Zero, a hypothetical planet, has a mass of 5.8 x 1023 kg, a radius of 2.7 x 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 kinetic 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?
To answer these questions just use the equations for potential energy using the mass and heights described. the potential energy at the prescribed heights = the initial kinetic energy required to reach that height.
Make sure you calculate the force of gravity on the surface using the radius of the planet.
