v much enjoyed that discussion. I heard that orbits around a black hole fool the observer into experiencing the motion as getting closer to a straight line, and then further in the orbit goes convex. Due to relativistic curvature. Can't find a write up of this, ring any bell?
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Extreme relativistic orbits entail less “centrifugal force”, going to zero as you approach a radius 1.5 times the Schwarzschild radius, and then negative. So there are no orbits smaller than that, because instead of balancing gravity it points in the same direction.
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