I understand there is a stabilizing force due to gravity gradient. What I'm unsure about is the stabilization part. How does it work?

It looks like to me that this tidal force would just make the craft swing around back and forth around the stable orintentation like a pendulum. What would damp this swinging?


This answer and the excellent article Gravity Gradient Stabilization of Earth Satellites explain that you need to use a damper of some kind, where friction or other lossy processes slowly absorb rotational energy, like a lossy pendulum slowing down.

One caveat is that in the the final state, the spacecraft is actually rotating once every time it revolves around the Earth, so that one face of the spacecraft is always pointing in the nadir direction.

See also this answer and the extensive series of comments be low it.

This can be done for example with a weight on a boom with a spring and dashpot, or with the flow of viscous liquids in curved tubes

two purposes that the gravity gradient serves are:

  1. Provide a non-symmetric resorting force so that the spacecrafts rotation rate has a non-uniform or oscillatory component. That causes the damper to be excited back and forth each orbit in order to produce friction.
  2. Define the final, lowest-energy orientation/attitude state (always pointing down as it orbits) when the damper has finished absorbing rotational energy. This takes on the order of days or weeks but it depends greatly on the details of the design.

The rotational angular momentum of the spacecraft on the other hand, is constantly sloshing (being exchanged) back and forth with the Earth's angular momentum relative to the Earth-spacecraft center of mass the on a timescale of hours, so there are no conservation law quandaries.

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  • $\begingroup$ This is a rather spartan answer; feel free to add links to other applicable answers, or references, or add another answer that illustrates some specific damping mechanisms. $\endgroup$ – uhoh Feb 18 '19 at 10:36
  • $\begingroup$ fyi I've just added a bounty to What are damper booms, how did they facilitate triaxial stabilization, and how did they “get out of DODGE”? $\endgroup$ – uhoh Feb 18 '19 at 10:38
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    $\begingroup$ "The rotational angular momentum of the spacecraft on the other hand, is constantly sloshing (being exchanged) back and forth with the Earth's rotational angular momentum" Is it really Earth's rotation? I mean the gravitational force is radial so it cannot rotate Earth (if we assume it's a perfect sphere). I think it's the orbital angular momentum instead, isn't it? $\endgroup$ – Calmarius Feb 18 '19 at 10:56
  • $\begingroup$ @Calmarius ya that;s the other tidal force. I've updated that sentence, thanks! $\endgroup$ – uhoh Feb 18 '19 at 11:21
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    $\begingroup$ So... one's basically stabilizing the spacecraft by heating it. Pretty cool :-) $\endgroup$ – Everyday Astronaut Feb 18 '19 at 11:46

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