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 ar of an object at a distance ro = 1.001Rh, from the center of a black hole is given by Eq. (it is, for large black holes).
(a) In terms of Mh, 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 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?