Zero, a hypothetical planet, has a mass of `5.0 xx 10^2` kg, a radius of `3.5 xx 10^6` 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 xx 10^7` J, what will be its kinetic energy when it is `4.0 xx 10^6`m from the center of Zero? (b) If the probe is to achieve a maximum distance of `8.0 xx 10^6` m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?

Explanation

(a) `3.8 xx 10^7 J`, (b) `5.4 xx 10^7 J`