Centripetal Force

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sugarbabee0

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Two identical communication satellites are orbiting the Earth as shown below. Satellite A is twice the distance from the center of the Earth as Satellite B.
What is the ratio of the centripetal force acting on Satellite A to that acting on Satellite B?

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The solution used the equation F=Gmm/r^2 instead of F=ma=mv^2/r... And that changes the answer.. Why did we not use the centripetal force equation?

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You can't use the centripetal force equation because you only know how their radii compare. Without knowing their relative velocities, you can't proceed with mv^2/2.

The centripetal force is the total force that must act on an object in order for that object to maintain circular motion. Sometimes it's a normal force, sometimes a tension, sometimes a magnetic force, often it's the sum of several different individual forces. In this case, there is only one force acting on the objects - gravity. As it's the only force, gravity is also the total force, which makes it the centripetal force. So solving for gravity lets us solve for centripetal force. This lets us avoid the problem of not knowing their respective velocities. Me only need to know their relative masses and distances from the center of the Earth.
 
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