# Gravitational Potential Energy of a planet

1. Jun 12, 2006

### sophzilla

I'd be grateful if someone can help me with this problem -

Zero, a hypothetical planet, has a mass of 4.4 × 10^23 kg, a radius of 3.2 × 10^6 m, and no atmosphere. A 2.4 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial energy of 7.4 × 10^7 J, what will be its kinetic energy when it is 4.8 × 10^6 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.9 × 10^6 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?

I started out by using the equation for energy which is E = KE + U (kinetic energy plus potential energy).

So I got 7.4x10^7 = KE + (mGR). But I have 2 main problems: one is, do I use G = 6.67x10^-11? The second question is, I know there is something I have to do with the radius, but I don't exactly know what. Do I do mass of probe/R? I did that but still got the answer wrong...I know I'm doing something wrong with the radius.

Thanks a lot.

*If I get part a, I'm sure I can get the second part by myself.

2. Jun 12, 2006

### NEWO

i think by G you mean g which is the gravitational field strength or the acceleration due to gravity, in earths case it is $$9.81ms^{-2}$$

also, the gravitational potential energy is $$V=\frac{GMm}{r}$$

because the potential decreases with 1/r. M is the mass of the earth and m is the mass of the probe in this case G is $$6.67x10^{-11}$$

hope this helps

newo

3. Jun 12, 2006

### NEWO

PS G=6.67x^-11 the $$x$$ was meant to be a multiplication sign sorry.

4. Jun 12, 2006

### sophzilla

Thanks for the gravitational potential energy equation.

Yet I'm still confused about what to use for r:

I don't know what the new radius would be. Does the height of the rocket matter?

5. Jun 12, 2006

### Staff: Mentor

In the equation for gravitational potential energy, r is the distance of the probe to the center of the planet:
$$U = -\frac{GMm}{r}$$
(note the minus sign)

6. Jun 12, 2006

### sophzilla

For some reason I'm not getting the right answer (I got part B though, for some unknown freaky psychotic reason).

I did: E = KE - GMm/R which became:

7.4 × 10E7J = KE - (6.67E-11)(4.4 × 10E23kg)(2.4kg)/4.8 × 10E6m

Then got the KE, which was the wrong answer.

I'm still thinking I have to do something with the radius.

7. Jun 12, 2006

### Staff: Mentor

You need to consider the change in potential energy as it moves from its initial to its final position.

8. Jun 12, 2006

### sophzilla

got it, thanks

9. Jun 13, 2006

### NEWO

oooops yeah i forgot that. lol