So with traditional orbit mechanics, an object coming in from outside a system will follow a hyperbolic path, and have greater speed when closer to the body. But my question is, how exactly does light behave with gravity, not being able to change its speed? I know it is bent, but is it a hyperbola? Can it orbit a black hole stably?

  • $\begingroup$ From General Relativity there has to be an additional term which expresses the decrease in velocity due to increase in mass of the central body. This seems to be paradox but the speed of light (from a third point of observation) decreases near huge masses. $\endgroup$ – HolgerFiedler Dec 10 '17 at 6:43
  • $\begingroup$ Hope to see in the answer that mathematical proof that a hyperbolic path could overgo into a circular path. Never thought about this. Know only that a circle is the special case of an ellipse. $\endgroup$ – HolgerFiedler Dec 10 '17 at 6:50
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    $\begingroup$ @HolgerFiedler - Typically light in a circular orbit around a black hole was emitted by infalling matter. The orbit is not stable. $\endgroup$ – mmesser314 Dec 10 '17 at 6:54
  • $\begingroup$ @mmesser314 See my quested here: math.stackexchange.com/questions/2559630/… $\endgroup$ – HolgerFiedler Dec 10 '17 at 8:24

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