Zero, a hypothetical planet, consists of a mass of 4.3 x 1023 kg, a radius of 3.4 x 106 m, and no atmosphere. A space probe of 10 kg is to be launched vertically from the surface.
(i) When the probe is launched having an initial kinetic energy of 5.0 x 107 J, then what will be the kinetic energy if it is 4.0 x 106 m from the center of Zero?
(ii) When the probe is to attain a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy should it be launched from the surface of Zero?