Physics/Math

Zero, a hypothetical planet, has a mass of 1.0 1023 kg, a radius of 3.0 106 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 5.0 107 J, what will be its kinetic energy when it is 4.0 106 m from the center of Zero?
(b) If the probe is to achieve a maximum distance of 8.0 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?

Use the rel;ationship
KE + Potential energy) = constant.

The potential energy at distance R from the center is
-GMm/R
M is the planet's mass and m is the probes.
That means (1/2) mV^2 - GMm/R = constant
Use that fact to compute the unknown kinetic energy in each problem

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