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Tethered satellites (Posted on 2005-04-13) Difficulty: 3 of 5
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.

See The Solution Submitted by Larry    
Rating: 3.5000 (4 votes)

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re: Just a guess | Comment 3 of 13 |
(In reply to Just a guess by Jer)

It sounds reasonable they should start to tumble about one another, like satellites of each other, but with the elastic force of the tether taking the place of gravity.  But the force between them is not related in an inverse square relationship the way gravity is, so you're not going to get the usual conic-section type of orbit about each other.
  Posted by Charlie on 2005-04-13 19:32:24

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