# Energy required to transfer an object to a higher orbit

1. Jan 19, 2010

### wrongusername

1. The problem statement, all variables and given/known data
A spaceship of mass m circles a planet (mass = M) in an orbit of radius R. How much energy is required to transfer the spaceship to a circular orbit of radius 3R?

2. Relevant equations
K=.5mv$$^{2}$$
U$$_{g}$$=-$$\frac{GMm}{r}$$
v=2(pi)r/T
v=(ar)^.5

3. The attempt at a solution
I had no idea how to do this problem. I thought about subtracting the total final energy from the total initial energy to get the energy input required, but I didn't know how to find v. The two equations I could think of for find v are listed above

It would be nice if you guys could at least give me a hint as to how to solve this test problem, since I get to have a second try at it tomorrow.

2. Jan 19, 2010

### D H

Staff Emeritus
What force is needed to keep something in uniform circular motion? How does this relate to the gravitational force that makes a the spaceship orbit the planet?

3. Jan 19, 2010

### wrongusername

That would be the centripetal force, which is mv^2/r
And that's equal to the gravitational force, GMm/r^2

Which leads me to v^2 = GM/r
I substituted that into the equations I had and got -GMm/3r for a final answer. Jeez, the solution was that simple??? Thank you very much for helping me! :)

4. Jan 19, 2010

### D H

Staff Emeritus
That simple. However -- are you sure about the sign of your result? Does that make sense?

5. Jan 19, 2010

### wrongusername

Dang... you're right. It doesn't make sense since the energy should be greater at the higher orbit. And all the answer choices are positive anyways.

I see where I went wrong now. Thanks for the heads up!

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