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My experience with Kerbal Space Program gives me the impression that it's impossible to transfer from a stable orbit of one body to the stable orbit of another without deceleration. But is this true for a photon? Could light enter a stable orbit of a black hole if fired at the correct angle from a distance?

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    $\begingroup$ I was wondering if starlight could build up near the orbital altitude of a black hole, creating a brief flash of light for any matter falling below that altitude. $\endgroup$
    – Wesley Adams
    Apr 8 at 2:55
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    $\begingroup$ @StarMan I know about that, but my question had more to do with the entry of photons from outside of the photon sphere into it, and more broadly the orbital mechanics of photons. $\endgroup$
    – Wesley Adams
    Apr 8 at 2:59
  • $\begingroup$ @WesleyAdams Well then how did light enter the photon sphere in the first place? The photons had to be fired into the sphere. Thus answering your question (mostly) $\endgroup$
    – Star Man
    Apr 8 at 3:00
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    $\begingroup$ This is essentially a duplicate of this. The answer is no because there are no stable photon orbits (there are however unstable photon orbits) (I dont have enough reputation to recommend this be closed as a duplicate I think). $\endgroup$
    – user38308
    Apr 8 at 14:54
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    $\begingroup$ @uhoh This information was the basis for my question. Thanks anyway! $\endgroup$ Apr 8 at 21:56
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There are no stable photon orbits around black holes (see this answer).

Black holes do have an unstable photon orbit though. "Unstable" here means that any tiny deviation from this orbit, will case the photon to be either scattered to infinity or sent into the black hole. It should be emphasized that there such orbits are always circular an can exist at only one radius (1.5 times the Schwarzschild radius for a Schwarzschild black hole). There are no elliptic photon orbits. This orbit is often called the "light ring" (or sometimes "photonsphere")

As long as we treat the photon as a perfect massless point (test) particle, we can find a highly fine-tuned trajectory that will asymptote to the light-ring. Of course, in reality, a photon always needs to be a wave packet with a finite size, making this fine tuning impossible in practice.

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  • $\begingroup$ Can a photon emitted from a distant location be captured into an orbit if not emitted from a point that intersects with that orbit? $\endgroup$ Apr 8 at 22:01
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    $\begingroup$ You don’t have stable photon orbits, so a photon cannot be captured in one. $\endgroup$
    – mmeent
    Apr 8 at 22:12
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    $\begingroup$ But as I said for any unstable orbit you can find a trajectory that approaches it asymptotically. $\endgroup$
    – mmeent
    Apr 8 at 22:14
  • $\begingroup$ Do the photons on such orbits move in the same direction as black hole's spin? $\endgroup$
    – Anixx
    Apr 10 at 20:11
  • $\begingroup$ If a photon shifts inward from such orbit, how many revolution it still can do before being swallowed by the event horizon? $\endgroup$
    – Anixx
    Apr 10 at 20:14

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