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 re: Just a guess by Charlie)

And I fear that it gets even more difficult.

Once the elastic force starts to really influence the orbits, the lowest one will slow down and get in a lower orbit.  While the higher one will speed up and be forced in a higher orbit.  Which will put even more stress on the tether.
Now combine this with the tumbling which will have a vertical force that tries to let the spheres do the opposite of what is discribed above.

And if the centre of the assemble is placed in a non stable Lagrange point, then it is a difficulty 6 problem.

Posted by Hugo on 2005-04-13 19:51:45