perplexus.info :: Science : Tethered satellites

Tethered satellites (Posted on 2005-04-13)

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.

Submitted by Larry

Rating: 3.5000 (4 votes)

Solution: (Hide)

Since the radius of orbit of each sphere is slightly different, the ideal velocity for a stable orbit is different for the two spheres. The sphere closer to the earth would have to be going a little faster, but it's not. So the one closer to earth will tend to fall even closer to earth; the sphere in the higher orbit will tend to go even higher. This creates tension in the tether. The more the tether stretches, the greater the difference in the orbits, and the greater the tendancy to pull apart. I believe the effect of gravity between the two spheres is a much smaller force. I also believe the situation is unstable and oscillations can develop: sinusoidal spring like oscillations, pendulum like oscillations, or the two spheres rotating about the point half way in between. Or the tether could break, which happened in 1996 during an experiment conducted by Space Shuttle Columbia with a 13 mile long tether.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
my answer	Jud	2005-08-11 12:35:06
No Subject	Jason Taylor	2005-08-01 02:23:07
Interesting sites	Hugo	2005-04-14 15:22:22
No strings attached.	Leming	2005-04-14 01:48:25
re(2): more thoughts	ajosin	2005-04-13 23:06:57
A naive guess.	ajosin	2005-04-13 23:00:42
re: more thoughts	Eric	2005-04-13 22:59:39
more thoughts	Charlie	2005-04-13 22:42:39
Difficulty 5+++?	Hugo	2005-04-13 21:29:15
re(2): Just a guess	Hugo	2005-04-13 19:51:45
re: Just a guess	Charlie	2005-04-13 19:32:24
A start	Charlie	2005-04-13 19:29:35
Just a guess	Jer	2005-04-13 19:28:16

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