Chapter 12, Problem 86GP

Approaching the ISS A Russian Soyuz module, with three astronauts and a full load of cargo, has a mass of 7500 kg. The International Space Station (ISS) has a mass of 420,000 kg. When Soyuz docks at the ISS, the two centers of mass are separated by 9.5 m. (a) Find the average of the gravitational force of attraction between the two spacecraft when Soyuz is docked and when it is 110 m from the ISS. (b) If Soyuz approached the ISS from rest at a distance of 110 m, a thruster would have to counteract the average force of gravitational attraction between it and the ISS. If this thruster has an exhaust velocity of 590 m/s, at what average rate must it burn fuel (in kg/s) to counteract the pull of the ISS? (See Section 9-8 for a discussion of thrust.) (c) If the approach requires 330 s, how much fuel will the thruster burn in order to counteract the gravitational attraction?