# Kinetic energy of a chain of rotating masses

Assume Earth of mass $M_E$ is rotating around sun in a uniform circular motion of radius $R_E$ and angular velocity $\omega_E$ and Moon of mass $M_m$ is rotating similarily, but around Earth with radius $R_M$ and angular velocity $\omega_M$. Sun is stationary, and assume no gravitational forces present between them, What is the total kinetic energy of the combined system? Does it change with time?

• How can there be 'no gravitational forces present between them'? Uniform circular motion requires centripetal force, here supplied by gravitation. The total $K$ is just that: the $\Sigma$ of all $K$. It's not a "chain" of rotating masses. – Gert Jan 9 '17 at 11:46
• @Gert He might mean "suppose the motion is constrained to ...". This means forces shouldn't be considered. But then the second part can't be answered. – AHB Jan 9 '17 at 11:48
• If the motion is constrained to a circle revolving about a point on another circle, the kinetic energy of the system depends on the direction of orbit of the moon. It can turn a sum into a subtraction. – AHB Jan 9 '17 at 11:50
• @AHB : I just used sun and moon for colorful language. I just mean two point masses in a plane. One rotating uniformly around a fixed point and other uniformly around the first one. – Rajesh Dachiraju Jan 9 '17 at 12:13