Question

A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 380 kg. It has strayed too close to a black hole having a mass 108 times that of the Sun. The nose of the spacecraft points toward the black hole, and the distance between the nose and the center of the black hole is 10.0 km. Black hole 100m- 10.0 km2 (a) Determine the total force on the spacecraft. 1 x A black hole can be treated in the same manner as any other point mass and used in the equation for the gravitational force as long as you are outside the Schwarzschild radius. N (b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole? (This difference in acceleration grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.) N/kg

Answer 1

A)

Force, F = GMm/(R + L)^2

F = (6.67 x 10^-11 x 108 x 1.99 x 10^30 x 1380)/(10000 + 50)^2 = 1.96 x 10^17 N

B)

dg = Gm(1/R1^2 - 1/R2^2)

dg = (6.67 x 10^-11 x 108 x 1.99 x 10^30)(-1/(10000 + 100)^2 + 1/(10000)^2)

dg = 2.82 x 10^12 N/kg

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