The 1st All-Female Spacewalk Is Back on As NASA Gears Up for 10-EVA Marathon & Muitos laboratórios fazem pesquisa usando camundongos desde muito tempo, resultando até na obtenção de prêmios para os pesquisadores, como o prêmio Nobel. Por ex: a Jackson Laboratory nos Estados Unidos &@ LinkedIn, Facebook and Twitter Images & James Peebles, Michel Mayor and Didier Queloz share Nobel Prize for Physics & European Animal Research Association (EARA) – The search for better animal models of Alzheimer’s disease – Improved cellular and animal models of the condition could provide a much needed boost for drug development @ Astronomers find 20 new moons around Saturn and you can help name them @ ´´Gravity (from Latin gravitas, meaning ‘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 brought toward (or gravitate toward) one another. On Earth, gravity gives weight to physical objects, and the Moon’s gravity causes the ocean tides.´´

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SubscribeSearchLoginOUTLOOK  25 JULY 2018

The search for better animal models of Alzheimer’s disease

Improved cellular and animal models of the condition could provide a much needed boost for drug development.

Anthony King

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Two researchers examine a glass slide containing a tissue sample.
Tisianna Kamba and Bruce Lamb work with mouse models of Alzheimer’s disease.Credit: Indiana Univ. School of Medicine

In the past three decades, scientists’ knowledge of the biology that underlies Alzheimer’s disease has advanced tremendously. In particular, the roles of aberrant accumulation in the brain of the peptide amyloid-β, which is derived from amyloid precursor protein (APP), and microtubule-associated protein tau are now much better understood. But efforts to convert this insight into gains in the clinic have floundered. Although researchers have conducted more than 400 trials in people of potential treatments for Alzheimer’s disease, almost no drugs have been brought to the market. And despite the blame being placed on a variety of factors, one of the main sources of researchers’ concern is the animal models that are used in the initial stages of drug development.

The proposal that amyloid-β peptides aggregate into structures known as plaques, from which other features of Alzheimer’s disease stem, became the leading hypothesis of the condition in the 1990s. Ever since, removing these peptide deposits has been viewed as a promising therapeutic strategy. However, no animal model of Alzheimer’s disease was available in which such experiments could be performed. This is because researchers could find no evidence of the condition in organisms other than humans, which hampered the discovery and development of potential drugs.Part of Nature Outlook: Alzheimer’s disease

Then, in 1995, researchers made a breakthrough — the creation of transgenic mice carrying a single gene mutation associated with the uncommon, inherited form of Alzheimer’s disease, which is characterized by an early onset, at around the age of 45. Known as PD-APP mice, these animals express high levels of mutant APP in their brains and develop many hallmarks of Alzheimer’s disease, including plaques and cognitive deficits. Researchers drew confidence from the structural similarity between the mouse plaques and those found in people. Subsequent models similarly focused on the expression of mutant APP. In 2006, several research groups generated mice containing multiple gene mutations associated with familial Alzheimer’s disease. The mice accumulated amyloid-β deposits faster than did AD-APP mice, with plaques appearing in the brain after only around 2 months, compared with at least 6 months in the single-mutation mice.

Such models provided researchers with important insight into Alzheimer’s disease. They showed, for instance, that mutations associated with inherited Alzheimer’s disease favour the production of a variant of amyloid-β called amyloid-β(1–42), which is two amino acids longer than the usual form and aggregates more readily. The models also served as crucial preclinical test beds for drugs. In 1999, an experimental vaccine was able to clear amyloid-β from the brains of PD-APP mice. Several monoclonal antibodies have since been shown to clear plaques in mouse models. But all have failed to provide benefit to people with Alzheimer’s disease in trials. Even in cases in which the drugs cleared plaques from the brain, participants did not show improvements in memory.

“While mouse models have provided astounding new insights into disease mechanisms,” says Bruce Lamb, a neuroscientist at Indiana University School of Medicine in Indianapolis, “they don’t reflect the entire biology of the disease.” Researchers are now seeking to create mouse models that better reflect the more common, sporadic form of Alzheimer’s disease, as well as to develop alternative animal models.

Starting small

Alzheimer’s disease is generally considered to be a disease of old age — unless a person has inherited a rare mutation, the average age of onset is around 80. But in many mouse models of the condition, plaques can appear in animals that are only a few months old. This difference provides a possible explanation for why drugs that successfully treat mice do not work in people. “A lot of the data in mice is from young animals, and their immune system is quite different from an aged individual,” says Matthew Campbell, a geneticist at Trinity College Dublin, Ireland. The mouse models, therefore, might best reflect the early stages of Alzheimer’s disease, including the period before a patient’s diagnosis. If that were the case, clinical trials of drugs that target amyloid-β could be failing because people are treated too late to halt the death of brain cells. “Most of the animal work has seen mice treated at the beginning of plaque build-up, which is more a prevention than treatment paradigm,” says Cynthia Lemere, a neuroscientist at Brigham and Women’s Hospital in Boston, Massachusetts. Work to discover biomarkers that could help doctors to identify Alzheimer’s disease in people before they show symptoms is now under way.

If clearing amyloid-β from the brains of such individuals was shown to prevent them from developing the condition, the mouse models would be partially exonerated. But researchers know that there are areas in which the condition, as modelled in mice, deviates considerably from Alzheimer’s disease in humans. The first mouse models were designed to overexpress proteins containing mutations that lead to greater aggregation of amyloid-β. These include APP and PSEN1, a subunit of an enzyme called γ-secretase that is involved in APP processing. However, although this strategy reliably produces cellular hallmarks that mimic those of Alzheimer’s disease in people, the mechanism by which they are created is not the same. “Humans do not overexpress APP or PSEN1,” says Takaomi Saido, a neuroscientist at the RIKEN Centre for Brain Science in Saitama, Japan. The profusion of mutant protein generated by the overexpression throws grit into the metabolic cogs of the brain cells of mice, causing problems that are unrelated to Alzheimer’s disease. “Many of these mice show cognitive defects before amyloid-β pathology starts, and many die early,” Saido explains.

In 2014, he developed a mouse model that overproduces amyloid-β(1–42) without overexpressing APP. In these mice, mutant human APP is produced at physiologically normal levels, as well as in the expected regions of the brain. The animals show memory impairment that Saido thinks could reflect early cognitive decline in people. “It was hard to tease apart effects due to amyloid and effects due to the overexpression of the precursor proteins,” says Lemere, of the first mouse models. Now, she and the members of more than 300 laboratories worldwide use Saido’s mice.

But amyloid-β represents only part of the story of Alzheimer’s disease. Most mouse models under development still struggle to replicate another important aspect of the disease: dysfunction of tau. In people, amyloid-β aggregation is followed by the formation of insoluble tau aggregates, known as neurofibrillary tangles, inside neurons. But PD-APP mice loaded with amyloid-β plaques do not develop tau tangles, and they show limited loss of neurons. In 2002, Michel Goedert, a neuroscientist at the University of Cambridge, UK, produced one of the first transgenic mouse models to generate tau tangles. The model, and others similar to it, have revealed much about tau tangles and how they propagate, says Goedert. “In human disease, the tau pathology seems to become self-sustaining,” he says. Saido and Lamb are now developing mouse models that produce humanized tau. Mice that express physiological levels of both human APP and human tau would be ideal for testing potential drugs, says Lemere.

Unfortunately, no mutation in tau has yet been linked to Alzheimer’s disease. “There is probably a pathway from amyloid-β aggregation to tau aggregation,” says Goedert. But in the absence of a clear mechanism, current mouse models use tau mutations implicated in another cognitive disorder of humans known as frontotemporal dementia. Sometimes these mutations are combined with others that generate amyloid-β plaques to achieve models that get even closer to mimicking Alzheimer’s disease. Still, many researchers question the value of such models. “That combination is not seen in people. When you force together mutations, you have to ask what that model is representing,” says Lamb.

In 2016, the US National Institute on Aging assigned a group of researchers, led by Lamb, the task of developing mouse models that more closely reflect Alzheimer’s disease. Called MODEL-AD, the consortium — a collaboration between Indiana University, the Jackson Laboratory in Bar Harbor, Maine, Sage Bionetworks of Seattle, Washington (a non-profit organization that promotes open science) and the University of California, Irvine — aims to accurately represent the sporadic, late-onset form of Alzheimer’s disease in mice, which has been largely overlooked by current models. “That to me is the biggest disconnect with the models,” says Lamb.

The consortium has already created a mouse model that incorporates the ε4 variant of the gene APOE, which is closely associated with an increased risk of the sporadic form of Alzheimer’s disease. It encodes apolipoprotein E, a protein that transports cholesterol in the central nervous system and influences amyloid-β aggregation and clearance in the brain. People with a single copy of APOE ε4 have a 3-fold greater risk of developing the condition; those with two copies have a 12-fold greater risk. The model also expresses a variant of the gene TREM2, which encodes a cell-surface receptor on microglia (the immune cells of the brain). That variant increases the risk of developing sporadic Alzheimer’s disease by up to four times. The consortium plans to introduce up to ten new mouse models per year during the project’s first five years of funding. It will also use the genome-editing technology CRISPR in mice to stack up gene variants identified as risk factors in humans. “APOE ε4 is the biggest risk factor for Alzheimer’s disease beyond ageing,” says Lemere, who will soon begin to use mouse models expressing the ε4 variant — as well as another APOE variant called ε3, which has a more neutral effect on risk. “If you put the APOE ε4 variant into a mouse model, it causes earlier and more robust plaque deposition — just like in humans,” she says.

Standard species

Although mice have been productive workhorses for research on Alzheimer’s disease, the difficulties that researchers have experienced in translating promising findings from mice into successful trials in people are driving the field to explore other options for animal models. “The predictive value of transgenic mouse models for therapeutics has been limited,” says Lary Walker, a neuroscientist at Emory University School of Medicine in Atlanta, Georgia. One route to closing the gap between people and animal models is to start with a species more-closely related to humans, such as one of the non-human primates. “If a genetically modified primate can be generated that develops bona fide Alzheimer’s disease within a reasonable time frame, this would be a boon to the field,” Walker says.

Non-human primates, which include rhesus macaques and marmosets, are not known to develop Alzheimer’s disease. However, like humans, they do accumulate deposits of amyloid-β in their brains. The brains of these animals also undergo structural and biochemical changes as they age that mirror those seen in people. However, most such primates do not develop tau tangles, and their use in research is accompanied by a host of practical challenges and ethical considerations.

A marmoset sits on a tree branch.
Researchers are developing marmoset models of Alzheimer’s disease.Credit: Mike Powles/Getty Images

Macaques are the most popular choice of non-human primate for researchers who work on Alzheimer’s disease, but no particular species or model is accepted over others. “Non-human primate models are not used much in academia or in industry because they are not validated,” says Erwan Bezard, director of the Institute of Neurodegenerative Diseases at the University of Bordeaux, France. This could soon change. The European Union is sponsoring a consortium of research organizations called IMPRiND that is striving to develop a standardized macaque model of Alzheimer’s disease.

As part of the project, Bezard is working to recreate the condition’s progression in macaques by injecting them with brain tissue from humans, which leads the animals to develop plaques and tau tangles, as well as cognitive impairment. This approach has already produced a primate model of the neurodegenerative disorder Parkinson’s disease. Validating a macaque model of Alzheimer’s disease could convince a wary pharmaceutical industry that, although expensive, it would be sensible to work with such a model before embarking on clinical trials. Indeed, Bezard argues, had non-human primate models already been in wider use, many failed clinical trials could have been avoided. “It was expected, based on the rodent work, that removing plaques would help the cognitive status of patients,” he says. Tests in non-human primates could have shown that this would not be the case.

At RIKEN, Saido is creating a marmoset model of Alzheimer’s disease by using CRISPR to insert mutations into the gene PSEN1 in fertilized eggs. Marmosets hold two big advantages over macaques: they can develop both amyloid-β plaques and tau tangles, and plaques are established more quickly (taking 7 years, rather than around 25 years, to appear). Although researchers will still have to wait for a long time, Saido’s mutations will accelerate plaque formation so that the models become useful even faster — in just a year or two, he expects. The first of his modified marmosets is expected to be born later this year.

As researchers learn more about how immunological processes influence the onset and progression of Alzheimer’s disease, there will be an increasing need to test potential drugs on non-human primates, which have immune systems similar to those of humans. Saido hopes to take advantage of marmosets’ similarity to humans to identify biomarkers that might not be found in mice. But there is no sign that the high costs and ethical controversy associated with research on non-human primates will disappear.

Mini-brains

In the past five years, researchers have been given a further option for use in preclinical testing — 3D tissue models of the brain. These small organoids are grown from stem cells over periods of a few weeks, and they enable large numbers of drugs to be evaluated in a short amount of time.

A false-coloured microscopy image of a brain organoid.
Stem-cell-derived brain organoids can provide an alternative to animal models of Alzheimer’s disease.Credit: Mehdi Jorfi/Doo Yeon Kim/Rudolph Tanzi

Rudy Tanzi, a neuroscientist at Harvard Medical School in Boston, Massachusetts, reported in 2014 that his lab had grown human neural stem cells containing APP and PSEN1 mutations in a 3D culture system supported by a gel matrix (S. H. Choi et al. Nature 515, 274–278; 2014). The results were startling: the tissue that developed contained neurons that deposited amyloid-β into the gel, and plaques formed after 5 to 6 weeks. A week or two later, the elusive tau tangles also appeared. The finding provided considerable support for the idea that amyloid-β accumulation leads to tangle formation in Alzheimer’s disease — known as the amyloid hypothesis. “All previous models failed to show the plaques going into tangles,” says Doo Yeon Kim, a neurologist at Harvard Medical School who worked on the project with Tanzi. “These are real tau filaments, indistinguishable from those you see in the Alzheimer’s-patient brain,” Tanzi adds. In mice, the brain generates a single variety of tau known as 4-repeat tau. But the human neurons in 3D culture generated both 4-repeat tau and another type of tau (3-repeat tau) in a 50 : 50 ratio — as occurs in the adult human brain.

Li-Huei Tsai, a cognitive neuroscientist at the Massachusetts Institute of Technology in Cambridge, is also using human brain organoids in her research on Alzheimer’s disease. In 2014, her lab transformed cells from people with the condition who had either an APP duplication or a PSEN1 mutation into induced pluripotent stem (iPS) cells. The cells formed small brain-like tissues that developed aggregates of amyloid-β and tau protein. Both hallmarks of Alzheimer’s disease were reduced when the secretases that chop up APP were inhibited — a strategy also being pursued in clinical trials.

“This is a new platform for drug discovery,” says Tsai. Earlier this year, Tsai and her colleagues reported that brain cells derived from iPS cells carrying the APOE ε4 variant secreted more of the stickier amyloid-β(1–42), which encouraged aggregation of amyloid-β and tau (Y. T. Lin et al. Neuron 98, 1141–1154; 2018). Using CRISPR to edit the cells so that the risk-conferring variant ε4 was replaced with the risk-neutral variant ε3 led to a reduction in signs of the condition, including increased amyloid-β production, in neurons, immune cells and even organoids.

The race is on to add different cell types to organoids, so that they can better represent real brain tissue. Tanzi has already incorporated microglia into his model. Initially held in a reservoir outside the dish in which the organoids grow, the microglia travel down microfluidic channels into the main plate in response to the release of pro-inflammatory compounds by stressed neurons (J. Park et al. Nature Neurosci. 21, 941–951; 2018). The microglia then respond to any plaques by pruning the junctions between neurons — effectively trimming the connections that underpin memory. Tanzi thinks that this is how the immune system responds to plaques and tangles, and inflicts harm on the brain.

A considerable advantage of growing model brains in a dish is that it enables rapid screening of compounds for potential drugs. “We are testing all FDA-approved drugs — about 1,200 of them — in these 3D cell-culture models,” says Kim. The number of mice needed to conduct such a screen would be prohibitive. “The dish is faster, more effective and less expensive,” adds Tanzi. His group has found 38 drugs that reduce tangles by at least 90%, as well as 13 drugs that can curb inflammation of nerve tissue.

The cost of variety

Many researchers now use more than one model of Alzheimer’s disease in their work. “The availability of transgenic mouse models has been a fantastic boon for neurodegenerative disorders,” says Thomas Wisniewski, a neuroscientist at NYU Langone Medical Center in New York City. “But they are a mixed blessing, and should be used with caution.” He advocates diversification — at present, he is working with four mouse models, as well as a squirrel-monkey model. “That should be a more-typical approach,” Wisniewski says. Lamb agrees: “Different models can give different results.”More from Nature Outlooks

The cost associated with using several animal models at once is a concern. Even mouse models, which have dominated preclinical research for decades, are not as affordable as some researchers would like. “There are still proprietary mouse models that cost €300 (US$349) to €400 per mouse,” says Campbell, noting that such costs stop him from using certain models. For its part, MODEL-AD will make its mouse models and associated imaging and phenotypic data freely available. “The field has been slowed because of restrictions placed on some models,” says Lamb, who cites lawsuits initiated against academics and companies for their use of certain strains that contain patented DNA sequences.

As more scientists embrace a multitude of models in their research, Tsai expects the cost of research on Alzheimer’s disease to climb. There are signs, however, that funding bodies are taking note — given that an increasing number of people are expected to be affected by dementia. In March, the US Congress gave the US National Institutes of Health an extra $414 million for research on Alzheimer’s disease and dementia, bringing the total amount dedicated to work on dementia in 2018 to $1.8 billion. It seems that the human cost of the consistent failure of clinical trials of drugs for Alzheimer’s disease outweighs all others.

Nature 559, S13-S15 (2018)doi: 10.1038/d41586-018-05722-9

This article is part of Nature Outlook: Alzheimer’s disease, an editorially independent supplement produced with the financial support of third parties. About this content.

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Gravity

From Wikipedia, the free encyclopediaJump to navigationJump to searchFor other uses, see Gravity (disambiguation).”Gravitation” and “Law of Gravity” redirect here. For other uses, see Gravitation (disambiguation) and Law of Gravity (disambiguation).

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{\displaystyle {\vec {F}}=m{\vec {a}}}{\vec {F}}=m{\vec {a}}Second law of motion
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File:Apollo 15 feather and hammer drop.ogv

Hammer and feather drop: astronautDavid Scott (from mission Apollo 15) on the Moon enacting the legend of Galileo‘s gravity experiment. (1.38 MBogg/Theora format).

Gravity (from Latin gravitas, meaning ‘weight’[1]), or gravitation, is a natural phenomenon by which all things with mass or energy—including planetsstarsgalaxies, and even light[2]—are brought toward (or gravitate toward) one another. On Earth, gravity gives weight to physical objects, and the Moon‘s gravity causes the ocean tides. The gravitational attraction of the original gaseous matter present in the Universe caused it to begin coalescingforming stars—and for 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 increasingly weaker as objects get further 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 a consequence of the curvature of spacetime caused by the uneven distribution of mass. 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 which causes any two bodies to be attracted to each other, with the force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Gravity is the weakest of the four fundamental interactions of physics, 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 consequence, it has no significant influence at the level of subatomic particles.[4] In contrast, it is the dominant interaction at the macroscopic scale, and is the cause of the formation, shape and trajectory (orbit) of astronomical bodies.

The earliest instance of gravity in the Universe, possibly in the form of quantum gravitysupergravity 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 vacuumquantum vacuum or virtual particle, in a currently unknown manner.[5] Attempts 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, are a current area of research.

Contents

History of gravitational theory

Main article: History of gravitational theory

Ancient world

The ancient Greek philosopher Archimedes discovered the center of gravity of a triangle.[6] 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.[7]

The Roman architect and engineer Vitruvius in De Architectura postulated that gravity of an object did not depend on weight but its “nature”.[8]Main article: List of Indian inventions and discoveries § Sciences

In ancient India, Aryabhata first identified the force to explain why objects are not thrown outward as the earth rotates. Brahmagupta described gravity as an attractive force and used the term “gurutvaakarshan” for gravity.[9][10]

Scientific revolution

Main article: Scientific revolution

Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and early 17th centuries. In his famous (though possibly apocryphal[11]) experiment dropping balls from the Tower of Pisa, and later with careful measurements of balls rolling down inclines, Galileo showed that gravitational acceleration is the same for all objects. This was a major departure from Aristotle‘s belief that heavier objects have a higher gravitational acceleration.[12] Galileo postulated air resistance as the reason that objects with less mass fall more slowly in an atmosphere. Galileo’s work set the stage for the formulation of Newton’s theory of gravity.[13]

Newton’s theory of gravitation

Main article: Newton’s law of universal gravitationEnglish physicist and mathematician, Sir Isaac Newton (1642–1727)

In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. In his own words, “I deduced 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: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly.”[14] The equation is the following:

{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}\ }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 theory enjoyed its greatest success when it 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’s calculations are what led Johann Gottfried Galle to the discovery of Neptune.

A discrepancy in Mercury‘s orbit pointed out flaws in Newton’s theory. By the end of the 19th century, it was known that its orbit showed slight perturbations that could not be accounted for entirely under Newton’s theory, but all searches for another perturbing body (such as a planet orbiting the Sun even closer than Mercury) had been fruitless. The issue was resolved in 1915 by Albert Einstein‘s new theory of general relativity, which accounted for the small discrepancy in Mercury’s orbit. This discrepancy was the advance in the perihelion of Mercury of 42.98 arcseconds per century.[15]

Although Newton’s theory has been superseded by Einstein‘s general relativity, most modern non-relativistic gravitational calculations are still made using Newton’s theory because it is simpler to work with and it gives sufficiently accurate results for most applications involving sufficiently small masses, speeds and energies.

Equivalence principle

The equivalence principle, explored by a succession of researchers including Galileo, Loránd Eötvös, and Einstein, expresses the idea that all objects fall in the same way, and that the effects of gravity are indistinguishable from certain aspects of acceleration and deceleration. The simplest way to test the weak equivalence principle is to drop two objects of different masses or compositions in a vacuum and see whether they hit the ground at the same time. Such experiments demonstrate that all objects fall at the same rate when other forces (such as air resistance and electromagnetic effects) are negligible. More sophisticated tests use a torsion balance of a type invented by Eötvös. Satellite experiments, for example STEP, are planned for more accurate experiments in space.[16]

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.[17]
  • The Einsteinian equivalence principle: The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.[18]
  • The strong equivalence principle requiring both of the above.

General relativity

See also: Introduction to general relativityTwo-dimensional analogy of spacetime distortion generated by the mass of an object. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. White lines do not represent the curvature of space but instead represent the coordinate system imposed on the curved spacetime, which would be rectilinear in a flat spacetime.

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General relativity
{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={8\pi G \over c^{4}}T_{\mu \nu }}
IntroductionHistoryMathematical formulationTests
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Phenomena[show]
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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 free fall with inertial motion and describes free-falling inertial objects as being accelerated relative to non-inertial observers on the ground.[19][20] In Newtonian physics, however, no such acceleration can occur unless at least one of the objects is being operated on by a force.

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

Einstein discovered the 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 simultaneousnon-lineardifferential 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:[21]

  • General relativity accounts for the anomalous perihelion precession of Mercury.[22]
  • 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.[23][24] 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.[25] 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.[26] 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.[27]
  • The theory’s prediction of frame dragging was consistent with the recent Gravity Probe B results.[28]
  • 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

Main articles: Graviton and Quantum gravity

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. As of 2020, bringing together these two frameworks of general relativity and quantum mechanics is incompatible. [29]

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[30][31] . This description reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length,[29] where a more complete theory of quantum gravity (or a new approach to quantum mechanics) is required.

Specifics

Earth’s gravity

An initially-stationary object that is allowed to fall freely under gravity drops a distance that is proportional to the square of the elapsed time. This image spans half a second and was captured at 20 flashes per second.Main article: 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.If an object with comparable mass to that of the Earth were to fall towards it, then the corresponding acceleration of the Earth would be observable.

The strength of the gravitational field is numerically equal to the acceleration of objects under its influence.[32] 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.[33] 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).[34][35]

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.[36] 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”.[37]

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:[38] (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 the 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

Main article: Equations for a falling body

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 energyEp, 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}}}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

Gravity acts on stars that form the Milky Way.[39]

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 vacuumquantum 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.Main article: Gravitational wave

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

The first indirect evidence for gravitational radiation was through measurements of the 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.[40][41] 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.[42] Neutron star and black hole formation also create detectable amounts of gravitational radiation.[43]. This research was awarded the Nobel Prize in physics in 2017. [44]

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

Speed of gravity

Main article: 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.[45] This means that if the Sun suddenly disappeared, the Earth would keep orbiting it 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.[46]

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.[47]

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.Rotation curve of a typical spiral 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 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,[48] however this conclusion is disputed.[49]
  • 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.[50]
  • 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.[50]

Alternative theories

Main article: Alternatives to general relativity

Historical alternative theories

Modern alternative theories

See also

Footnotes

  1. ^ dict.cc dictionary :: gravitas :: English-Latin translation
  2. ^ Comins, Neil F.; Kaufmann, William J. (2008). Discovering the Universe: From the Stars to the Planets. MacMillan. p. 347. Bibcode:2009dufs.book…..CISBN 978-1429230421.
  3. ^ “HubbleSite: Black Holes: Gravity’s Relentless Pull”hubblesite.org. Retrieved 7 October 2016.
  4. ^ Krebs, Robert E. (1999). Scientific Development and Misconceptions Through the Ages: A Reference Guide(illustrated ed.). Greenwood Publishing Group. p. 133. ISBN 978-0-313-30226-8.
  5. Jump up to:a b Staff. “Birth of the Universe”University of Oregon. Retrieved 24 September 2016. – discusses “Planck time” and “Planck era” at the very beginning of the Universe
  6. ^ 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.
  7. ^ CJ Tuplin, Lewis Wolpert (2002). Science and Mathematics in Ancient Greek Culture. Hachette UK. p. xi. ISBN 978-0-19-815248-4.
  8. ^ Vitruvius, Marcus Pollio (1914). “7”. In Alfred A. Howard (ed.). De Architectura libri decem [Ten Books on Architecture]. VII. Herbert Langford Warren, Nelson Robinson (illus), Morris Hicky Morgan. Harvard University, Cambridge: Harvard University Press. p. 215.
  9. ^ Pickover, Clifford (16 April 2008). Archimedes to Hawking: Laws of Science and the Great Minds Behind Them. Oxford University Press. ISBN 9780199792689.
  10. ^ *Sen, Amartya (2005). The Argumentative Indian. Allen Lane. p. 29. ISBN 978-0-7139-9687-6.
  11. ^ Ball, Phil (June 2005). “Tall Tales”. Nature Newsdoi:10.1038/news050613-10.
  12. ^ 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.”
  13. ^ Bongaarts, Peter (2014). Quantum Theory: A Mathematical Approach (illustrated ed.). Springer. p. 11. ISBN 978-3-319-09561-5.
  14. ^ *Chandrasekhar, Subrahmanyan (2003). Newton’s Principia for the common reader. Oxford: Oxford University Press. (pp. 1–2). The quotation comes from a memorandum thought to have been written about 1714. As early as 1645 Ismaël Bullialdus had argued that any force exerted by the Sun on distant objects would have to follow an inverse-square law. However, he also dismissed the idea that any such force did exist. See, for example, Linton, Christopher M. (2004). From Eudoxus to Einstein – A History of Mathematical Astronomy. Cambridge: Cambridge University Press. p. 225. ISBN 978-0-521-82750-8.
  15. ^ Nobil, Anna M. (March 1986). “The real value of Mercury’s perihelion advance”. Nature320 (6057): 39–41. Bibcode:1986Natur.320…39Ndoi:10.1038/320039a0.
  16. ^ M.C.W.Sandford (2008). “STEP: Satellite Test of the Equivalence Principle”Rutherford Appleton Laboratory. Archived from the original on 28 September 2011. Retrieved 14 October 2011.
  17. ^ Paul S Wesson (2006). Five-dimensional Physics. World Scientific. p. 82. ISBN 978-981-256-661-4.
  18. ^ Haugen, Mark P.; C. Lämmerzahl (2001), “Principles of Equivalence: Their Role in Gravitation Physics and Experiments that Test Them”, Gyros, Lecture Notes in Physics, 562 (562, Gyros, Clocks, and Interferometers…: Testing Relativistic Gravity in Space): 195–212, arXiv:gr-qc/0103067Bibcode:2001LNP…562..195Hdoi:10.1007/3-540-40988-2_10
  19. ^ “Gravity and Warped Spacetime”. black-holes.org. Archived from the original on 21 June 2011. Retrieved 16 October 2010.
  20. ^ Dmitri Pogosyan. “Lecture 20: Black Holes – The Einstein Equivalence Principle”. University of Alberta. Retrieved 14 October 2011.
  21. ^ Pauli, Wolfgang Ernst (1958). “Part IV. General Theory of Relativity”. Theory of Relativity. Courier Dover Publications. ISBN 978-0-486-64152-2.
  22. ^ 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.)
  23. ^ 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. A220 (571–581): 291–333. Bibcode:1920RSPTA.220..291Ddoi:10.1098/rsta.1920.0009.. 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.”
  24. ^ Weinberg, Steven (1972). Gravitation and cosmology. John Wiley & Sons.. 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″.”
  25. ^ Earman, John; Glymour, Clark (1980). “Relativity and Eclipses: The British eclipse expeditions of 1919 and their predecessors”Historical Studies in the Physical Sciences11 (1): 49–85. doi:10.2307/27757471JSTOR 27757471.
  26. ^ Weinberg, Steven (1972). Gravitation and cosmology. John Wiley & Sons. p. 194.
  27. ^ See W.Pauli, 1958, pp. 219–220
  28. ^ “NASA’s Gravity Probe B Confirms Two Einstein Space-Time Theories”. Nasa.gov. Retrieved 23 July 2013.
  29. Jump up to:a b Randall, Lisa (2005). Warped Passages: Unraveling the Universe’s Hidden Dimensions. Ecco. ISBN 978-0-06-053108-9.
  30. ^ Feynman, R.P.; Morinigo, F.B.; Wagner, W.G.; Hatfield, B. (1995). Feynman lectures on gravitation. Addison-Wesley. ISBN 978-0-201-62734-3.
  31. ^ Zee, A. (2003). Quantum Field Theory in a Nutshell. Princeton University Press. ISBN 978-0-691-01019-9.
  32. ^ 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.
  33. ^ Nemiroff, R.; Bonnell, J., eds. (15 December 2014). “The Potsdam Gravity Potato”Astronomy Picture of the DayNASA.
  34. ^ Bureau International des Poids et Mesures (2006). “The International System of Units (SI)” (PDF) (8th ed.): 131. 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.
  35. ^ “SI Unit rules and style conventions”. National Institute For Standards and Technology (USA). September 2004. Variables and quantity symbols are in italic type. Unit symbols are in Roman type.
  36. ^ List, R.J. editor, 1968, Acceleration of Gravity, Smithsonian Meteorological Tables, Sixth Ed. Smithsonian Institution, Washington, DC, p. 68.
  37. ^ U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976. (Linked file is very large.)
  38. ^ 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”.
  39. ^ “Milky Way Emerges as Sun Sets over Paranal”http://www.eso.org. European Southern Obseevatory. Retrieved 29 April 2015.
  40. ^ Clark, Stuart (11 February 2016). “Gravitational waves: scientists announce ‘we did it!’ – live”the Guardian. Retrieved 11 February2016.
  41. ^ Castelvecchi, Davide; Witze, Witze (11 February 2016). “Einstein’s gravitational waves found at last”Nature Newsdoi:10.1038/nature.2016.19361. Retrieved 11 February 2016.
  42. ^ “WHAT ARE GRAVITATIONAL WAVES AND WHY DO THEY MATTER?”. popsci.com. Retrieved 12 February 2016.
  43. ^ 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 Letters119 (16): 161101. arXiv:1710.05832Bibcode:2017PhRvL.119p1101Adoi:10.1103/PhysRevLett.119.161101PMID 29099225.
  44. ^ Devlin, Hanna (3 October 2017). “Nobel prize in physics awarded for discovery of gravitational waves”the Guardian. Retrieved 3 October 2017.
  45. ^ Chinese scientists find evidence for speed of gravity, astrowatch.com, 12/28/12.
  46. ^ 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 Bulletin58 (4–5): 474–477. Bibcode:2013ChSBu..58..474Tdoi:10.1007/s11434-012-5603-3.
  47. ^ “GW170817 Press Release”LIGO Lab – Caltech.
  48. ^ Dark energy may just be a cosmic illusionNew Scientist, issue 2646, 7 March 2008.
  49. ^ Swiss-cheese model of the cosmos is full of holesNew Scientist, issue 2678, 18 October 2008.
  50. Jump up to:a b Chown, Marcus (16 March 2009). “Gravity may venture where matter fears to tread”New Scientist. Retrieved 4 August 2013.
  51. ^ Brans, C.H. (March 2014). “Jordan-Brans-Dicke Theory”. Scholarpedia9 (4): 31358. arXiv:gr-qc/0207039Bibcode:2014Schpj…931358Bdoi:10.4249/scholarpedia.31358.
  52. ^ Horndeski, G.W. (September 1974). “Second-Order Scalar-Tensor Field Equations in a Four-Dimensional Space”. International Journal of Theoretical Physics88 (10): 363–384. Bibcode:1974IJTP…10..363Hdoi:10.1007/BF01807638.
  53. ^ Milgrom, M. (June 2014). “The MOND paradigm of modified dynamics”. Scholarpedia9 (6): 31410. Bibcode:2014SchpJ…931410Mdoi:10.4249/scholarpedia.31410.
  54. ^ Haugan, Mark P; Lämmerzahl, C (2011). “Einstein gravity from conformal gravity”. arXiv:1105.5632 [hep-th].

References

Further reading

External links

Look up gravity in Wiktionary, the free dictionary.
Wikisource has the text of the 1911 Encyclopædia Britannica article Gravitation.
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