Gravitational Potential Energy - Orbits

[Nicolaus]

Homework Statement

A satellite is in a circular orbit 655km above Earth's surface. Determine the magnitude of the gravitational acceleration at this height.

Homework Equations

Eg=mgh
Eg=-GMm/r

The Attempt at a Solution

Would I just set the aforementioned eqations equal to each other and re-arrange to solve for g? I would also have to solve for the change in Eg, as well, right?

 

[Doc Al]

Would I just set the aforementioned eqations equal to each other and re-arrange to solve for g?

No. Instead of potential energy, think in terms of forces and acceleration. What is the gravitational force on the satellite. (Tip: Don't be so quick to plug in numbers.)

 

[Nicolaus]

Well, it's also experiencing a centripetal force. If we set Fc=Fg, we can get the velocity of the orbit, but, other than that, I'm not sure how to do this without the mass of the sat.

 

[Doc Al]

Well, it's also experiencing a centripetal force. If we set Fc=Fg, we can get the velocity of the orbit, but, other than that, I'm not sure how to do this without the mass of the sat.

You won't need the mass--just call it 'm'. When you calculate the acceleration, it will drop out.

What is Newton's law of Universal Gravity?

 

[Nicolaus]

Got it - I was overthinking a rather simple question..., thanks.

 

[frogjg2003]

Also, E=mgh only works for constant gravitational fields. i.e. at the surface of a very large mass (like the Earth).