Find K/Ug: Solving a Constant Ratio of Kinetic and Potential Energy

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The discussion centers on determining the constant ratio of kinetic energy (K) to gravitational potential energy (Ug) for a satellite in circular orbit. It is established that this ratio is independent of the masses involved and the orbital parameters. The relationship between gravitational force and potential energy is highlighted, with the equation F = -dU/dr = mv^2/r provided as a key reference. Participants suggest using gravitational and centripetal force equations to derive expressions for K and Ug. Ultimately, the goal is to calculate the constant value of K/Ug.
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I don't really know how to approach this problem...
A satellite is in a circular orbit around its parent body. The ratio of the satellite's kinetic energy to its potential energy, K/Ug, is a constant independent of the masses of the satellite and parent, and of the radius and velocity of the orbit. Find the value of this constant. Potential energy is taken to be zero at infinite separation.
 
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F = -\frac{dU}{dr} = \frac{mv^2}{r}

From these relations you should be able to calculate this easily. Using the equations for gravitational and centripetal force to find U and K.
 

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