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Gravitational Lensing Abstract
Gravitational Lensing Abstract

... Clusters of galaxies at Z ≈ 0.2 with masses of order 1014 M¯ are very effective lenses. Their Einstein radii are of the order of 20 arcseconds. No complete Einstein ring has been found around clusters due to the facts that most clusters are not really spherical mass distributions and since the align ...
Solutions - faculty.ucmerced.edu
Solutions - faculty.ucmerced.edu

... Solution (a) There are two Doppler shifts in this problem, one from the redshift z, and the other from the rotational motion of the galaxy. The redshift from the galaxy shifts the wavelength λobs = 1 + z = 1.9. λemit Thus, the observed wavelength to the center of the galaxy is λobs = (1 + z) λemit = ...
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Chapter 8, Part V
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Forces and Motion - Cortez High School
Forces and Motion - Cortez High School

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Physics Review - WLWV Staff Blogs

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Universal Gravitation Worksheet

... (1.08x10-7N) 2. What gravitational force does the moon produce on the earth if the centers of the moon and earth are 3.88x108m apart and the moon has a mass of 7.34x1022kg? (1.94x1020N) 3. If the gravitational force between two objects of equal mass is 2.30x10-8N when the objects are 10.0m apart, wh ...
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Calculating Net Force with the Second Law

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Newton`s Laws and Classical Mechanics

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Newton`s Laws

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Forces and Motion

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The Motions of the Planets
The Motions of the Planets

... Kepler’s Laws Revisited • Newton showed that if you start with his four laws and consider a small object in orbit around a large one, one can derive all three of Kepler's laws exactly – Note that Newton's laws are much more fundamental than those of Kepler ...
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Modified Newtonian dynamics



In physics, modified Newtonian dynamics (MOND) is a theory that proposes a modification of Newton's laws to account for observed properties of galaxies. Created in 1983 by Israeli physicist Mordehai Milgrom, the theory's original motivation was to explain the fact that the velocities of stars in galaxies were observed to be larger than expected based on Newtonian mechanics. Milgrom noted that this discrepancy could be resolved if the gravitational force experienced by a star in the outer regions of a galaxy was proportional to the square of its centripetal acceleration (as opposed to the centripetal acceleration itself, as in Newton's Second Law), or alternatively if gravitational force came to vary inversely with radius (as opposed to the inverse square of the radius, as in Newton's Law of Gravity). In MOND, violation of Newton's Laws occurs at extremely small accelerations, characteristic of galaxies yet far below anything typically encountered in the Solar System or on Earth.MOND is an example of a class of theories known as modified gravity, and is an alternative to the hypothesis that the dynamics of galaxies are determined by massive, invisible dark matter halos. Since Milgrom's original proposal, MOND has successfully predicted a variety of galactic phenomena that are difficult to understand from a dark matter perspective. However, MOND and its generalisations do not adequately account for observed properties of galaxy clusters, and no satisfactory cosmological model has been constructed from the theory.
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