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.

This strikes me as a "rings of Saturn" problem.  The moons and moonlets of Saturn constantly pull (gravity) on one another, causing a shift in the kinetic and potential energy of each body.  Using only this steady state example and thus no proof, I would say that the two objects would behave in a simple harmonic fashion about the local center of mass, which is of course orbiting the earth.

But then the moonlets of Saturn do not have strings attached, and elastic tethers increase force with distance between objects vice decrease with distance as in gravity.

Edited on April 14, 2005, 2:01 am

Posted by Leming on 2005-04-14 01:48:25