the spacecraft Discovery 1 has gotten too close to a black hole!The ship has a large rear section containing the nuclear engines,with a mass of 3,000 kg; a front section for the crew quarters,also with a mass of 3,000 kg; and a thin, essentially massless 100m-long steel frame between their centers of mass, to keep the crewas far as possible from the engines’ radiation.

The ship is pointing directly away from the black hole, firingits engines at maximum thrust to try to escape. The black hole is10 times the mass of the Sun.

(a) The nuclear thermal rocket engines can consume up to 10.kg/s of fuel, expelling it from the thrusters with a velocity of8.0 km/s. What force they can provide? (If you need to reviewrocket thrust, it’s covered in Chapter 9.)

(b) When it’s still 1 million km away, what is the gravitationalforce of the black hole on the entire ship? Can it escape??

(c) When the rear of the ship is 10,000 km from the black hole,what is the gravitational force on the rear section? What is theforce on the front section? Write down as many digits as needed toshow that they differ.

(d) The difference in force between the two sections will causetension on the long frame connecting them. The frame has across-sectional area of 100 cm2 and is made of steel. By how muchdoes it stretch?

(e) If it stretches by more than 10 cm, it will snap. What isthe distance from the hole at which the ship breaks apart? If youcan’t solve for the answer directly, you can always try plugging invarious distances to narrow in on an approximate value.

(f) In a class whiteboard problem, we derived the radius arounda black hole at which the escape velocity is equal to the speed oflight. The surface at this radius is known as the event horizon. Itis not a solid surface, but simply the line beyond which there isno possible return. Will the Discovery 1 break apart before fallingthrough the horizon?