Walker, Halliday & Resnick — Gravitation: Problem 51

51 Zero, a hypothetical planet, has a mass of \(5.0 \times 10^{23} \text{ kg}\), a radius of \(3.5 \times 10^6 \text{ m}\), and no atmosphere. A \(10 \text{ kg}\) space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial energy of \(5.0 \times 10^7 \text{ J}\), what will be its kinetic energy when it is \(4.0 \times 10^6 \text{ m}\) from the center of Zero? (b) If the probe is to achieve a maximum distance of \(8.0 \times 10^6 \text{ m}\) from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?