celestial machine. On the other hand Kepler viewed the force of the Sun on the planets as magnetic and acting tangential to their orbits and he assumed with Aristotle that inertia meant objects tend to come to rest.Dijksterhuis, E. J. (1954). History of Gravity and Attraction before Newton. Cahiers d'Histoire Mondiale. Journal of World History. Cuadernos de Historia Mundial, 1(4), 839. In 1666,
Giovanni Alfonso Borelli Giovanni Alfonso Borelli (; 28 January 1608 – 31 December 1679) was a Renaissance Italy, Italian physiologist, physicist, and mathematician who is often described as the father of biomechanics. He contributed to the modern principle of scientif ...
avoided the key problems that limited Kepler. By Borelli's time the concept of inertia had its modern meaning as the tendency of objects to remain in uniform motion and he viewed the Sun as just another heavenly body. Borelli developed the idea of mechanical equilibrium, a balance between inertia and gravity. Newton cited Borelli's influence on his theory. In 1657,
Robert Hooke Robert Hooke (; 18 July 16353 March 1703) was an English polymath who was active as a physicist ("natural philosopher"), astronomer, geologist, meteorologist, and architect. He is credited as one of the first scientists to investigate living ...
published his ''
Micrographia ''Micrographia: or Some Physiological Descriptions of Minute Bodies Made by Magnifying Glasses. With Observations and Inquiries Thereupon'' is a historically significant book by Robert Hooke about his observations through various lenses. It wa ...
'', in which he hypothesized that the Moon must have its own gravity. In a communication to the Royal Society in 1666 and his 1674 Gresham lecture, ''An Attempt to prove the Annual Motion of the Earth'', Hooke took the important step of combining related hypothesis and then forming predictions based on the hypothesis. He wrote: Hooke was an important communicator who helped reformulate the scientific enterprise. He was one of the first professional scientists and worked as the then-new
Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
's curator of experiments for 40 years. However his valuable insights remained hypotheses since he was unable to convert them in to a mathematical theory of gravity and work out the consequences. For this he turned to Newton, writing him a letter in 1679, outlining a model of planetary motion in a void or vacuum due to attractive action at a distance. This letter likely turned Newton's thinking in a new direction leading to his revolutionary work on gravity. When Newton reported his results in 1686, Hooke claimed the inverse square law portion was his "notion".


Newton's theory of gravitation

Before 1684, scientists including
Christopher Wren Sir Christopher Wren FRS (; – ) was an English architect, astronomer, mathematician and physicist who was one of the most highly acclaimed architects in the history of England. Known for his work in the English Baroque style, he was ac ...
,
Robert Hooke Robert Hooke (; 18 July 16353 March 1703) was an English polymath who was active as a physicist ("natural philosopher"), astronomer, geologist, meteorologist, and architect. He is credited as one of the first scientists to investigate living ...
and
Edmund Halley Edmond (or Edmund) Halley (; – ) was an English astronomer, mathematician and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720. From an observatory he constructed on Saint Helena in 1676–77, H ...
determined that Kepler's third law, relating to planetary orbital periods, would prove the
inverse square law In science, an inverse-square law is any scientific law stating that the observed "intensity" of a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cau ...
if the orbits where circles. However the orbits were known to be ellipses. At Halley's suggestion, Newton tackled the problem and was able to prove that ellipses also proved the inverse square relation from Kepler's observations. In 1684,
Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...
sent a manuscript to
Edmond Halley Edmond (or Edmund) Halley (; – ) was an English astronomer, mathematician and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720. From an observatory he constructed on Saint Helena in 1676–77, Hal ...
titled ''
De motu corporum in gyrum (from Latin: "On the motion of bodies in an orbit"; abbreviated ) is the presumed title of a manuscript by Isaac Newton sent to Edmond Halley in November 1684. The manuscript was prompted by a visit from Halley earlier that year when he had qu ...
('On the motion of bodies in an orbit')'', which provided a physical justification for
Kepler's laws of planetary motion In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler in 1609 (except the third law, which was fully published in 1619), describe the orbits of planets around the Sun. These laws replaced circular orbits and epicycles in ...
. Halley was impressed by the manuscript and urged Newton to expand on it, and a few years later Newton published a groundbreaking book called ''
Philosophiæ Naturalis Principia Mathematica (English: ''The Mathematical Principles of Natural Philosophy''), often referred to as simply the (), is a book by Isaac Newton that expounds Newton's laws of motion and his law of universal gravitation. The ''Principia'' is written in Lati ...
'' (''Mathematical Principles of Natural Philosophy''). The revolutionary aspect of Newton's theory of gravity was the unification of Earth-bound observations of acceleration with celestial mechanics. In his book, Newton described gravitation as a universal force, and claimed that it operated on objects "according to the quantity of solid matter which they contain and propagates on all sides to immense distances always at the inverse square of the distances". This formulation had two important parts. First was equating inertial mass and gravitational mass. Newton's 2nd law defines force via F=ma for inertial mass, his law of gravitational force uses the same mass. Newton did experiments with pendulums to verify this concept as best he could. The second aspect of Newton's formulation was the inverse square of distance. This aspect was not new: the astronomer Ismaël Bullialdus proposed it around 1640. Seeking proof, Newton made quantitative analysis around 1665, considering the period and distance of the Moon's orbit and considering the timing of objects falling on Earth. Newton did not publish these results at the time because he could not prove that the Earth's gravity acts as if all its mass were concentrated at its center. That proof took him twenty years. Newton's ''Principia'' was well received by the scientific community, and his law of gravitation quickly spread across the European world. 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 Neptune is the eighth and farthest known planet from the Sun. It is the List of Solar System objects by size, fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 t ...
. In that year, the French astronomer Alexis Bouvard used this theory to create a table modeling the orbit of
Uranus Uranus is the seventh planet from the Sun. It is a gaseous cyan-coloured ice giant. Most of the planet is made of water, ammonia, and methane in a Supercritical fluid, supercritical phase of matter, which astronomy calls "ice" or Volatile ( ...
, 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 its orbit. In 1846, the astronomers
John Couch Adams John Couch Adams ( ; 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 was predicting the existence and position o ...
and
Urbain Le Verrier Urbain Jean Joseph Le Verrier (; 11 March 1811 – 23 September 1877) was a French astronomer and mathematician who specialized in celestial mechanics and is best known for predicting the existence and position of Neptune using only mathematics. ...
independently used Newton's law to predict Neptune's location in the night sky, and the planet was discovered there within a day. Newton's formulation was later condensed into the inverse-square law: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
gravitational constant The gravitational constant is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general relativity, theory of general relativity. It ...
While is also called
Newton's constant The gravitational constant is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity. It is also known as t ...
, Newton did not use this constant or formula, he only discussed proportionality. But this allowed him to come to an astounding conclusion we take for granted today: the gravity of the Earth on the Moon is the same as the gravity of the Earth on an apple:M_\text \propto a_\textR_\text^2 = a_\textR_\text^2 Using the values known at the time, Newton was able to verify this form of his law. The value of was eventually measured by
Henry Cavendish Henry Cavendish ( ; 10 October 1731 – 24 February 1810) was an English experimental and theoretical chemist and physicist. He is noted for his discovery of hydrogen, which he termed "inflammable air". He described the density of inflammable a ...
in 1797.


Einstein's general relativity

Eventually, astronomers noticed an eccentricity in the orbit of the planet Mercury which could not be explained by Newton's theory: the
perihelion An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides perta ...
of the orbit was increasing by about 42.98
arcseconds A minute of arc, arcminute (abbreviated as arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of a degree. Since one degree is of a turn, or complete rotation, one arcminute is of a tu ...
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. In 1915,
Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
developed a theory of
general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
which was able to accurately model Mercury's orbit. Einstein's theory brought two other ideas with independent histories into the physical theories of gravity: the
principle of relativity In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference. For example, in the framework of special relativity, the Maxwell equations ...
and
non-Euclidean geometry In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean ge ...
The principle of relativity, introduced by Galileo and used as a foundational principle by Newton, lead to a long and fruitless search for a
luminiferous aether Luminiferous aether or ether (''luminiferous'' meaning 'light-bearing') was the postulated Transmission medium, medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empt ...
after
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, Electrical network, electr ...
demonstrated that light propagated at a fixed speed independent of reference frame. In Newton's mechanics, velocities add: a cannon ball shot from a moving ship would travel with a trajectory which included the motion of the ship. Since light speed was fixed, it was assumed to travel in a fixed, absolute medium. Many experiments sought to reveal this medium but failed and in 1905 Einstein's
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Ele ...
theory showed the aether was not needed. Special relativity proposed that mechanics be reformulated to use the
Lorentz transformation In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a Frame of Reference, coordinate frame in spacetime to another frame that moves at a constant vel ...
already applicable to light rather than the
Galilean transformation In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. These transformations together with spatial rotati ...
adopted by Newton. Special relativity, as in
special case In logic, especially as applied in mathematics, concept is a special case or specialization of concept precisely if every instance of is also an instance of but not vice versa, or equivalently, if is a generalization of .Brown, James Robert. ...
, specifically did not cover gravity. While relativity was associated with mechanics and thus gravity, the idea of altering geometry only joined the story of gravity once mechanics required the Lorentz transformations.
Geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
was an ancient science that gradually broke free of Euclidean limitations when
Carl Gauss Carl may refer to: *Carl, Georgia, city in USA *Carl, West Virginia, an unincorporated community *Carl (name), includes info about the name, variations of the name, and a list of people with the name *Carl², a TV series * "Carl", an episode of tel ...
discovered in the 1800s that surfaces in any number of dimensions could be characterized by a
metric Metric or metrical may refer to: Measuring * Metric system, an internationally adopted decimal system of measurement * An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement Mathematics ...
, a distance measurement along the shortest path between two points that reduces to Euclidean distance at infinitesimal separation. Gauss' student
Bernhard Riemann Georg Friedrich Bernhard Riemann (; ; 17September 182620July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the f ...
developed this into a complete geometry by 1854. These geometries are locally flat but have global
curvature In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
. In 1907, Einstein took his first step by using special relativity to create a new form of the
equivalence principle The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same t ...
. The equivalence of inertial mass and gravitational mass was a known empirical law. The in Newton's first law, F=ma, has the same value as the in Newton's law of gravity on Earth, F=GMm/r^2. In what he later described as "the happiest thought of my life" Einstein realized this meant that in free-fall, an accelerated coordinate system exists with no local
gravitational field In physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space around itself. A gravitational field is used to explain gravitational phenomena, such as ...
. Every description of gravity in any other coordinate system must transform to give no field in the free-fall case, a powerful invariance constraint on all theories of gravity. Einstein's description of gravity was accepted by the majority of physicists for two reasons. First, by 1910 his special relativity was accepted in German physics and was spreading to other countries. Second, his theory explained experimental results like the perihelion of Mercury and the bending of light around the Sun better than Newton's theory. In 1919, the British astrophysicist
Arthur Eddington Sir Arthur Stanley Eddington, (28 December 1882 – 22 November 1944) was an English astronomer, physicist, and mathematician. He was also a philosopher of science and a populariser of science. The Eddington limit, the natural limit to the lu ...
was able to confirm the predicted deflection of light during that year's solar eclipse. Eddington measured starlight deflections twice those predicted by Newtonian corpuscular theory, in accordance with the predictions of general relativity. Although Eddington's analysis was later disputed, this experiment made Einstein famous almost overnight and caused general relativity to become widely accepted in the scientific community. In 1959, American physicists Robert Pound and Glen Rebka performed an experiment in which they used
gamma ray A gamma ray, also known as gamma radiation (symbol ), is a penetrating form of electromagnetic radiation arising from high energy interactions like the radioactive decay of atomic nuclei or astronomical events like solar flares. It consists o ...
s to confirm the prediction of
gravitational time dilation Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events, as measured by observers situated at varying distances from a gravitating mass. The lower the gravitational potential (the closer ...
. By sending the rays down a 74-foot tower and measuring their frequency at the bottom, the scientists confirmed that light is
Doppler shift The Doppler effect (also Doppler shift) is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. The ''Doppler effect'' is named after the physicist Christian Doppler, who described t ...
ed as it moves towards a source of gravity. The observed shift also supports the idea that time runs more slowly in the presence of a gravitational field (many more wave crests pass in a given interval). If light moves outward from a strong source of gravity it will be observed with a
redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and increase in frequency and e ...
. The time delay of light passing close to a massive object was first identified by
Irwin I. Shapiro Irwin Ira Shapiro is an American astrophysicist and Harvard University Professor, Timken University Professor at Harvard University. He has been a professor at Harvard since 1982. He was the director of the Harvard-Smithsonian Center for Astr ...
in 1964 in interplanetary spacecraft signals. In 1971, scientists discovered the first-ever black hole in the galaxy Cygnus. The black hole was detected because it was emitting bursts of
x-rays An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
as it consumed a smaller star, and it came to be known as Cygnus X-1. This discovery confirmed yet another prediction of general relativity, because Einstein's equations implied that light could not escape from a sufficiently large and compact object. Frame dragging, the idea that a rotating massive object should twist spacetime around it, was confirmed by
Gravity Probe B Gravity Probe B (GP-B) was a satellite-based experiment whose objective was to test two previously-unverified predictions of general relativity: the geodetic effect and frame-dragging. This was to be accomplished by measuring, very precisely, t ...
results in 2011. In 2015, the
LIGO The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory designed to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Prior to LIG ...
observatory detected faint
gravitational waves Gravitational waves are oscillations of the gravitational field that travel through space at the speed of light; they are generated by the relative motion of gravitating masses. They were proposed by Oliver Heaviside in 1893 and then later by H ...
, the existence of which had been predicted by general relativity. Scientists believe that the waves emanated from a
black hole merger Black is a color that results from the absence or complete Absorption (electromagnetic radiation), absorption of visible spectrum, visible light. It is an achromatic color, without Colorfulness#Chroma, chroma, like white and grey. It is ofte ...
that occurred 1.5 billion
light-years A light-year, alternatively spelled light year (ly or lyr), is a unit of length used to express astronomical distances and is equal to exactly , which is approximately 9.46 trillion km or 5.88 trillion mi. As defined by the International Astro ...
away.


On Earth

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 The standard acceleration of gravity or standard acceleration of free fall, often called simply standard gravity and denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is a constant ...
value is defined by the
International Bureau of Weights and Measures The International Bureau of Weights and Measures (, BIPM) is an List of intergovernmental organizations, intergovernmental organisation, through which its 64 member-states act on measurement standards in areas including chemistry, ionising radi ...
, under the
International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...
(SI). The force of gravity experienced by objects on Earth's surface is the
vector sum In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scal ...
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 Centrifugal force is a fictitious force in Newtonian mechanics (also called an "inertial" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It appears to be directed radially away from the axi ...
caused by the Earth's rotation and because points on the equator are farthest from the center of the Earth. The force of gravity varies with latitude, and the resultant acceleration increases from about 9.780 m/s2 at the Equator to about 9.832 m/s2 at the poles.


Gravity wave

Waves on oceans, lakes, and other bodies of water occur when the gravitational equilibrium at the surface of the water is disturbed by for example wind. Similar effects occur in the
atmosphere An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosph ...
where equilibrium is disturbed by thermal
weather fronts A weather front is a boundary separating air masses for which several characteristics differ, such as air density, wind, temperature, and humidity. Disturbed and unstable weather due to these differences often arises along the boundary. For in ...
or mountain ranges.


Astrophysics


Stars and black holes

During star formation, gravitational attraction in a cloud of hydrogen gas competes with thermal gas pressure. As the gas density increases, the temperature rises, then the gas radiates energy, allowing additional gravitational condensation. If the mass of gas in the region is low, the process continues until a
brown dwarf Brown dwarfs are substellar objects that have more mass than the biggest gas giant planets, but less than the least massive main sequence, main-sequence stars. Their mass is approximately 13 to 80 Jupiter mass, times that of Jupiter ()not big en ...
or gas-giant planet is produced. If more mass is available, the additional gravitational energy allows the central region to reach pressures sufficient for
nuclear fusion Nuclear fusion is a nuclear reaction, reaction in which two or more atomic nuclei combine to form a larger nuclei, nuclei/neutrons, neutron by-products. The difference in mass between the reactants and products is manifested as either the rele ...
, forming a
star A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...
. In a star, again the gravitational attraction competes, with thermal and radiation pressure in
hydrostatic equilibrium In fluid mechanics, hydrostatic equilibrium, also called hydrostatic balance and hydrostasy, is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. I ...
until the star's atomic fuel runs out. The next phase depends upon the total mass of the star. Very low mass stars slowly cool as
white dwarf A white dwarf is a Compact star, stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very density, dense: in an Earth sized volume, it packs a mass that is comparable to the Sun. No nuclear fusion takes place i ...
stars with a small core balancing gravitational attraction with
electron degeneracy pressure In astrophysics and condensed matter physics, electron degeneracy pressure is a quantum mechanical effect critical to understanding the stability of white dwarf stars and metal solids. It is a manifestation of the more general phenomenon of quan ...
. Stars with masses similar to the Sun go through a
red giant A red giant is a luminous giant star of low or intermediate mass (roughly 0.3–8 solar masses ()) in a late phase of stellar evolution. The stellar atmosphere, outer atmosphere is inflated and tenuous, making the radius large and the surface t ...
phase before becoming white dwarf stars. Higher mass stars have complex core structures that burn helium and high atomic number elements ultimately producing an
iron Iron is a chemical element; it has symbol Fe () and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, forming much of Earth's o ...
core. As their fuel runs out, these stars become unstable producing a
supernova A supernova (: supernovae or supernovas) is a powerful and luminous explosion of a star. A supernova occurs during the last stellar evolution, evolutionary stages of a massive star, or when a white dwarf is triggered into runaway nuclear fusion ...
. The result can be a
neutron star A neutron star is the gravitationally collapsed Stellar core, core of a massive supergiant star. It results from the supernova explosion of a stellar evolution#Massive star, massive star—combined with gravitational collapse—that compresses ...
where gravitational attraction balances neutron degeneracy pressure or, for even higher masses, a
black hole A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...
where gravity operates alone with such intensity that even light cannot escape.


Gravitational radiation

General relativity predicts that energy can be transported out of a system through gravitational radiation also known as gravitational waves. The first indirect evidence for gravitational radiation was through measurements of the Hulse–Taylor binary in 1973. This system consists of a
pulsar A pulsar (''pulsating star, on the model of quasar'') is a highly magnetized rotating neutron star that emits beams of electromagnetic radiation out of its Poles of astronomical bodies#Magnetic poles, magnetic poles. This radiation can be obse ...
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 The Nobel Prize in Physics () is an annual award given by the Royal Swedish Academy of Sciences for those who have made the most outstanding contributions to mankind in the field of physics. It is one of the five Nobel Prizes established by the ...
in 1993. The first direct evidence for gravitational radiation was measured on 14 September 2015 by the
LIGO The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory designed to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Prior to LIG ...
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 A neutron star is the gravitationally collapsed Stellar core, core of a massive supergiant star. It results from the supernova explosion of a stellar evolution#Massive star, massive star—combined with gravitational collapse—that compresses ...
and
black hole A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...
formation also create detectable amounts of gravitational radiation. This research was awarded the Nobel Prize in Physics in 2017.


Dark matter

At the cosmological scale, gravity is a dominant player. About 5/6 of the total mass in the universe consists of dark matter which interacts through gravity but not through electromagnetic interactions. The gravitation of clumps of dark matter known as
dark matter halo In modern models of physical cosmology, a dark matter halo is a basic unit of cosmological structure. It is a hypothetical region that has decoupled from cosmic expansion and contains gravitationally bound matter. A single dark matter halo ma ...
s attract hydrogen gas leading to stars and galaxies.


Gravitational lensing

Gravity acts on light and matter equally, meaning that a sufficiently massive object could warp light around it and create a gravitational lens. This phenomenon was first confirmed by observation in 1979 using the 2.1 meter telescope at
Kitt Peak National Observatory The Kitt Peak National Observatory (KPNO) is a United States astronomy, astronomical observatory located on Kitt Peak of the Quinlan Mountains in the Arizona-Sonoran Desert on the Tohono Oʼodham Nation, west-southwest of Tucson, Arizona. With ...
in Arizona, which saw two mirror images of the same quasar whose light had been bent around the galaxy YGKOW G1. Many subsequent observations of gravitational lensing provide additional evidence for substantial amounts of dark matter around galaxies. Gravitational lenses do not focus like
eyeglass Glasses, also known as eyeglasses (American English), spectacles ( Commonwealth English), or colloquially as specs, are vision eyewear with clear or tinted lenses mounted in a frame that holds them in front of a person's eyes, typically ...
lenses, but rather lead to annular shapes called Einstein rings.


Speed of gravity

In December 2012, a research team in China announced that it had produced measurements of the phase lag of
Earth tide Earth tide (also known as solid-Earth tide, crustal tide, body tide, bodily tide or land tide) is the displacement of the solid earth's surface caused by the gravity of the Moon and Sun. Its main component has meter-level amplitude at periods of a ...
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 ''
Science Bulletin ''Science Bulletin'' (shortened as ''Sci. Bull.'') is a semi-monthly peer-reviewed international journal sponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China. Published by Elsevier on behalf of Science ...
'' in February 2013. In October 2017, the
LIGO The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory designed to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Prior to LIG ...
and
Virgo interferometer The Virgo interferometer is a large-scale scientific instrument near Pisa, Italy, for detecting gravitational waves. The detector is a Michelson interferometer, which can detect the minuscule length variations in its two arms induced by the p ...
detectors received gravitational wave signals within 2 seconds of
gamma ray A gamma ray, also known as gamma radiation (symbol ), is a penetrating form of electromagnetic radiation arising from high energy interactions like the radioactive decay of atomic nuclei or astronomical events like solar flares. It consists o ...
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. * Galaxy rotation curves: Stars in galaxies follow a distribution of velocities where stars on the outskirts are moving faster than they should according to the observed distributions of luminous matter. Galaxies within
galaxy clusters A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. Clusters consist of galax ...
show a similar pattern. The pattern is considered strong evidence for
dark matter In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relat ...
, which would interact through gravitation but not electromagnetically; various modifications to Newtonian dynamics have also been proposed. * Accelerated expansion: The
expansion of the universe The expansion of the universe is the increase in proper length, distance between Gravitational binding energy, gravitationally unbound parts of the observable universe with time. It is an intrinsic and extrinsic properties (philosophy), intrins ...
seems to be accelerating.
Dark energy In physical cosmology and astronomy, dark energy is a proposed form of energy that affects the universe on the largest scales. Its primary effect is to drive the accelerating expansion of the universe. It also slows the rate of structure format ...
has been proposed to explain this. *
Flyby anomaly The flyby anomaly is a discrepancy between current scientific models and the actual increase in speed (i.e. increase in ''kinetic energy'') observed during a planetary flyby (usually of Earth) by a spacecraft. In multiple cases, spacecraft have ...
: Various spacecraft have experienced greater acceleration than expected during
gravity assist A gravity assist, gravity assist maneuver, swing-by, or generally a gravitational slingshot in orbital mechanics, is a type of spaceflight flyby (spaceflight), flyby which makes use of the relative movement (e.g. orbit around the Sun) and gra ...
maneuvers. The Pioneer anomaly has been shown to be explained by thermal recoil due to the distant sun radiation on one side of the space craft.


General relativity

In
modern physics Modern physics is a branch of physics that developed in the early 20th century and onward or branches greatly influenced by early 20th century physics. Notable branches of modern physics include quantum mechanics, special relativity, and genera ...
, general relativity is considered the most successful theory of gravitation. Physicists continue to work to find
solutions Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Solutio ...
to the
Einstein field equations In the General relativity, general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of Matter#In general relativity and cosmology, matter within it. ...
that form the basis of general relativity and continue to test the theory, finding excellent agreement in all cases.


Constraints

Any theory of gravity must conform to the requirements of special relativity and experimental observations. Newton's theory of gravity assumes
action at a distance Action at a distance is the concept in physics that an object's motion (physics), motion can be affected by another object without the two being in Contact mechanics, physical contact; that is, it is the concept of the non-local interaction of ob ...
and therefore cannot be reconciled with special relativity. The simplest generalization of Newton's approach would be a scalar theory with the gravitational potential represented by a single number in a 4 dimensional spacetime. However this type of theory fails to predict gravitational redshift or the deviation of light by matter and gives values for the precession of Mercury which are incorrect. A
vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space \mathbb^n. A vector field on a plane can be visualized as a collection of arrows with given magnitudes and dire ...
theory predicts negative energy gravitational waves so it also fails. Furthermore, no theory without curvature in spacetime can be consistent with special relativity. The simplest theory consistent with special relativity and the well-studied observations is general relativity.


General characteristics

Unlike Newton's formula with one parameter, , force in general relativity is terms of 10 numbers formed in to a
metric tensor In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows ...
.In general relativity the effects of gravitation are described in different ways in different frames of reference. In a free-falling or co-moving
coordinate system In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...
, an object travels in a straight line. In other coordinate systems, the object accelerates and thus is seen to move under a force. The path in
spacetime In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...
(not 3D space) taken by a free-falling object is called a
geodesic In geometry, a geodesic () is a curve representing in some sense the locally shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a conn ...
and the length of that path as measured by time in the objects frame is the shortest (or rarely the longest) one. Consequently the effect of gravity can be described as curving spacetime. In a weak stationary gravitational field, general relativity reduces to Newton's equations. The corrections introduced by general relativity on Earth are on the order of 1 part in a billion.


Einstein field equations

The Einstein field equations are a
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its open system (systems theory), environment, is described by its boundaries, str ...
of 10
partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...
s which describe how matter affects the curvature of spacetime. The system is may be expressed in the form G_ + \Lambda g_ = \kappa T_, where is the
Einstein tensor In differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature of a pseudo-Riemannian manifold. In general relativity, it occurs in the Einstein field e ...
, is the
metric tensor In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows ...
, is the
stress–energy tensor The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress ...
, is the
cosmological constant In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant, is a coefficient that Albert Einstein initially added to his field equations of general rel ...
, G is the Newtonian constant of gravitation and c is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
. The constant \kappa = \frac is referred to as the Einstein gravitational constant.


Solutions

The non-linear second-order Einstein field equations are extremely complex and have been solved in only a few special cases. These cases however has been transformational in our understanding of the cosmos. Several solutions are the basis for understanding
black holes A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...
and for our modern model of the evolution of the universe since the
Big Bang The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including th ...
.


Tests of general relativity

Testing the predictions of general relativity has historically been difficult, because they are almost identical to the predictions of Newtonian gravity for small energies and masses. A wide range of experiments provided support of general relativity. Today, Einstein's theory of relativity is used for all gravitational calculations where absolute precision is desired, although Newton's inverse-square law is accurate enough for virtually all ordinary calculations.


Gravity and quantum mechanics

Despite its success in predicting the effects of gravity at large scales, general relativity is ultimately incompatible with
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
. This is because general relativity describes gravity as a smooth, continuous distortion of spacetime, while quantum mechanics holds that all forces arise from the exchange of discrete particles known as quanta. This contradiction is especially vexing to physicists because the other three fundamental forces (strong force, weak force and electromagnetism) were reconciled with a quantum framework decades ago. As a result, researchers have begun to search for a theory that could unite both gravity and quantum mechanics under a more general framework. One path is to describe gravity in the framework of
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
(QFT), which has been successful to accurately describe the other
fundamental interaction In physics, the fundamental interactions or fundamental forces are interactions in nature that appear not to be reducible to more basic interactions. There are four fundamental interactions known to exist: * gravity * electromagnetism * weak int ...
s. The electromagnetic force arises from an exchange of virtual
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can ...
s, where the QFT description of gravity is that there is an exchange of virtual
graviton In theories of quantum gravity, the graviton is the hypothetical elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathematical problem with re ...
s. This description reproduces general relativity in the
classical limit The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters. The classical limit is used with physical theories that predict n ...
. However, this approach fails at short distances of the order of the
Planck length In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: '' c'', '' G'', '' ħ'', and ''k''B (described further below). Expressing one of ...
, where a more complete theory of
quantum gravity Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the v ...
(or a new approach to quantum mechanics) is required.


Alternative theories

General relativity has withstood many
tests Test(s), testing, or TEST may refer to: * Test (assessment), an educational assessment intended to measure the respondents' knowledge or other abilities Arts and entertainment * ''Test'' (2013 film), an American film * ''Test'' (2014 film) ...
over a large range of mass and size scales. When applied to interpret astronomical observations, cosmological models based on general relativity introduce two components to the universe,
dark matter In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relat ...
and
dark energy In physical cosmology and astronomy, dark energy is a proposed form of energy that affects the universe on the largest scales. Its primary effect is to drive the accelerating expansion of the universe. It also slows the rate of structure format ...
, the nature of which is currently an unsolved problem in physics. The many successful, high precision predictions of the standard model of cosmology has led astrophysicists to conclude it and thus general relativity will be the basis for future progress. However, dark matter is not supported by the
standard model of particle physics The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles. It ...
, physical models for dark energy do not match cosmological data, and some cosmological observations are inconsistent. These issues have led to the study of alternative theories of gravity.


See also

* * * * * * * * * * *


References


Further reading

* * * * * *


External links


The Feynman Lectures on Physics Vol. I Ch. 7: The Theory of Gravitation
* * {{Authority control Fundamental interactions Acceleration Articles containing video clips Empirical laws