**Sample Problem**

(a) An astronaut whose height h is 1.70 m floats feet down in an orbiting space shuttle.

SOLUTION: One Key Idea here is that we can approximate Earth as a uniform sphere of mass M.

(b) If the astronaut is now feet down at the same orbital radius r of 6.77 X 106 m about a black hole of mass?

SOLUTION: The Key Idea here is that we again have a differential change in r between the astronaut’s feet and head, so we can again use . However, now we substitute M.

This means that the gravitational acceleration of the astronaut’s feet toward the black hole is noticeably larger than that of her head. The resulting tendency to stretch her body would be bearable but quite painful. If she drifted closer to the black hole, the stretching tendency would increase drastically.

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