Chapter 13, Problem 36P

Zero, a hypothetical planet, has a mass of 5.0 × 10²³ kg, a radius of 3.0 × 10⁶ m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface, (a) If the probe is launched with an initial energy of 5.0 × 10⁷ J, what will be its kinetic energy when it is 4.0 × 10⁶ m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 × 10⁶ m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?