mond

In astrophysics, the modified Newtonian dynamics (MOND) is a burgeoning theory that attempts to explain the galaxy rotation problem by modifying Newton's second law of motion. (The most widely accepted approach to explaining this problem postulates the existence of dark matter.) MOND was proposed in 1983 by Mordehai Milgrom. The central pillar of MOND is the assumption that !Newton's_laws_of_motion#Newton .27s_Second_Law:_Fundamental_l aw_of_dynamicsNewton's Second Law ($F\; =\; ma$) is a high-acceleration approximation of a more accurate law that describes all accelerations. The proposed modification would only become relevant when the total acceleration of a body falls significantly below the constant $a\_0$. Consequently, observations of this behavior could never be made on Earth. Although Milgrom and others have catalogued a respectable sum of persuasive evidence in favor of MOND, there has not been enough compelling research to conclusively substantiate or disprove the theory. Calculations suggest that the parameters required to gather direct experimental evidence can be found only far outside our solar system (beyond the overwhelming influence of the Sun's gravitational field). Therefore, it will be some time before the validity of MOND can be directly tested. Phenomena such as !Low_surface_brightness_galaxy< bara>low surface brightness galaxies have yielded an abundance of indirect evidence on the matter, but in the absence of more varied data, such successes have been viewed as isolated. Many researchers have criticized MOND for 'adapting' its mathematics to the observed galaxy rotation problemmass discrepancy instead of hypothesizing a true physical explanation. The theory is the minority view in the astrophysicist community.

Overview: Galaxy dynamics - At the start of the 1980s, the first observational evidence was reported that Galaxygalaxies do not spin as current theories predict. A galaxy is a vast group of starstars orbitorbiting a ''bulge'' at the center of a galaxy. Since the orbit of stars is driven solely by Gravitygravitational force, it was expected that stars at the edge would have a much larger orbital period than those near the bulge. For example, the Earth, which is 150 million km from the sun, completes an orbit in one year, while it takes Saturn (planet)Saturn, at a distance of 1.4 billion kilometers from the sun, 30 years to do the same. A similar behavior was expected from galaxies, even if the distribution of stars is more cloud-like . However, it became increasingly apparent that stars at the edge of a galaxy move faster than predicted by conventional theory. Astronomers call this phenomenon the "flattening of galaxies' rotation curve". In simple terms, drawing a curve to describe the velocity of stars as a function of their distance from the center of a galaxy should yield curve A (the dashed line in Figure 1); however, data from telescopes yield curve B (the plain line). Instead of decreasing asymptoticasymptotically to zero as the effect of gravity wanes, this curve remains flat at large distances from the bulge. By comparison, the same curve for our solar system—properly scaled—is provided (curve C in Figure 1). Reluctant to change Newton's law and Albert EinsteinEinstein's general relativitytheory of relativity for galaxies alone, scientists have simply assumed that the rotation curve was flat because of the presence of a large amount of matter outside galaxies. Their new theory was that galaxies are embedded in a spherical halo of invisible, Dark matter"dark" matter (Figure 2); however, the search for dark matter has since been met with limited success. The hypothesis of dark matter halos has encountered many problems that have cast doubt on the validity of this model. While it is still the most widely accepted model, alternative approaches have been considered, of which MOND is one.

The MOND Theory - In 1983, Mordehai Milgrom, a physicist at the Weizmann Institute in Israel, published two papers on the Astrophysical Journal to propose a modification of Newton's laws of motionNewton's second law of motion. Basically, this law states that an object of mass ''m'', subject to a force ''F'' undergoes an acceleration ''a'' satisfying the simple equation ''F=ma''. This law is well known to students, and has been verified in a variety of situations. However, it has never been verified in the case where the acceleration a is extremely small. And that is exactly what's happening at the scale of galaxies, where the distances between stars are so large that the gravitational force is extremely small.

The change - The modification proposed by Milgrom is the following: instead of ''F=ma'', the equation should be !''F=mµ(a/a0)a'',? where ''µ(x)'' is a function that for a given variable ''x'' gives 1 if ''x'' is much larger than 1 ( ''x≫1'' ) and gives ''x'' if ''x'' is much smaller than 1 ( ''x≪1'' ). The term ''a₀''? is some new constant, in the same sense that ''c'' (the speed of light) is a constant, except that ''a₀'' is acceleration whereas ''c'' is speed.Here is the simple set of equations for the Modified Newtonian Dynamics::$\backslash vec\; =\; m\; \backslash cdot\; \backslash mu\backslash !\backslash left(\; \backslash right)\; \backslash \; \backslash vec$:$\backslash mu\; (x)\; =\; 1\; \backslash mbox\; x\backslash gg\; 1$:$\backslash mu\; (x)\; =\; x\; \backslash mbox\; x\backslash ll\; 1\; !$">Article

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