(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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/c^2, where M is the mass of the black hole and c is the speed of light. Suppose that a person who is 1.7 m tall wishes to study black holes near them, at a radial distance of 50Rh. However, the person doesn't want the difference in gravitational acceleration between their feet and head to exceed dag = 10 m/s^2 when they are feet down (or head down) toward the black hole.

(a) As a multiple of our sun's mass, what is the limit to the mass of the black hole the person can tolerate at the given radial distance?

2. Relevant equations

Rh=(2GM)/c^2

Fg=G((Mm)/r^2)

3. The attempt at a solution

I can solve for Rh and eventually get a mass, but that in no way accounts for the acceleration difference of the person. My question is, how must I account for this?

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# Homework Help: Fg and planetary motion

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