Calculate the radius of the event horizon (i-e.. the Schwnnachild radius) for ea

Question

Calculate the radius of the event horizon (i-e.. the Schwnnachild radius) for each of the following black holes assuming they are spherically symmetric and not rotating: Cygmus X-l (8.7.V ) supermassive black hole at the center of Milky Way Galaxy (4 million,M ) supermassive black hole at the center of MST Elliptical Galaxy in Virgo Supercluster (3 billion M ) Recall the calculation of tidal acceleration in Homework #1 Problem 2(b). Which event horizons in tlie previous part* will you be atile to croera "comfortably"?

Explanation / Answer

The Schwarzschild radius is proportional to the mass with a proportionality constant involving the gravitational constant and the speed of light from the perspective of an observer at infinity and not in motion relative to the black hole           r s = 2 Gm / c 2   here G ios universal gravitational constant            c is speed of light a) mass of Cygaus X-1 is m = 8.7 (mass of sun )                                           = 8.7*1.988*1030 kg                                            = 17.2956*1030 k g               The Schwarzschild radius                               r = 2 ( 6.67*10-11 ) (   17.2956*1030 kg  ) / ( 3*108 ) 2                                 =  25635.922 m b) mass of super massive black hole at the center of milky way galax                        m = 4 million ( mass of sun )                             = 4*106 * 1.988*1030 kg        The Schwarzschild radius                               r = 2 ( 6.67*10-11 ) (   4*106 * 1.988*1030 kg) / ( 3*108 ) 2                                 =  11.7866*109 m c) mass of super massive black hole at the center of M87 elliptical galax in virgo super cluster       m = 3 billion( mass of sun )                             = 3*1012 * 1.988*1030 kg        The Schwarzschild radius                               r = 2 ( 6.67*10-11 ) (   3*1012 * 1.988*1030 kg) / ( 3*108 ) 2                                 =  8.8399*1015 m                  b) mass of super massive black hole at the center of milky way galax                        m = 4 million ( mass of sun )                             = 4*106 * 1.988*1030 kg        The Schwarzschild radius                               r = 2 ( 6.67*10-11 ) (   4*106 * 1.988*1030 kg) / ( 3*108 ) 2                                 =  11.7866*109 m c) mass of super massive black hole at the center of M87 elliptical galax in virgo super cluster       m = 3 billion( mass of sun )                             = 3*1012 * 1.988*1030 kg        The Schwarzschild radius                               r = 2 ( 6.67*10-11 ) (   3*1012 * 1.988*1030 kg) / ( 3*108 ) 2                                 =  8.8399*1015 m                  c) mass of super massive black hole at the center of M87 elliptical galax in virgo super cluster       m = 3 billion( mass of sun )                             = 3*1012 * 1.988*1030 kg        The Schwarzschild radius                               r = 2 ( 6.67*10-11 ) (   3*1012 * 1.988*1030 kg) / ( 3*108 ) 2                                 =  8.8399*1015 m                 

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