Is Gravity A Force That Can Be Changed

Phenomenon of allure between objects with mass

Gravity (from Latin gravitas 'weight'^[1]), or gravitation, is a natural phenomenon by which all things with mass or energy, including planets, stars, galaxies and even light,^[2] are attracted to (or gravitate toward) one another. On Earth, gravity gives weight to physical objects, and the Moon's gravity causes the tides of the oceans. The gravitational attraction of the original gaseous thing present in the Universe acquired it to begin coalescing and forming stars and caused the stars to group together into galaxies, so gravity is responsible for many of the large-scale structures in the Universe. Gravity has an infinite range, although its effects become weaker every bit objects get farther away.

Gravity is most accurately described past 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 past the uneven distribution of mass, and causing masses to movement along geodesic lines. The most extreme example of this curvature of spacetime is a black hole, from which nothing—non even light—tin escape one time past the blackness hole's effect horizon.^[3] Nonetheless, for nigh applications, gravity is well approximated past Newton's law of universal gravitation, which describes gravity as a force causing any two bodies to exist attracted toward each other, with magnitude proportional to the production of their masses and inversely proportional to the square of the distance between them.

Gravity is the weakest of the four cardinal interactions of physics, approximately 10³⁸ times weaker than the potent interaction, 10³⁶ times weaker than the electromagnetic force and x²⁹ times weaker than the weak interaction. As a issue, it has no significant influence at the level of subatomic particles.^[iv] In contrast, information technology is the dominant interaction at the macroscopic scale, and is the cause of the formation, shape and trajectory (orbit) of astronomical bodies.

Current models of particle physics imply that the earliest instance of gravity in the Universe, perhaps in the form of quantum gravity, supergravity or a gravitational singularity, along with ordinary space and time, developed during the Planck epoch (upward to x⁻⁴³ seconds after the nascence of the Universe), possibly from a primeval state, such equally a false vacuum, quantum vacuum or virtual particle, in a currently unknown mode.^[5] Attempts to develop a theory of gravity consequent with breakthrough mechanics, a quantum gravity theory, which would allow gravity to be united in a mutual mathematical framework (a theory of everything) with the other iii central interactions of physics, are a current area of research.

History of gravitational theory

Ancient globe

The ancient Greek philosopher Archimedes discovered the centre of gravity of a triangle.^[6] He as well postulated that if 2 equal weights did non have the aforementioned center of gravity, the center of gravity of the ii weights together would exist in the middle of the line that joins their centers of gravity.^[7]

The Roman architect and engineer Vitruvius in De Architectura postulated that gravity of an object did not depend on weight simply its "nature".^[8]

The Indian mathematician-astronomer Aryabhata first identified gravity to explicate why objects exercise non spin out when the Earth rotates, and Brahmagupta described gravity equally an attractive force and used the term gurutvākarṣaṇ for gravity.^{[9] [10] [11]}

Scientific revolution

In the mid-16th century, diverse Europeans experimentally disproved the Aristotelian notion that heavier objects fall at a faster rate.^[12] For example, the Spanish Dominican priest, Domingo de Soto, wrote in 1551 that bodies in free fall uniformly accelerate.^[12] De Soto may have been influenced by earlier experiments conducted by other Dominican priests in Italy, including those past Benedetto Varchi, Francesco Beato, Luca Ghini, and Giovan Bellaso which contradicted Aristotle'south teachings on the fall of bodies.^[12] The mid-16th century Italian physicist Giambattista Benedetti published papers challenge that, due to specific gravity, objects of the same cloth but dissimilar weights would autumn at the aforementioned speed.^[xiii] With the 1586 Delft tower experiment the Flemish physicist Simon Stevin demonstrated that, when dropped from a tower, two cannonballs of differing sizes and weights would in fact reach the footing at the same fourth dimension.^[fourteen] In the belatedly 16th century, Galileo Galilei demonstrated the premise (perhaps as a idea experiment) that ii balls of different weights dropped from a tower would fall at the same rate.^[15] Combining this knowledge with conscientious measurements of balls rolling downwardly inclines, Galileo firmly established that gravitational dispatch is the aforementioned for all objects.^[16] Galileo postulated that air resistance is the reason that objects with a low density and loftier 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 fourth dimension elapsed.^[17]

The relation of the distance of objects in free fall to the square of the time taken was confirmed by Italian Jesuits Grimaldi and Riccioli between 1640 and 1650. They also made a calculation of Earth's gravity by recording the oscillations of a pendulum.^[xviii]

Newton'due south theory of gravitation

English physicist and mathematician, Sir Isaac Newton (1642–1727)

In 1679, Robert Hooke wrote to English language mathematician Isaac Newton of his hypothesis apropos orbital movement, which partly depends on an changed-square force.^[19] In 1684, both Hooke and Newton told Edmond Halley that they had proven the inverse-foursquare police force of planetary motion.^[20] Hooke refused to produce his proofs, but Newton produced De motu corporum in gyrum ('On the motion of bodies in an orbit'), in which he derives Kepler's laws of planetary motion.^[20] Halley supported Newton's expansion of his work into the Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), in which he hypothesizes the inverse-square police of universal gravitation.^[20]

According to Newton, he "deduced that the forces which keep the planets in their orbs must [be] reciprocally every bit the squares of their distances from the centers about which they circumduct: and thereby compared the force requisite to proceed the Moon in her Orb with the forcefulness of gravity at the surface of the Globe; and found them answer pretty nigh."^[21] The equation is the following:

$${\displaystyle F=G{\frac {m_{1}m_{ii}}{r^{2}}},}$$

where F is the force, grand _one and one thousand _ii are the masses of the objects interacting, r is the altitude betwixt the centers of the masses and Thou is the gravitational constant.

Newton's theory enjoyed its greatest success when information technology was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams and Urbain Le Verrier predicted the general position of the planet, and Le Verrier'southward calculations are what led Johann Gottfried Galle to the discovery of Neptune.

A discrepancy in Mercury'due south orbit pointed out flaws in Newton's theory. By the end of the 19th century, it was known that its orbit showed slight perturbations that could non be accounted for entirely nether Newton's theory, but all searches for another perturbing trunk (such as a planet orbiting the Sun even closer than Mercury) had been fruitless. The issue was resolved in 1915 by Albert Einstein'south new theory of full general relativity, which accounted for the small discrepancy in Mercury'due south orbit. This discrepancy was the advance in the perihelion of Mercury of 42.98 arcseconds per century.^[22]

Although Newton's theory has been superseded by Albert Einstein's general relativity, most modern not-relativistic gravitational calculations are even so made using Newton's theory considering information technology is simpler to work with and it gives sufficiently accurate results for most applications involving sufficiently modest masses, speeds and energies.

Equivalence principle

The equivalence principle, explored by a succession of researchers including Galileo, Loránd Eötvös, and Einstein, expresses the idea that all objects fall in the same style, and that the effects of gravity are indistinguishable from certain aspects of acceleration and deceleration. The simplest mode to test the weak equivalence principle is to drop two objects of different masses or compositions in a vacuum and run across whether they hit the ground at the same time. Such experiments demonstrate that all objects autumn at the same charge per unit when other forces (such as air resistance and electromagnetic furnishings) are negligible. More sophisticated tests use a torsion balance of a type invented by Eötvös. Satellite experiments, for example STEP, are planned for more accurate experiments in space.^[23]

Formulations of the equivalence principle include:

• The weak equivalence principle: The trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and is independent of its composition. ^[24]
• The Einsteinian equivalence principle: The event of any local not-gravitational experiment in a freely falling laboratory is contained of the velocity of the laboratory and its location in spacetime. ^[25]
• The potent equivalence principle requiring both of the to a higher place.

General relativity

2-dimensional analogy of spacetime distortion generated past the mass of an object. Thing changes the geometry of spacetime, this (curved) geometry existence interpreted every bit gravity. White lines practise non represent the curvature of space but instead represent the coordinate arrangement imposed on the curved spacetime, which would be rectilinear in a flat spacetime.

In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of a force. The starting point for general relativity is the equivalence principle, which equates costless autumn with inertial movement and describes free-falling inertial objects as beingness accelerated relative to non-inertial observers on the ground.^{[26] [27]} In Newtonian physics, however, no such acceleration can occur unless at least ane of the objects is being operated on by a force.

Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. These direct paths are chosen geodesics. Like Newton's get-go law of motion, Einstein's theory states that if a force is applied on an object, it would deviate from a geodesic. For instance, nosotros are no longer following geodesics while standing because the mechanical resistance of the Earth exerts an upward force on the states, and nosotros are non-inertial on the ground as a result. This explains why moving along the geodesics in spacetime is considered inertial.

Einstein discovered the field equations of general relativity, which chronicle the presence of matter and the curvature of spacetime and are named subsequently him. The Einstein field equations are a set of 10 simultaneous, not-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.

Solutions

Notable solutions of the Einstein field equations include:

• The Schwarzschild solution, which describes spacetime surrounding a spherically symmetric non-rotating uncharged massive object. For compact plenty objects, this solution generated a black pigsty with a central singularity. For radial distances from the center which are much greater than the Schwarzschild radius, the accelerations predicted by the Schwarzschild solution are practically identical to those predicted by Newton's theory of gravity.
• The Reissner-Nordström solution, in which the central object has an electrical accuse. For charges with a geometrized length which are less than the geometrized length of the mass of the object, this solution produces black holes with double event horizons.
• The Kerr solution for rotating massive objects. This solution as well produces black holes with multiple event horizons.
• The Kerr-Newman solution for charged, rotating massive objects. This solution also produces black holes with multiple consequence horizons.
• The cosmological Friedmann-Lemaître-Robertson-Walker solution, which predicts the expansion of the Universe.

Tests

The tests of full general relativity included the following:^[28]

• General relativity accounts for the anomalous perihelion precession of Mercury.^[29]
• The prediction that time runs slower at lower potentials (gravitational time dilation) has been confirmed past the Pound–Rebka experiment (1959), the Hafele–Keating experiment, and the GPS.
• The prediction of the deflection of light was commencement confirmed by Arthur Stanley Eddington from his observations during the Solar eclipse of 29 May 1919.^{[30] [31]} Eddington measured starlight deflections twice those predicted by Newtonian corpuscular theory, in accordance with the predictions of general relativity. However, his estimation of the results was later disputed.^[32] More recent tests using radio interferometric measurements of quasars passing behind the Lord's day take more than accurately and consistently confirmed the deflection of light to the degree predicted by general relativity.^[33] See likewise gravitational lens.
• The time delay of light passing close to a massive object was start identified by Irwin I. Shapiro in 1964 in interplanetary spacecraft signals.
• Gravitational radiation has been indirectly confirmed through studies of binary pulsars. On 11 Feb 2016, the LIGO and Virgo collaborations appear the first observation of a gravitational wave.
• Alexander Friedmann in 1922 institute that Einstein equations have non-stationary solutions (even in the presence of the cosmological constant). In 1927 Georges Lemaître showed that static solutions of the Einstein equations, which are possible in the presence of the cosmological abiding, are unstable, and therefore the static Universe envisioned past Einstein could not exist. Later, in 1931, Einstein himself agreed with the results of Friedmann and Lemaître. Thus general relativity predicted that the Universe had to be non-static—it had to either expand or contract. The expansion of the Universe discovered by Edwin Hubble in 1929 confirmed this prediction.^[34]
• The theory's prediction of frame dragging was consistent with the recent Gravity Probe B results.^[35]
• General relativity predicts that light should lose its energy when traveling away from massive bodies through gravitational redshift. This was verified on Earth and in the Solar System around 1960.

Gravity and breakthrough mechanics

An open question is whether information technology is possible to describe the small-scale interactions of gravity with the same framework as quantum mechanics. Full general relativity describes large-calibration bulk backdrop whereas breakthrough mechanics is the framework to depict the smallest scale interactions of matter. Without modifications these frameworks are incompatible.^[36]

One path is to depict gravity in the framework of quantum field theory, which has been successful to accurately describe the other cardinal interactions. The electromagnetic force arises from an substitution of virtual photons, where the QFT description of gravity is that there is an commutation of virtual gravitons.^{[37] [38]} This description reproduces general relativity in the classical limit. Even so, this approach fails at short distances of the guild of the Planck length,^[36] where a more than consummate theory of breakthrough gravity (or a new approach to breakthrough mechanics) is required.

Specifics

Earth'due south gravity

An initially-stationary object that is allowed to fall freely under gravity drops a distance that is proportional to the foursquare of the elapsed time. This epitome spans one-half a 2d and was captured at 20 flashes per 2d.

Every planetary body (including the World) 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'south mass and inversely proportional to the foursquare of the distance from the center of the body.

If an object with comparable mass to that of the Globe were to autumn towards it, then the corresponding dispatch of the Earth would be observable.

The strength of the gravitational field is numerically equal to the acceleration of objects nether its influence.^[39] The rate of acceleration of falling objects near the World'south surface varies very slightly depending on latitude, surface features such every bit mountains and ridges, and perhaps unusually high or depression sub-surface densities.^[xl] For purposes of weights and measures, a standard gravity value is defined by the International Agency of Weights and Measures, under the International System of Units (SI).

That value, denoted g, is k = 9.80665 thou/southwardⁱⁱ (32.1740 ft/southward²).^{[41] [42]}

The standard value of nine.80665 m/s² is the 1 originally adopted by the International Commission on Weights and Measures in 1901 for 45° breadth, even though it has been shown to be too high by about 5 parts in ten thousand.^[43] This value has persisted in meteorology and in some standard atmospheres as the value for 45° breadth even though it applies more precisely to latitude of 45°32'33".^[44]

Assuming the standardized value for g and ignoring air resistance, this ways that an object falling freely nigh 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 accomplish a velocity of 9.80665 m/s (32.1740 ft/due south) after one 2nd, approximately xix.62 m/s (64.4 ft/southward) after two seconds, and and so on, calculation 9.80665 thou/s (32.1740 ft/s) to each resulting velocity. Also, once again ignoring air resistance, whatsoever and all objects, when dropped from the same meridian, volition hitting the ground at the same time.

Co-ordinate to Newton's 3rd Law, the Earth itself experiences a strength equal in magnitude and contrary in direction to that which information technology exerts on a falling object. This ways that the Earth also accelerates towards the object until they collide. Considering 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 finer balances the bonny force of gravity and prevents further dispatch.

The strength of gravity on Earth is the resultant (vector sum) of ii forces:^[45] (a) The gravitational attraction in accordance with Newton'due south universal constabulary of gravitation, and (b) the centrifugal force, which results from the choice of an earthbound, rotating frame of reference. The strength of gravity is weakest at the equator considering of the centrifugal forcefulness caused by the Earth's rotation and because points on the equator are furthest from the center of the World. The force of gravity varies with breadth and increases from about 9.780 m/due south² at the Equator to virtually 9.832 m/s² at the poles.

Equations for a falling body near the surface of the Earth

Under an supposition of abiding 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/s² on Earth. This resulting force is the object's weight. The acceleration due to gravity is equal to this g. An initially stationary object which is allowed to fall freely under gravity drops a distance which is proportional to the square of the elapsed fourth dimension. The paradigm on the right, spanning one-half a second, was captured with a stroboscopic flash at 20 flashes per second. During the first 1⁄xx of a 2d the brawl 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 , ix units and and so on.

Under the same constant gravity assumptions, the potential free energy, East _p, of a body at height h is given by East _p = mgh (or E _p = Wh, with W pregnant weight). This expression is valid only over small distances h from the surface of the Earth. Similarly, the expression ${\displaystyle h={\tfrac {v^{2}}{2g}}}$ for the maximum height reached by a vertically projected torso with initial velocity v is useful for modest heights and small initial velocities only.

Gravity and astronomy

The application of Newton's law of gravity has enabled the acquisition of much of the detailed information we have about the planets in the Solar Arrangement, 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 considering of the strength 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 past some other is direct proportional to the product of those objects' masses and inversely proportional to the foursquare of the altitude between them.

The earliest gravity (maybe in the form of breakthrough gravity, supergravity or a gravitational singularity), along with ordinary infinite and time, developed during the Planck epoch (upward to 10⁻⁴³ seconds afterwards the birth of the Universe), possibly from a primeval state (such as a simulated vacuum, breakthrough vacuum or virtual particle), in a currently unknown manner.^[5]

Gravitational radiation

The LIGO Hanford Observatory located in Washington, US where gravitational waves were first observed in September 2015.

General relativity predicts that energy tin can be transported out of a system through gravitational radiations. Whatever accelerating matter tin can create curvatures in the spacetime metric, which is how the gravitational radiation is transported away from the arrangement. Co-orbiting objects can generate curvatures in spacetime such every bit the Earth-Dominicus organisation, pairs of neutron stars, and pairs of blackness holes. Another astrophysical organisation predicted to lose free energy in the form of gravitational radiations 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 i some other. 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 beginning directly evidence for gravitational radiations was measured on 14 September 2015 by the LIGO detectors. The gravitational waves emitted during the collision of two black holes ane.iii billion-light years from Earth were measured.^{[47] [48]} This ascertainment confirms the theoretical predictions of Einstein and others that such waves exist. It also opens the style for practical observation and understanding of the nature of gravity and events in the Universe including the Big Bang.^[49] Neutron star and black hole formation also create detectable amounts of gravitational radiation.^[50] This research was awarded the Nobel Prize in physics in 2017.^[51]

Equally of 2020^[update], the gravitational radiation emitted past the Solar System is far too modest to measure out with current technology.

Speed of gravity

In Dec 2012, a inquiry team in People's republic of china appear that it had produced measurements of the phase lag of Earth tides during full and new moons which seem to show that the speed of gravity is equal to the speed of light.^[52] This means that if the Sun suddenly disappeared, the Globe would keep orbiting the vacant betoken normally for eight minutes, which is the time calorie-free takes to travel that altitude. The team's findings were released in the Chinese Science Bulletin in February 2013.^[53]

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 aforementioned management. This confirmed that the speed of gravitational waves was the aforementioned as the speed of light.^[54]

Anomalies and discrepancies

There are some observations that are non adequately deemed for, which may indicate to the need for better theories of gravity or mayhap be explained in other ways.

Rotation curve of a typical screw galaxy: predicted (A) and observed (B). The discrepancy between the curves is attributed to dark matter.

• Extra-fast stars: Stars in galaxies follow a distribution of velocities where stars on the outskirts are moving faster than they should co-ordinate to the observed distributions of normal affair. Galaxies inside milky way clusters show a similar design. Dark matter, which would interact through gravitation simply not electromagnetically, would account for the discrepancy. Various modifications to Newtonian dynamics have also been proposed.
• Flyby anomaly: Diverse spacecraft accept experienced greater acceleration than expected during gravity aid maneuvers.
• Accelerating expansion: The metric expansion of space seems to be speeding upward. Dark energy has been proposed to explicate this. A recent alternative explanation is that the geometry of space is not homogeneous (due to clusters of galaxies) and that when the data are reinterpreted to have this into account, the expansion is not speeding up subsequently all,^[55] however this conclusion is disputed.^[56]
• Dissonant increase of the astronomical unit: Recent measurements indicate that planetary orbits are widening faster than if this were solely through the Sun losing mass by radiating energy.
• Actress energetic photons: Photons travelling through milky way clusters should gain energy and and then lose it again on the way out. The accelerating expansion of the Universe should stop the photons returning all the free energy, simply even taking this into account photons from the cosmic microwave background radiation proceeds twice as much energy as expected. This may indicate that gravity falls off faster than inverse-squared at certain distance scales.^[57]
• Extra massive hydrogen clouds: The spectral lines of the Lyman-alpha forest advise that hydrogen clouds are more clumped together at sure scales than expected and, like dark flow, may betoken that gravity falls off slower than inverse-squared at certain distance scales.^[57]

Alternative theories

Historical alternative theories

• Aristotelian theory of gravity
• Le Sage's theory of gravitation (1784) also called LeSage gravity only originally proposed by Fatio and further elaborated by Georges-Louis Le Sage, based on a fluid-based explanation where a low-cal gas fills the unabridged Universe.
• Ritz'south theory of gravitation, Ann. Chem. Phys. 13, 145, (1908) pp. 267–271, Weber-Gauss electrodynamics practical to gravitation. Classical advocacy of perihelia.
• Nordström's theory of gravitation (1912, 1913), an early on competitor of general relativity.
• Kaluza Klein theory (1921)
• Whitehead'due south theory of gravitation (1922), another early competitor of full general relativity.

Modern culling theories

• Brans–Dicke theory of gravity (1961)^[58]
• Induced gravity (1967), a proposal by Andrei Sakharov according to which general relativity might ascend from quantum field theories of thing
• String theory (late 1960s)
• ƒ(R) gravity (1970)
• Horndeski theory (1974)^[59]
• Supergravity (1976)
• In the modified Newtonian dynamics (MOND) (1981), Mordehai Milgrom proposes a modification of Newton's second law of motion for small accelerations^[threescore]
• The self-creation cosmology theory of gravity (1982) by G.A. Hairdresser in which the Brans-Dicke theory is modified to allow mass cosmos
• Loop quantum gravity (1988) past Carlo Rovelli, Lee Smolin, and Abhay Ashtekar
• Nonsymmetric gravitational theory (NGT) (1994) by John Moffat
• Tensor–vector–scalar gravity (TeVeS) (2004), a relativistic modification of MOND by Jacob Bekenstein
• Chameleon theory (2004) by Justin Khoury and Amanda Weltman.
• Pressuron theory (2013) by Olivier Minazzoli and Aurélien Hees.
• Conformal gravity^[61]
• Gravity as an entropic force, gravity arising as an emergent miracle from the thermodynamic concept of entropy.
• In the superfluid vacuum theory the gravity and curved infinite-time arise as a collective excitation fashion of non-relativistic groundwork superfluid.
• Massive gravity, a theory where gravitons and gravitational waves take a non-zero mass

Run into also

• Anti-gravity, the idea of neutralizing or repelling gravity
• Bogus gravity
• Gauss's law for gravity
• Gravitational potential
• Micro-g surroundings, also called microgravity
• Newton's laws of motion
• Standard gravitational parameter
• Weightlessness

Footnotes

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2. ^ Comins, Neil F.; Kaufmann, William J. (2008). Discovering the Universe: From the Stars to the Planets. MacMillan. p. 347. Bibcode:2009dufs.volume.....C. ISBN978-1429230421. Archived from the original on 25 January 2020. Retrieved 8 May 2018.
3. ^ "HubbleSite: Black Holes: Gravity'due south Relentless Pull". hubblesite.org. Archived from the original on 26 December 2018. Retrieved 7 Oct 2016.
4. ^ Krebs, Robert E. (1999). Scientific Development and Misconceptions Through the Ages: A Reference Guide (illustrated ed.). Greenwood Publishing Group. p. 133. ISBN978-0-313-30226-8.
5. ^ ^{a b} Staff. "Nascence of the Universe". Academy of Oregon. Archived from the original on 28 Nov 2018. Retrieved 24 September 2016. – discusses "Planck time" and "Planck era" at the very beginning of the Universe
6. ^ Reviel Neitz; William Noel (xiii October 2011). The Archimedes Codex: Revealing The Secrets of the Earth's Greatest Palimpsest. Hachette UK. p. 125. ISBN978-1-78022-198-iv. Archived from the original on 7 January 2020. Retrieved ten April 2019. {{cite book}}: CS1 maint: multiple names: authors listing (link)
7. ^ CJ Tuplin, Lewis Wolpert (2002). Science and Mathematics in Aboriginal Greek Civilisation. Hachette Uk. p. xi. ISBN978-0-19-815248-iv. Archived from the original on 17 January 2020. Retrieved x Apr 2019.
8. ^ Vitruvius, Marcus Pollio (1914). "7". In Alfred A. Howard (ed.). De Architectura libri decem [10 Books on Architecture]. VII. Herbert Langford Warren, Nelson Robinson (illus), Morris Hicky Morgan. Harvard University, Cambridge: Harvard University Press. p. 215. Archived from the original on 13 October 2016. Retrieved 10 April 2019.
9. ^ Pickover, Clifford (16 Apr 2008). Archimedes to Hawking: Laws of Science and the Great Minds Backside Them. Oxford Academy Press. ISBN9780199792689. Archived from the original on xviii Jan 2017. Retrieved 29 August 2017.
10. ^ Bose, Mainak Kumar (1988). Late classical India. A. Mukherjee & Co. Archived from the original on xiii August 2021. Retrieved 28 July 2021.
11. ^ *Sen, Amartya (2005). The Belligerent Indian. Allen Lane. p. 29. ISBN978-0-7139-9687-6.
12. ^ ^{a b c} Wallace, William A. (2018) [2004]. Domingo de Soto and the Early Galileo: Essays on Intellectual History. Abingdon, Britain: Routledge. pp. 119, 121–22. ISBN978-ane-351-15959-three. Archived from the original on 16 June 2021. Retrieved four August 2021.
13. ^ Drabkin, I. E. (1963). "Two Versions of One thousand. B. Benedetti's Demonstratio Proportionum Motuum Localium". Isis. 54 (2): 259–262. doi:10.1086/349706. ISSN 0021-1753. JSTOR 228543. S2CID 144883728.
14. ^ Schilling, Govert (31 July 2017). Ripples in Spacetime: Einstein, Gravitational Waves, and the Future of Astronomy. Harvard University Printing. p. 26. ISBN9780674971660. Archived from the original on xvi Dec 2021. Retrieved 16 December 2021.
15. ^ Ball, Phil (June 2005). "Tall Tales". Nature News. doi:10.1038/news050613-x.
16. ^ Galileo (1638), Two New Sciences, First Day Salviati speaks: "If this were what Aristotle meant you would burden him with another fault which would amount to a falsehood; because, since in that location is no such sheer height available on earth, information technology is clear that Aristotle could non take made the experiment; even so he wishes to give us the impression of his having performed information technology when he speaks of such an effect as one which we see."
17. ^ Gillispie, Charles Coulston (1960). The Edge of Objectivity: An Essay in the History of Scientific Ideas. Princeton University Press. pp. 3–6. ISBN0-691-02350-vi.
18. ^ J.50. Heilbron, Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics (Berkeley: University of California Printing, 1979), 180.
19. ^ Cohen, I. Bernard; Smith, George Edwin (2002). The Cambridge Companion to Newton. Cambridge Academy Printing. pp. 11–12, 96–97. ISBN978-0-521-65696-2.
20. ^ ^{a b c} Sagan, Carl & Druyan, Ann (1997). Comet. New York: Random House. pp. 52–58. ISBN978-0-3078-0105-0. Archived from the original on 15 June 2021. Retrieved five August 2021.
21. ^ *Chandrasekhar, Subrahmanyan (2003). Newton'southward Principia for the common reader. Oxford: Oxford University Printing. (pp. 1–2). The quotation comes from a memorandum idea to have been written nigh 1714. As early as 1645 Ismaël Bullialdus had argued that whatsoever force exerted by the Dominicus on distant objects would have to follow an changed-square law. However, he too dismissed the idea that any such force did be. See, for example,Linton, Christopher M. (2004). From Eudoxus to Einstein – A History of Mathematical Astronomy . Cambridge: Cambridge University Printing. p. 225. ISBN978-0-521-82750-eight.
22. ^ Nobil, Anna M. (March 1986). "The existent value of Mercury's perihelion accelerate". Nature. 320 (6057): 39–41. Bibcode:1986Natur.320...39N. doi:ten.1038/320039a0. S2CID 4325839.
23. ^ Chiliad.C.West.Sandford (2008). "STEP: Satellite Test of the Equivalence Principle". Rutherford Appleton Laboratory. Archived from the original on 28 September 2011. Retrieved 14 Oct 2011.
24. ^ Paul S Wesson (2006). Five-dimensional Physics . World Scientific. p. 82. ISBN978-981-256-661-4.
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References

• Halliday, David; Robert Resnick; Kenneth Due south. Krane (2001). Physics v. 1. New York: John Wiley & Sons. ISBN978-0-471-32057-9.
• Serway, Raymond A.; Jewett, John Westward. (2004). Physics for Scientists and Engineers (6th ed.). Brooks/Cole. ISBN978-0-534-40842-eight.
• Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.). Due west.H. Freeman. ISBN978-0-7167-0809-4.

Further reading

• Thorne, Kip S.; Misner, Charles W.; Wheeler, John Archibald (1973). Gravitation. Westward.H. Freeman. ISBN978-0-7167-0344-0.
• Panek, Richard (2 Baronial 2019). "Everything you thought you knew almost gravity is incorrect". Washington Mail service.

External links

• "Gravitation", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
• "Gravitation, theory of", Encyclopedia of Mathematics, European monetary system Press, 2001 [1994]

Source: https://en.wikipedia.org/wiki/Gravity

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