Physics
posted by Shawna .
Zero, a hypothetical planet, has a mass of 2.7 x 10^23 kg, a radius of 2.8 x 10^6 m, and no atmosphere. A 3.6 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 8.0 × 10^7 J, what will be its kinetic energy when it is 3.7 × 10^6 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 4.6 × 10^6 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?

Intial total energy= final total energy
Initial KE+INitial PE=KE2+PE2
where ke2= 1/2 mv^r at some r, and pe2=GMm/r
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The Formula you use is the correct one. However, consider this. If the initial PE existed, wouldn't you have to add it to the initial KE then subtract the PE at some R from the center? 
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