Energy required to transfer an object to a higher orbit

[wrongusername]

Homework Statement

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?

Homework Equations

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

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.

 

[D H]

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?

 

[wrongusername]

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?

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! :)

 

[D H]

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

 

[wrongusername]

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

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!