The Schwarzschild radius RBH for an object of mass Mis defined as GM BH where c

Question

The Schwarzschild radius RBH for an object of mass Mis defined as GM BH where c is the speed of light and Gis the universal gravitational constant. RBH gives the radius of the event horizon of a black hole with mass M (in other words, it gives the radius to which some amount of mass M would need to be compressed in order to form a black hole) The mass of the Sun is about 1 99 x 1030 kg. What would be the radius of a black hole with this mass? Number BH The mass of Mars is about 6.42 x 102 kg. What would be the radius of a black hole with this mass? Number BH Suppose you want to make a black hole that is roughly the size of an atom (take ReH 1.10 x 10-10 m). What would be the mass M of such a black hole? Number kg

Explanation / Answer

(a) We know that RBH = 2GM/c2
G = 6.67*10-11  c= 3*108 m/s , M = 1.99*1030
RBH = 2*(6.67*10-11)(1.99*1030) /(3*108)2 = 2*1.4748*103 = 2.9496*103 m
(b) Similarly
RBH = 2*(6.67*10-11)(6.42*1023) /(3*108)2 =2* 4.757*10-4 = 9.514*10-4 m
(c) M = (RBH*c2) / 2(G) = (1.1*10-10)(3*108)2 /2*(6.67*10-11) = 0.742*1017 kg

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