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? We normally make ground zero PE level, but for this...

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?
What equation do I start with?

I tried using:
E = KE - GMm/R and came up with the wrong answer. Am I doing something wrong? PLEASE HELP!

How about the equation:
KE(initial)-(GMm)/R = KE(final)-(GMm)/10R

I am still confused as to what value to use for R for a...Do I use 4e6 for both R's?


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