Halliday, Resnick & Walker — Gravitation: Problem Problem_70

Suppose that you wish to study a black hole at a radial distance of \(50R_h\). However, you do not want the difference in gravitational acceleration between your feet and your head to exceed \(10 \text{ m/s}^2\) when you are feet down (or head down) toward the black hole. (a) As a multiple of our Sun’s mass \(M_S\), 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)?