# hw4 - 30 kg), calculate the Schwarzschild radius in both...

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ASTR 2010 - Modern Cosmology Professor Michael Shull (Astrophysics) HOMEWORK #4 (February 28, 2008) due: Thursday March 6, in class 1 Black Hole Sizes and Time-Variability In both Newton’s and Einstein’s theories of gravity, there is a radius of a spherical object of mass M that corresponds to a dark object or “Black Hole”. Nothing can escape from inside this radius, not even light. This radius is called the Schwarzschild Radius and is given by the formula: R s = 2 GM c 2 , (1) where M is the mass of the object (expressed in kilograms), c = 3 × 10 8 meters/second is the speed of light, and G = 6 . 67 × 10 11 m 3 /kg/s 2 is Newton’s universal gravitation constant. Note: If one uses G and c in these units, R s will be given in meters. Make sure to square c in the above formula. (a) For a black hole of mass ten times that of the Sun (where 1 M = 2 × 10
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Unformatted text preview: 30 kg), calculate the Schwarzschild radius in both meters (m) and kilometers (km). Note that 1 km equals 1000 meters. b) Some quasars appear, from their luminosities, to be active galactic nuclei with central black holes of mass one hundred million (10 8 ) times that of the Sun. Calculate the Schwarzschild radius of these black holes. Give your answer in both meters and Astronomical Units (recall, the EarthSun distance of 1 AU = 1 . 5 10 11 meters). (c) What would be the typical timescale for ux variability of this 10 8 M black hole, assuming the usual argument about the time for light to travel from opposite sides? That is, evaluate the time (in seconds) it takes for light to cross the black holes diameter ( c = 3 10 8 m/s). 1...
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## This note was uploaded on 04/09/2008 for the course ASTR 2010 taught by Professor Shull during the Fall '08 term at Colorado.

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