Gravitational Potential Energy - Orbits

AI Thread Summary
To determine the gravitational acceleration of a satellite in a circular orbit 655 km above Earth's surface, focus on the forces acting on the satellite rather than potential energy equations. The gravitational force acting on the satellite can be equated to the centripetal force required for circular motion. The mass of the satellite is not needed in calculations, as it cancels out when deriving the acceleration. It's important to remember that the equation E=mgh is only applicable for constant gravitational fields, such as near Earth's surface. The discussion emphasizes simplifying the problem by using fundamental principles of gravity and motion.
Nicolaus
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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?
 
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Nicolaus said:
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.)
 
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.
 
Nicolaus said:
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?
 
Got it - I was overthinking a rather simple question..., thanks.
 
Also, E=mgh only works for constant gravitational fields. i.e. at the surface of a very large mass (like the Earth).
 
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