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