A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass

Question

A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 530 kg. It has strayed too close to a black hole having a mass 99 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.

(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.)

Explanation / Answer

Kind of a strange question. In Newton's theory of gravitation there are no black holes (although there are somewhat similar objects called dark stars) and in General Relativity gravity isn't a force.

Given that neither part really makes sense in terms of GR I'm assuming this is to be answered with Newton's theory of gravitation.

F = GmM/ r^2

G is the gravitational constant, m and M are the masses of the spacecraft and black hole, r is the distance between the two

G = 6.673 * 10^(-11)

M = 99 * 1.98892 * 10^(30)

Force on the nose (r = 10 km) F = GmM / r^2 = 6.96 * 10^(16) N

Force on the back (r = 10,100 m) F = 6.82 * 10^(16) Newtons

The acceleration of the spacecraft is given by removing its mass from the force equations

Acceleration of front 1.313 * 10^(14) m/s^(2)

Acceleration of back 1.288 * 10^(14) m/s^(2)

Difference in acceleration = 2.5 * 10^(12) m/s^(2) this is ridiculously large acceleration difference, its very easy to see why the ship gets torn apart.

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