Energy of a Binary System (Gravitation)

AI Thread Summary
The discussion centers on calculating the kinetic energy and total mechanical energy of a binary system of identical spheres orbiting their common center of mass. It highlights the gravitational force equation, GM^2/2R, and the kinetic energy equation, K = 1/2MV^2. There is uncertainty regarding whether to double the kinetic energy due to the presence of two spheres and the need to sum their individual kinetic energies for the total. Additionally, there is a critique of the gravitational force equation presented in the homework statement. Clarifying these points is essential for accurately solving the problem.
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Homework Statement


What is the kinetic energy and total mechanical energy of a binary system of identical spheres orbiting around their common center of mass?
M = mass
R = radius

Homework Equations


Force of gravity = GM^2/2R
K = 1/2MV^2

The Attempt at a Solution


I don't know whether or not you double the kinetic energy since there are two spheres.
 
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Of course you would have to add the K.E of the two spheres for the total K.E.
And your eqn. for force is wrong??
 

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