Two identical spheres are connected by an elastic tether. The tether obeys Hooke's Law for ideal springs. At a particular moment in time, the tether is in a straight line, at its resting length, neither stretching nor contracting. This assembly is then placed into a circular orbit around the Earth, and oriented so that a line drawn from one sphere through the tether and the other sphere points directly at the Earth.

Give a qualitative description of the motion of the two spheres relative to each other over time.

(In reply to more thoughts by Charlie)

I think that we can expect the center of gravity of the assembly to remain at a constant altitude and velocity as it orbits the Earth.  If we reduce this to a 2-D problem, we might say that the assembly orbits the Earth Clockwise in which case the spheres will begin to rotate about the assembly's center of gravity counter-clockwise.  We would also expect to see oscillation in the size of the separation between the spheres along the tether with the behavior becoming chaotic as they inevitably collide.  Even so, the behavior of their center of gravity should remain predictable. 

Posted by Eric on 2005-04-13 22:59:39