A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass
ID: 1263805 • Letter: A
Question
A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1550 kg. It has strayed too close to a black hole having a mass 109 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.
(a) Determine the total force on the spacecraft.
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
Explanation / Answer
Force on the space craft F = GMm / r2
where M = 109 Msun
r =rbh +(rfs / 2) = 10 km + 0.05 km = 10.05 km = 10.05 x 103m
F = (6.67 x 10-11) (109) (1.99 x 1030) (1550) / (10.05)2 x 106
= 0.220 x 1018 N
(b) Change in gravitational field is
dg = GM [ rbh2 - rfs2 ] / [rbh * rfs]2
= 6.67 x 10-11 * 109 * 1.99 x 1030 [ (1.01x 104) 2 - (1x 104)2 ] / [(1.01x 104)*(1x 104)2]2
= 2.850x 1012 N/kg
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