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 43Rh. 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) Take your height to be 2.0 m. What is the limit to the mass of the black hole you can tolerate at the given radial distance? Give the ratio of this mass to the mass MS of our Sun. (b) Is the ratio an upper limit estimate or a lower limit estimate?
Rh = 2GM/c^2
The Attempt at a Solution
Using the two expressions of the gravitational attraction: a=GM/(R+∂R)^2=10
and we have R=43*Rh=86GM/c^2
and my height is ∂R=2 metres
now sub the expression for R in, and do the massive calculation I got M=1.0125*10^32 kg
the sun has mass Msun=1.99*10^30 kg
thus the ratios is M/Msun=50.879...
This is not however the correct answer
Please let me know where I might have gone wrong