# Homework Help: Gravitational potential energy problem.

1. Apr 13, 2010

### Tyyoung

1. The problem statement, all variables and given/known data
A satellite with a mass of 5.00 x 10^2 kg is in a circular orbit, whose radius is 2re, around Earth. Then it is moved to a circular orbit with a radius of 3re.

a) Determine the satellite's gravitational potential energy in each orbit.

2. Relevant equations

Ep= -GMm/r

3. The attempt at a solution

Ep= -GMm/r
= -(6.67*10^-11)(5.98*10^24)(5.00*10^2)/2(6.38*10^6)
Ep= -1.56*10^10

I'm uncertain about that answer, I don't necessarily have a reason to believe it is wrong but I don't trust my judgment on this one. Any feedback as to what I may have done wrong would be greatly appreciated.
(I answered for only the 2re orbit.)

Last edited: Apr 13, 2010
2. Apr 13, 2010

### ideasrule

Ep= -GMm/r is the right equation, so that answer is right.

3. Apr 13, 2010

### Tyyoung

So I got the answer for both 2re and 3re which are
Ep = -1.56*10^10
Ep = -1.041969697*10^10

and then for the next question it asks to determine the change in gravitational potential energy which I'm pretty sure is (Delta)Ep=Ep2-Ep1 which I got 5180303030 J ( I just subtracted the two answers above to arrive at that)

now in the third question it asks me to determine the work done in moving the satellite from the first orbit to the second orbit (2re to 3re) apply energy conservation. Isn't the change in gravitational potential energy also the work?? (Delta)Ep=W=F*d

Last edited: Apr 13, 2010
4. Apr 13, 2010

### Tyyoung

also d) for the same problem asks me to Calculate the speed it would need in order to maintain its new orbit.

I did v = sq.root of Gme/r

so I got v = sq.root of (6.67x10^-11)(500)/3(6.38x10^6)
v = sq.root of 1.742424242x10^-15
v = 0.000000042 m/s
that seems way to small to me, can someone show me where I went wrong plzzzz.