Zero, a hypothetical planet, has a mass of 5.0 x 1023 kg, u radius of 3.0 x 106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surf ace.

(a) If the probe is launched with an initial energy of 5.0 x 107 J, what will be its kinetic energy when it is 4.0 x 106 m from the center of Zero?

(b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?