Question

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 100 m-long steel frame between their centers of mass, to keep the crew as far as possible from the engines’ radiation.

The ship is pointing directly away from the black hole, firing its engines at maximum thrust to try to escape. The black hole is 10 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 of 8.0 km/s. What force they can provide? (If you need to review rocket thrust, it’s covered in Chapter 9.)

(b) When it’s still 1 million km away, what is the gravitational force 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 the force on the front section? Write down as many digits as needed to show that they differ.

(d) The difference in force between the two sections will cause tension on the long frame connecting them. The frame has a cross-sectional area of 100 cm2 and is made of steel. By how much does it stretch?

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

(f) In a class whiteboard problem, we derived the radius around a black hole at which the escape velocity is equal to the speed of light. The surface at this radius is known as the event horizon. It is not a solid surface, but simply the line beyond which there is no possible return. Will the Discovery 1 break apart before falling through the horizon?

Answer 1