Can a planet in a stable clockwise orbit slow down into a spiral if orbiting a black hole spinning counter-clockwise?
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$\begingroup$ I am no General Relativity buff, but a quick scan of the relevant Wikipedia articles suggests that the planet would need to be in a polar rather than equatorial orbit to get the maximum effect, and that the effect would be a precession rather than the orbit decay you describe. A satellite is attempting to measure this effect in a polar orbit around Jupiter. $\endgroup$– Duncan HarrisCommented May 23, 2018 at 3:10
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$\begingroup$ so frame dragging cannot slow down an object? $\endgroup$– arcman77Commented May 23, 2018 at 5:45
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In this context you cannot really speak about "forces", since in any case the object will follow a geodesic through the curved spacetime.
However, there certainly is a noticeable effect of frame dragging on orbits. As you may or may not know, there exist a smallest possible circular orbit around any black hole. For a non-spinning black hole, for example, this orbit is at 3 times the Schwarzschild radius.
For spinning black holes the radius of this smallest circular orbit depends on the orientation of the orbit. In particular it is much smaller for prograde orbit than it is for retrograde orbits. You can certainly interpret this as the retrograde orbits being "destabilized into an inspiralling plunge" by the frame dragging effect.
