The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity, Rh = 2GM/c2, where M is the mass of the black hole and c is the speed of light. Suppose that you wish to study a black hole near it, at a radial distance of 50Rh. However, you do not want the difference in gravitational acceleration between your feet and your head to exceed 10 m/s2 when you are feet down (or head down) toward the black hole.

(a) As a multiple of our Sun's mass MS, approximately what is the limit to the mass of the black hole you can tolerate at the given radial distance? (You need to estimate your height.)

(b) Is the limit an upper limit (you can tolerate smaller masses) or a lower limit (you can tolerate larger masses)?