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Unformatted text preview: Astronomy 210 Fall 2010 Homework Set #3 Due in class: Friday, Feb. 11 Total Points: 50 + 5 bonus 1. Alternative Universes: Kepler’s Laws. [5 points] Consider an alternative universe, in which all of the laws of physics are the same as ours, except gravity. In this alternative universe, the strength of the gravitational force is still proportional to the masses of the two gravitating objects, and is still attractive and radial, but now depends differently on distance r . So we will write the Alternative gravitational force law as vector F = m 1 m 2 f ( r )ˆ r , with ˆ r = r /  r  , and f ( r ) an unknown (for the moment) function of r . In this strange universe, Alternative Kepler finds that for planets in circular orbits r = a = const , the orbit radius a and period P are related by the “Alternative Kepler’s Third Law” of P ∝ a 2 (1) Using this information, show how the function f ( r ) in the force law depends on r . Comment on the way that Kepler’s third law encodes information about the gravitational force law. 2. Strong Gravity and Light . Consider an object of mass M and radius R . (a) [5 points] If we keep the mass fixed but compress the object, find the radius at which the escape speed from the object’s surface is equal to the speed of light...
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This note was uploaded on 10/06/2011 for the course ASTRO 210 taught by Professor Fields during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Fields
 Astronomy

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