What is the Escape Velocity of a Satellite in Orbit?

[mike91]

Homework Statement

A satellite is in orbit around a planet with orbital speed determined to be 7080 m/s. Find the escape velocity from the planet from this position of its orbit.

Homework Equations

EV=sqrt(2GM/r)

The Attempt at a Solution

With a problem like this, I would just plug in the mass of the planet and its radius, but they aren't given in the statement, and nor is the satellite's position. It seems like I don't have enough information, but I'm likely missing one relevant formula. I've scanned my notes and can't find a solution - just a push in the right direction would be much appreciated.

 

[ehild]

The orbital speed is given. How is it related to the radius of the orbit and the mass of the planet?

How would you get the escape velocity from a distance R from the centre of the planet of mass M?

ehild

 

[mike91]

So since the satellite is likely much less massive than the planet it is orbiting, the orbital speed can be written as
v_o=sqrt(GM/r)..
EV = sqrt(2GM/r), so I can rewrite that as sqrt(GM/r) = EV/sqrt(2) and I get
v_o = EV/(sqrt(2)).
I have v_o = 7080, so solving for EV I get EV = sqrt(2)*v_o, or EV = 1.00*10^4. Aannd that's right, thanks for the help!