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 my mind the nearer to earth sphere tries to go faster, but as it gets ahead it begins to pull the other along.  The nearer loses energy (and pulls away from the earth) to the further (which gets nearer to the earth.)  Then they end up at the same distance from the earth with the one that was closer in the front.

Either that or the system ends up with enough rotational momentum that it begins to tumble.

 

Posted by Jer on 2005-04-13 19:28:16