# Satellite Energy and Orbit problem

1. Dec 2, 2014

### Dextrine

1. The problem statement, all variables and given/known data
A spy satellite of mass m is in a circular orbit with radius R and velocity v around
the earth. One of the satellites thrusters suddenly fires giving it an additional
velocity v in the outward radial direction (same v). What is the new total energy
of the satellite? What is the new orbit of the satellite?

2. Relevant equations
mv^2/r
GMm/r^2
-K=.5U
2K+U=0

3. The attempt at a solution
I honestly don't really have an idea how to even set up the problem. From what I understand mv^2=GMm/r^2 for circular orbit which should I could then use to find the energy, but I don't know how the velocity increasing radially will affect this. Any helpful nudge in the right direction would be greatly appreciated.

2. Dec 2, 2014

### haruspex

I think you mistyped the left hand side. As a result you have energy on the left and a force on the right.

What is the initial KE?
What is the initial PE?

3. Dec 2, 2014

### Dextrine

So initially I got my K=1/2GMm/r and my U=-GMm/r

Since we are adding another V, which is Sqrt[GM/r], i get that my new total energy = -.5GMm/r+.5GMm/r=0

however, this doesn't seem right

4. Dec 2, 2014

### haruspex

It's right :). Remember, the total energy beforehand was negative.
So what do you get for the new orbit?

5. Dec 2, 2014

### Dextrine

AH, infinite radius? so we get an open orbit? Thanks a ton. Didn't think it would be so simple

6. Dec 2, 2014

### haruspex

That's it. So what general rule do you deduce for vertical escape velocity from a given orbit?

7. Dec 2, 2014

### Dextrine

Hmm, it must be equal to or greater than tangential velocity?

8. Dec 2, 2014

### haruspex

Equal. ("Escape velocity" means the minimum necessary to escape the gravitational field.)