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Are the Voyager spacecraft completely still (fixated) when travelling through space or are they a little unstable because they are travelling at high velocities?

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    $\begingroup$ See www2.jpl.nasa.gov/basics/bsf11-2.php $\endgroup$ – innisfree Apr 11 '15 at 16:18
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    $\begingroup$ It says that Voyager 1 and 2 used "3-axis stabilization" to keep themselves pointing in particular directions. The alternative is to keep the whole thing spinning, like a big gyroscope. I don't know much about it, to be honest, but it sounds interesting. If I read enough to understand it properly, I'll try to write an answer. $\endgroup$ – innisfree Apr 11 '15 at 16:20
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    $\begingroup$ Why would a high speed make it unstable? $\endgroup$ – HDE 226868 Apr 11 '15 at 16:22
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    $\begingroup$ and @HDE226868, in addition considering Einsteinian or even classical relativity, how it is it that Voyager is even at high speed? from Voyager's point-of-view it's perfectly still. $\endgroup$ – robert bristow-johnson Apr 11 '15 at 18:54
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    $\begingroup$ @robertbristow-Johnson Exactly. $\endgroup$ – HDE 226868 Apr 11 '15 at 19:01
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Although the craft can be turned if necessary, the Voyager probes are not intentionally rotating. They use small thrusters that try to zero out any rotations.

These thrusters aren't infinitely precise, nor are the instruments that drive them. So there is some error in the firing that means the probe has a (small) residual rotation. Instead of having a perfectly fixed direction, it will slowly drift away from the intended attitude over time. When the residual rotation moves the platform too far from the antenna pointing at earth, the thrusters fire to to return the alignment.

This error in the rotation rate has nothing to do with the speed of the probe.

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