Referring to the preceding problem, if a different straight tunnel is drilled through the same asteroid, where
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Referring to the preceding problem, if a different straight tunnel is drilled through the same asteroid, where this time the tunnel misses the asteroid's center by a distance \(R / 2\),
(a) how long would it take the astronaut to fall from one end of the tunnel to the other and back, assuming no friction between the sides of the tunnel and the astronaut?
(b) Suppose that instead of falling through the tunnel, she is given an initial tangential velocity of just the right magnitude to insert her into a circular orbit just above the surface. How long will it take her to return to the starting point in this case?
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