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In a recent Science News, it mentioned two orbiting black holes (which later combined) were precessing; i.e. their motion did not remain in a stable plane, but rather the plane itself was changing. Which seemed odd to me.

Admittedly I need to read up on precession. And maybe in the case of black holes there were other causes (gravity waves? electro-magnetic fields?) But my first thought is: maybe the size of the objects matter. So could precession happen with point masses?

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Black holes are usually rotating very quickly. If their two rotational angular momentum vectors are not parallel and perpendicular to the orbital angular momentum vector, then the system should be able to exchange orbital and rotational angular momentum in such a way that the orbital plane itself tilts, even though the total angular momentum has to be conserved (except for the radiation of gravitational waves, as you mentioned). This isn't just restricted to black hole motion, of course. It is a perfectly "classical" effect.

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