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...or "How precisely does ISS face Earth with one side?"

We know "ISS always faces Earth with one side" - "spins at 1 revolution per orbit" which accounts for staying quite precisely parallel to Earth in the east-west axis.

But since the orbit is quite steeply inclined (51.6 degrees), if it's parallel to Earth in the north-south axis while passing over the equator, at northernmost point of its orbit the cupola would be facing 51.6 degrees north from the local "directly down", and respective 51.6 degrees south in the southernmost point.

Does ISS compensate for that with its CMGs or does it "look at Earth sideways" when away from the equator?

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The rotation matches the orbit inclination so cupola down is always towards the earth. You can watch the live stream from ustream to watch this (or at least you can when it's showing the exterior view), or there are any number of videos on youtube that show down being stable. Here's one collection of timelapse videos:

Orbits are ellipses, regardless of inclination. Rotating once per orbit around the same axis as the orbit can maintain down, regardless of what axis that is.

For help explaining this:

  • Consider the case of an equatorial orbit: the axis normal to the orbit is the north-south line through the earth, so rotating around that axis will match the orbit and down remains pointing directly at the earth.
  • Now consider the case of a 90 degree polar orbit: the earth rotates so we need an external reference frame. For simplicity let the axis normal to the orbit match the line from the earth to the sun (which itself changes as the earth orbits the sun, but only at a rate of about one degree per day so it's reasonably fixed short-term). If the station also rotates around the axis defined by the line from the sun to the earth then down will always point directly at the earth.
  • Now wait three months and due to the axial tilt of the earth relative to its orbit an orbit around the earth that's normal to the line from the earth to the sun will have shifted by about 23 degrees. The same rotation around the line between the earth and the sun will still maintain down as pointing at the earth.
  • Regardless of inclination the orbit there is a single axis that is normal to the orbit (defined in inertial space, which is fixed in space and doesn't rotate with the earth). Because of that, there is always a simple rotation axis that can be used to maintain down pointing at the center of the orbit.
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  • $\begingroup$ Thanks. Pretty obvious in retrospection, making the axis of the spin parallel to the axis of the orbit. So answering my questions "Yes, it wobbles, no, it doesn't use CMGs, that happens all by itself, thanks to orbital mechanics." $\endgroup$ – SF. Jan 8 '16 at 22:16
  • $\begingroup$ Your video got broken $\endgroup$ – Ferrybig Jan 16 at 13:42
  • $\begingroup$ video link still broken! $\endgroup$ – uhoh Jun 7 at 13:17

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