Chapter 13, Problem 47P

Ganymede is the largest of Jupiter’s moons. Consider a rocket on the surface of Ganymede, at the point farthest from the planet (Fig. P13.23). Model the rocket as a particle. (a) Does the presence of Ganymede make Jupiter exert a larger, smaller, or same size force on the rocket compared with the force it would exert if Ganymede were not interposed? (b) Determine the escape speed for the rocket from the planet–satellite system. The radius of Ganymede is 2.64 × 10⁶ m, and its mass is 1.495 × 10²³ kg. The distance between Jupiter and Ganymede is 1.071 × 10⁹ m, and the mass of Jupiter is 1.90 × 10²⁷ kg. Ignore the motion of Jupiter and Ganymede as they revolve about their center of mass.

Figure P13.23