The radius Rh and mass Mh of. a black hole are related by Rh, = 2GMh/c2, where c is the speed of light. Assume that the gravitational acceleration ag of an object at a distance ro = 1.001-Rh, from the center of a black hole is given by Eq. 13-11 (it is, for large black holes).(a) In terms of Mr, find ag at ro. (b) Does ag at ro increase or decrease as Mh increases? (c) What is ag at ro for a very large black hole whose mass is 1.55 x 1012 times the solar mass of 1.99 x 1030 kg? (d) If the astronaut of Sample Problem 13-3 is at ro, with her feet toward this black hole, what is the difference in gravitational acceleration between her head and her feet? (e) Is the tendency to stretch the astronaut severe?
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