# Gravity

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In physics, gravity (from Latin gravitas 'weight' [1] ) is a fundamental interaction which causes all things with mass or energy to be attracted (or gravitate) toward one another. Gravity is by far the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles. [2] However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light.

## Contents

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

The gravitational attraction between the original gaseous matter in the Universe allowed it to coalesce and form stars which eventually condensed into galaxies, so gravity is responsible for many of the large-scale structures in the Universe. Gravity has an infinite range, although its effects become weaker as objects get farther away.

Gravity is most accurately described by the general theory of relativity (proposed by Albert Einstein in 1915), which describes gravity not as a force, but as the curvature of spacetime, caused by the uneven distribution of mass, and causing masses to move along geodesic lines. The most extreme example of this curvature of spacetime is a black hole, from which nothing—not even light—can escape once past the black hole's event horizon. [3] However, for most applications, gravity is well approximated by Newton's law of universal gravitation, which describes gravity as a force causing any two bodies to be attracted toward each other, with magnitude proportional to the product of their masses and inversely proportional to the square of the distance between them.

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

## History

### Ancient world

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

Although he didn't understand gravity as a force, the ancient Greek philosopher Archimedes discovered the center of gravity of a triangle. [7] He also postulated that if two equal weights did not have the same center of gravity, the center of gravity of the two weights together would be in the middle of the line that joins their centers of gravity. [8]

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

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

### Scientific revolution

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

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

### Newton's theory of gravitation

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

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

where F is the force, m1 and m2 are the masses of the objects interacting, r is the distance between the centers of the masses and G is the gravitational constant.

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

### 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 of the orbit was increasing by about 42.98 arcseconds per century. The most obvious explanation for this discrepancy was an as-yet-undiscovered celestial body (such as a planet orbiting the Sun even closer than Mercury), but all efforts to find such a body turned out to be fruitless. Finally, in 1915, Albert Einstein developed a theory of general relativity which was able to accurately model Mercury's orbit. [26]

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

Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. These straight paths are called geodesics. As in Newton's first law of motion, Einstein believed that a force applied to an object would cause it to deviate from a geodesic. For instance, people standing on the surface of the Earth are prevented from following a geodesic path because the mechanical resistance of the Earth exerts an upward force on them. This explains why moving along the geodesics in spacetime is considered inertial.

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

## Modern understanding

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

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

### Solutions

Notable solutions of the Einstein field equations include:

### Tests

The tests of general relativity included the following: [36]

• General relativity accounts for the anomalous perihelion precession of Mercury. [37]
• The prediction that time runs slower at lower potentials (gravitational time dilation) has been confirmed by the Pound–Rebka experiment (1959), the Hafele–Keating experiment, and the GPS.
• The prediction of the deflection of light was first confirmed by Arthur Stanley Eddington from his observations during the Solar eclipse of 29 May 1919. [38] [39] Eddington measured starlight deflections twice those predicted by Newtonian corpuscular theory, in accordance with the predictions of general relativity. However, his interpretation of the results was later disputed. [40] More recent tests using radio interferometric measurements of quasars passing behind the Sun have more accurately and consistently confirmed the deflection of light to the degree predicted by general relativity. [41] See also gravitational lens.
• The time delay of light passing close to a massive object was first identified by Irwin I. Shapiro in 1964 in interplanetary spacecraft signals.
• Gravitational radiation has been indirectly confirmed through studies of binary pulsars. On 11 February 2016, the LIGO and Virgo collaborations announced the first observation of a gravitational wave.
• Alexander Friedmann in 1922 found that Einstein equations have non-stationary solutions (even in the presence of the cosmological constant). In 1927 Georges Lemaître showed that static solutions of the Einstein equations, which are possible in the presence of the cosmological constant, are unstable, and therefore the static Universe envisioned by Einstein could not exist. Later, in 1931, Einstein himself agreed with the results of Friedmann and Lemaître. Thus general relativity predicted that the Universe had to be non-static—it had to either expand or contract. The expansion of the Universe discovered by Edwin Hubble in 1929 confirmed this prediction. [42]
• The theory's prediction of frame dragging was consistent with the recent Gravity Probe B results. [43]
• 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 quantum mechanics

An open question is whether it is possible to describe the small-scale interactions of gravity with the same framework as quantum mechanics. General relativity describes large-scale bulk properties whereas quantum mechanics is the framework to describe the smallest scale interactions of matter. Without modifications these frameworks are incompatible. [44]

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

## Specifics

### Earth's gravity

Every planetary body (including the Earth) is surrounded by its own gravitational field, which can be conceptualized with Newtonian physics as exerting an attractive force on all objects. Assuming a spherically symmetrical planet, the strength of this field at any given point above the surface is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body.

The strength of the gravitational field is numerically equal to the acceleration of objects under its influence. [47] The rate of acceleration of falling objects near the Earth's surface varies very slightly depending on latitude, surface features such as mountains and ridges, and perhaps unusually high or low sub-surface densities. [48] For purposes of weights and measures, a standard gravity value is defined by the International Bureau of Weights and Measures, under the International System of Units (SI).

That value, denoted g, is g = 9.80665 m/s2 (32.1740 ft/s2). [49] [50]

The standard value of 9.80665 m/s2 is the one originally adopted by the International Committee on Weights and Measures in 1901 for 45° latitude, even though it has been shown to be too high by about five parts in ten thousand. [51] This value has persisted in meteorology and in some standard atmospheres as the value for 45° latitude even though it applies more precisely to latitude of 45°32'33". [52]

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

According to Newton's 3rd Law, the Earth itself experiences a force equal in magnitude and opposite in direction to that which it exerts on a falling object. This means that the Earth also accelerates towards the object until they collide. Because the mass of the Earth is huge, however, the acceleration imparted to the Earth by this opposite force is negligible in comparison to the object's. If the object does not bounce after it has collided with the Earth, each of them then exerts a repulsive contact force on the other which effectively balances the attractive force of gravity and prevents further acceleration.

The force of gravity on Earth is the resultant (vector sum) of two forces: [53] (a) The gravitational attraction in accordance with Newton's universal law of gravitation, and (b) the centrifugal force, which results from the choice of an earthbound, rotating frame of reference. The force of gravity is weakest at the equator because of the centrifugal force caused by the Earth's rotation and because points on the equator are furthest from the center of the Earth. The force of gravity varies with latitude and increases from about 9.780 m/s2 at the Equator to about 9.832 m/s2 at the poles.

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

Under an assumption of constant gravitational attraction, 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 time. The image on the right, spanning half a second, was captured with a stroboscopic flash at 20 flashes per second. During the first 120 of a second the ball drops one unit of distance (here, a unit is about 12 mm); by 220 it has dropped at total of 4 units; by 320, 9 units and so on.

Under the same constant gravity assumptions, the potential energy, Ep, of a body at height h is given by Ep = mgh (or Ep = Wh, with W meaning 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 body with initial velocity v is useful for small heights and small initial velocities only.

### Gravity and astronomy

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

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

General relativity predicts that energy can be transported out of a system through gravitational radiation. Any accelerating matter can create curvatures in the spacetime metric, which is how the gravitational radiation is transported away from the system. Co-orbiting objects can generate curvatures in spacetime such as the Earth-Sun system, pairs of neutron stars, and pairs of black holes. Another astrophysical system predicted to lose energy in the form of gravitational radiation are exploding supernovae.

The first indirect evidence for gravitational radiation was through measurements of the Hulse–Taylor binary in 1973. This system consists of a pulsar and neutron star in orbit around one another. Its orbital period has decreased since its initial discovery due to a loss of energy, which is consistent for the amount of energy loss due to gravitational radiation. This research was awarded the Nobel Prize in Physics in 1993.

The first direct evidence for gravitational radiation was measured on 14 September 2015 by the LIGO detectors. The gravitational waves emitted during the collision of two black holes 1.3 billion-light years from Earth were measured. [55] [56] This observation confirms the theoretical predictions of Einstein and others that such waves exist. It also opens the way for practical observation and understanding of the nature of gravity and events in the Universe including the Big Bang. [57] Neutron star and black hole formation also create detectable amounts of gravitational radiation. [58] This research was awarded the Nobel Prize in physics in 2017. [59]

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

### Speed of gravity

In December 2012, a research team in China announced that it had produced measurements of the phase lag of Earth tides during full and new moons which seem to prove that the speed of gravity is equal to the speed of light. [60] This means that if the Sun suddenly disappeared, the Earth would keep orbiting the vacant point normally for 8 minutes, which is the time light takes to travel that distance. The team's findings were released in the Chinese Science Bulletin in February 2013. [61]

In October 2017, the LIGO and Virgo detectors received gravitational wave signals within 2 seconds of gamma ray satellites and optical telescopes seeing signals from the same direction. This confirmed that the speed of gravitational waves was the same as the speed of light. [62]

## Anomalies and discrepancies

There are some observations that are not adequately accounted for, which may point to the need for better theories of gravity or perhaps be explained in other ways.

• Extra-fast stars: Stars in galaxies follow a distribution of velocities where stars on the outskirts are moving faster than they should according to the observed distributions of normal matter. Galaxies within galaxy clusters show a similar pattern. Dark matter, which would interact through gravitation but not electromagnetically, would account for the discrepancy. Various modifications to Newtonian dynamics have also been proposed.
• Flyby anomaly : Various spacecraft have experienced greater acceleration than expected during gravity assist maneuvers.
• Accelerating expansion: The metric expansion of space seems to be speeding up. Dark energy has been proposed to explain this. A recent alternative explanation is that the geometry of space is not homogeneous (due to clusters of galaxies) and that when the data are reinterpreted to take this into account, the expansion is not speeding up after all, [63] however this conclusion is disputed. [64]
• Anomalous 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.
• Extra energetic photons: Photons travelling through galaxy clusters should gain energy and then lose it again on the way out. The accelerating expansion of the Universe should stop the photons returning all the energy, but even taking this into account photons from the cosmic microwave background radiation gain twice as much energy as expected. This may indicate that gravity falls off faster than inverse-squared at certain distance scales. [65]
• Extra massive hydrogen clouds: The spectral lines of the Lyman-alpha forest suggest that hydrogen clouds are more clumped together at certain scales than expected and, like dark flow, may indicate that gravity falls off slower than inverse-squared at certain distance scales. [65]

## Footnotes

1. "dict.cc dictionary :: gravitas :: English-Latin translation". Archived from the original on 13 August 2021. Retrieved 11 September 2018.
2. Krebs, Robert E. (1999). (illustrated ed.). Greenwood Publishing Group. p.  133. ISBN   978-0-313-30226-8.
3. "HubbleSite: Black Holes: Gravity's Relentless Pull". hubblesite.org. Archived from the original on 26 December 2018. Retrieved 7 October 2016.
4. Staff. "Birth of the Universe". University of Oregon . Archived from the original on 28 November 2018. Retrieved 24 September 2016. – discusses "Planck time" and "Planck era" at the very beginning of the Universe
5. Cappi, Alberto. "The concept of gravity before Newton" (PDF). Culture and Cosmos.{{cite web}}: CS1 maint: url-status (link)
6. Bakker, Frederik; Palmerino, Carla Rita (1 June 2020). "Motion to the Center or Motion to the Whole? Plutarch's Views on Gravity and Their Influence on Galileo". Isis. 111 (2): 217–238. doi:10.1086/709138. ISSN   0021-1753.
7. Reviel Neitz; William Noel (13 October 2011). The Archimedes Codex: Revealing The Secrets of the World's Greatest Palimpsest. Hachette UK. p. 125. ISBN   978-1-78022-198-4. Archived from the original on 7 January 2020. Retrieved 10 April 2019.{{cite book}}: CS1 maint: multiple names: authors list (link)
8. CJ Tuplin, Lewis Wolpert (2002). Science and Mathematics in Ancient Greek Culture. Hachette UK. p. xi. ISBN   978-0-19-815248-4. Archived from the original on 17 January 2020. Retrieved 10 April 2019.
9. Pickover, Clifford (16 April 2008). Archimedes to Hawking: Laws of Science and the Great Minds Behind Them. Oxford University Press. ISBN   9780199792689. Archived from the original on 18 January 2017. Retrieved 29 August 2017.
10. Bose, Mainak Kumar (1988). Late classical India. A. Mukherjee & Co. Archived from the original on 13 August 2021. Retrieved 28 July 2021.
11. "Aryabhatta knew about gravity before Isaac Newton: ex-ISRO chief G Madhavan Nair". The Economic Times. Retrieved 2 May 2022.
12. Best, Shivali (19 August 2019). "Indian scientists 'discovered gravity centuries before Newton', minister claims". mirror. Retrieved 2 May 2022.
13. Starr, S. Frederick (2015). Lost Enlightenment: Central Asia's Golden Age from the Arab Conquest to Tamerlane. Princeton University Press. p. 260. ISBN   9780691165851.
14. {{Cite encyclopedia|encyclopedia=Encyclopedia of the History of Arabic Science|editor-first=Rāshid|editor-last=Rushdī|date=1996|publisher=Psychology Press|isbn=9780415124119|first1=Mariam |last1=Rozhanskaya |first2=I. S. |last2=Levinova |title=Statics |volume=2 |pages=614–642
15. Wallace, William A. (2018) [2004]. Domingo de Soto and the Early Galileo: Essays on Intellectual History. Abingdon, UK: Routledge. pp. 119, 121–22. ISBN   978-1-351-15959-3. Archived from the original on 16 June 2021. Retrieved 4 August 2021.
16. Drabkin, I. E. (1963). "Two Versions of G. B. Benedetti's Demonstratio Proportionum Motuum Localium". Isis. 54 (2): 259–262. doi:10.1086/349706. ISSN   0021-1753. JSTOR   228543. S2CID   144883728.
17. Schilling, Govert (31 July 2017). Ripples in Spacetime: Einstein, Gravitational Waves, and the Future of Astronomy. Harvard University Press. p. 26. ISBN   9780674971660. Archived from the original on 16 December 2021. Retrieved 16 December 2021.
18. Ball, Phil (June 2005). "Tall Tales". Nature News. doi:10.1038/news050613-10.
19. Galileo (1638), Two New Sciences , First Day Salviati speaks: "If this were what Aristotle meant you would burden him with another error which would amount to a falsehood; because, since there is no such sheer height available on earth, it is clear that Aristotle could not have made the experiment; yet he wishes to give us the impression of his having performed it when he speaks of such an effect as one which we see."
20. Gillispie, Charles Coulston (1960). The Edge of Objectivity: An Essay in the History of Scientific Ideas. Princeton University Press. pp. 3–6. ISBN   0-691-02350-6.
21. J.L. Heilbron, Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics (Berkeley: University of California Press, 1979), 180.
22. Sagan, Carl & Druyan, Ann (1997). Comet. New York: Random House. pp. 52–58. ISBN   978-0-3078-0105-0. Archived from the original on 15 June 2021. Retrieved 5 August 2021.
23. "The Reception of Newton's Principia" (PDF). Retrieved 6 May 2022.
24. "This Month in Physics History". www.aps.org. Retrieved 6 May 2022.
25. Nobil, Anna M. (March 1986). "The real value of Mercury's perihelion advance". Nature. 320 (6057): 39–41. Bibcode:1986Natur.320...39N. doi:10.1038/320039a0. S2CID   4325839.
26. Webb, Joh; Dougan, Darren (23 November 2015). "Without Einstein it would have taken decades longer to understand gravity" . Retrieved 21 May 2022.{{cite web}}: CS1 maint: url-status (link)
27. "Gravity and Warped Spacetime". black-holes.org. Archived from the original on 21 June 2011. Retrieved 16 October 2010.
28. Dmitri Pogosyan. "Lecture 20: Black Holes – The Einstein Equivalence Principle". University of Alberta. Archived from the original on 8 September 2013. Retrieved 14 October 2011.
29. Brush, S. G. (1 January 1999). "Why was Relativity Accepted?". Physics in Perspective. 1: 184–214. doi:10.1007/s000160050015. ISSN   1422-6944.
30. Lindley, David (12 July 2005). "The Weight of Light". Physics. 16.
31. "Hafele-Keating Experiment". hyperphysics.phy-astr.gsu.edu. Retrieved 22 May 2022.
32. "How the 1919 Solar Eclipse Made Einstein the World's Most Famous Scientist". Discover Magazine. Retrieved 22 May 2022.
33. "At Long Last, Gravity Probe B Satellite Proves Einstein Right". www.science.org. Retrieved 22 May 2022.
34. "Einstein showed Newton was wrong about gravity. Now scientists are coming for Einstein". NBC News. Retrieved 22 May 2022.
35. Pauli, Wolfgang Ernst (1958). "Part IV. General Theory of Relativity". Theory of Relativity. Courier Dover Publications. ISBN   978-0-486-64152-2.
36. Max Born (1924), Einstein's Theory of Relativity (The 1962 Dover edition, page 348 lists a table documenting the observed and calculated values for the precession of the perihelion of Mercury, Venus, and Earth.)
37. Dyson, F.W.; Eddington, A.S.; Davidson, C.R. (1920). "A Determination of the Deflection of Light by the Sun's Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919". Phil. Trans. Roy. Soc. A . 220 (571–581): 291–333. Bibcode:1920RSPTA.220..291D. doi:. Archived from the original on 15 May 2020. Retrieved 1 July 2019.. Quote, p. 332: "Thus the results of the expeditions to Sobral and Principe can leave little doubt that a deflection of light takes place in the neighbourhood of the sun and that it is of the amount demanded by Einstein's generalised theory of relativity, as attributable to the sun's gravitational field."
38. Weinberg, Steven (1972). . John Wiley & Sons. ISBN   9780471925675.. Quote, p. 192: "About a dozen stars in all were studied, and yielded values 1.98 ± 0.11" and 1.61 ± 0.31", in substantial agreement with Einstein's prediction θ = 1.75"."
39. Earman, John; Glymour, Clark (1980). "Relativity and Eclipses: The British eclipse expeditions of 1919 and their predecessors". Historical Studies in the Physical Sciences. 11 (1): 49–85. doi:10.2307/27757471. JSTOR   27757471. S2CID   117096916.
40. Weinberg, Steven (1972). . John Wiley & Sons. p.  194. ISBN   9780471925675.
41. See W.Pauli, 1958, pp. 219–220
42. "NASA's Gravity Probe B Confirms Two Einstein Space-Time Theories". Nasa.gov. Archived from the original on 22 May 2013. Retrieved 23 July 2013.
43. Randall, Lisa (2005). Warped Passages: Unraveling the Universe's Hidden Dimensions. Ecco. ISBN   978-0-06-053108-9.
44. Feynman, R.P.; Morinigo, F.B.; Wagner, W.G.; Hatfield, B. (1995). . Addison-Wesley. ISBN   978-0-201-62734-3.
45. Zee, A. (2003). Quantum Field Theory in a Nutshell. Princeton University Press. ISBN   978-0-691-01019-9.
46. Cantor, G.N.; Christie, J.R.R.; Hodge, M.J.S.; Olby, R.C. (2006). Companion to the History of Modern Science. Routledge. p. 448. ISBN   978-1-134-97751-2. Archived from the original on 17 January 2020. Retrieved 22 October 2017.
47. Nemiroff, R.; Bonnell, J., eds. (15 December 2014). "The Potsdam Gravity Potato". Astronomy Picture of the Day . NASA.
48. Bureau International des Poids et Mesures (2006). "The International System of Units (SI)" (PDF) (8th ed.): 131. Archived (PDF) from the original on 14 August 2017. Retrieved 3 April 2013. Unit names are normally printed in Roman (upright) type ... Symbols for quantities are generally single letters set in an italic font, although they may be qualified by further information in subscripts or superscripts or in brackets.{{cite journal}}: Cite journal requires |journal= (help)
49. "SI Unit rules and style conventions". National Institute For Standards and Technology (USA). September 2004. Archived from the original on 5 February 2008. Retrieved 3 April 2013. Variables and quantity symbols are in italic type. Unit symbols are in Roman type.
50. List, R.J. editor, 1968, Acceleration of Gravity, Smithsonian Meteorological Tables, Sixth Ed. Smithsonian Institution, Washington, DC, p. 68.
51. U.S. Standard Atmosphere Archived 1 February 2014 at the Wayback Machine , 1976, U.S. Government Printing Office, Washington, D.C., 1976. (Linked file is very large.)
52. Hofmann-Wellenhof, B.; Moritz, H. (2006). Physical Geodesy (2nd ed.). Springer. ISBN   978-3-211-33544-4. § 2.1: "The total force acting on a body at rest on the earth's surface is the resultant of gravitational force and the centrifugal force of the earth's rotation and is called gravity".{{cite book}}: CS1 maint: postscript (link)
53. "Milky Way Emerges as Sun Sets over Paranal". www.eso.org. European Southern Obseevatory. Archived from the original on 4 March 2016. Retrieved 29 April 2015.
54. Clark, Stuart (11 February 2016). "Gravitational waves: scientists announce 'we did it!' live". the Guardian. Archived from the original on 22 June 2018. Retrieved 11 February 2016.
55. Castelvecchi, Davide; Witze, Witze (11 February 2016). "Einstein's gravitational waves found at last". Nature News. doi:10.1038/nature.2016.19361. S2CID   182916902. Archived from the original on 12 February 2016. Retrieved 11 February 2016.
56. "WHAT ARE GRAVITATIONAL WAVES AND WHY DO THEY MATTER?". popsci.com. Archived from the original on 3 February 2016. Retrieved 12 February 2016.
57. Abbott, B. P.; et al. (LIGO Scientific Collaboration & Virgo Collaboration) (October 2017). "GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral" (PDF). Physical Review Letters . 119 (16): 161101. arXiv:. Bibcode:2017PhRvL.119p1101A. doi:. PMID   29099225. Archived (PDF) from the original on 8 August 2018. Retrieved 28 September 2019.
58. Devlin, Hanna (3 October 2017). "Nobel prize in physics awarded for discovery of gravitational waves". the Guardian. Archived from the original on 3 October 2017. Retrieved 3 October 2017.
59. Chinese scientists find evidence for speed of gravity Archived 8 January 2013 at the Wayback Machine , astrowatch.com, 12/28/12.
60. TANG, Ke Yun; HUA ChangCai; WEN Wu; CHI ShunLiang; YOU QingYu; YU Dan (February 2013). "Observational evidences for the speed of the gravity based on the Earth tide". Chinese Science Bulletin. 58 (4–5): 474–477. Bibcode:2013ChSBu..58..474T. doi:.
61. "GW170817 Press Release". LIGO Lab – Caltech. Archived from the original on 17 October 2017. Retrieved 24 October 2017.
62. Dark energy may just be a cosmic illusion Archived 13 August 2021 at the Wayback Machine , New Scientist, issue 2646, 7 March 2008.
63. Swiss-cheese model of the cosmos is full of holes Archived 6 May 2015 at the Wayback Machine , New Scientist, issue 2678, 18 October 2008.
64. Chown, Marcus (16 March 2009). "Gravity may venture where matter fears to tread". New Scientist. Archived from the original on 18 December 2012. Retrieved 4 August 2013.
65. Brans, C.H. (March 2014). "Jordan-Brans-Dicke Theory". Scholarpedia. 9 (4): 31358. arXiv:. Bibcode:2014Schpj...931358B. doi:10.4249/scholarpedia.31358.
66. Horndeski, G.W. (September 1974). "Second-Order Scalar-Tensor Field Equations in a Four-Dimensional Space". International Journal of Theoretical Physics. 88 (10): 363–384. Bibcode:1974IJTP...10..363H. doi:10.1007/BF01807638. S2CID   122346086.
67. Milgrom, M. (June 2014). "The MOND paradigm of modified dynamics". Scholarpedia. 9 (6): 31410. Bibcode:2014SchpJ...931410M. doi:.
68. Haugan, Mark P; Lämmerzahl, C (2011). "Einstein gravity from conformal gravity". arXiv: [hep-th].

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