Zeros, an imaginary planet, consists of a mass of 5.0 x 10^23 kg, a radius of 3.0 x 10^6 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 10^7 J then determine the kinetic energy if it is 4.0x10^6 m from the center of Zeros?
(ii) When the probe is to accomplish a maximum distance of 8.0 x 10^6 m from the center of Zeros, with what initial kinetic energy should it be launched from the surface of Zero?