What is the Kinetic Energy of a Space Probe Launched from Zero?

[Feldoh]

Homework Statement

Zero, a hypothetical planet, has a mass of 5.0*10^23 kg, a radius of 3.0*10^6m, and no atmosphere. A 10kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial energy of 5.0*10^7 J, what will its kinetic energy be when it is 4.0*10^6m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0*10^6m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?

Homework Equations

$$U = -\frac{GMm}{r}$$

$$U_f + K_f = U_i + K_i$$

The Attempt at a Solution

For part a I attempted to find the potential energy while the probe was on the surface of the planet then find the final potential energy when the probe is at the correct distance then since I knew the total energy and the gravity force is conservative I though I'd use conservation of energy and find the change in potential energy and use that to somehow find K, but it didn't work and I'm clueless...

For part b I don't even know where to begin...

 

[Dick]

It sounds like you have the right idea for a). But I can't tell what went wrong without knowing what your numbers are. For b) it's the same thing, you know the difference in potential energy between the surface and the destination, final kinetic energy is zero, then just solve for initial.

 

[Feldoh]

It sounds like you have the right idea for a). But I can't tell what went wrong without knowing what your numbers are. For b) it's the same thing, you know the difference in potential energy between the surface and the destination, final kinetic energy is zero, then just solve for initial.

Ah for b I though about doing that but I wasn't sure if the probe started to orbit the plant, wouldn't it have kinetic energy if it did? And is there anyway to tell it isn't since the problem never stated anything about that.

Thanks for the help by the way.

 

[Dick]

Ah for b I though about doing that but I wasn't sure if the probe started to orbit the plant, wouldn't it have kinetic energy if it did? And is there anyway to tell it isn't since the problem never stated anything about that.

Thanks for the help by the way.

Well, it doesn't say anything about orbiting, so I'd assume all motion was vertical.

 

[Feldoh]

Ah ok, thanks