# If you were on a planet orbiting a star that has a black hole companion, could you see light from your host star bent 180 degrees?

I realize that there is a distance from a black hole where photons can orbit. I understand that this orbit is very unstable, but I am concerned with photons just outside this range. Could the black hole cause them to 'u-turn' so that you could see some light from your star when looking at the black hole?

• Aug 12, 2023 at 23:29
• Oops! I just fixed a typo in the b value for 180° deflection in that Physics.SE answer. i.stack.imgur.com/LsG0C.png Here are more precise values of those parameters: b = 2.678479315370894344, delta = 0.080403104017578404, r = 1.760308981575963230 Aug 13, 2023 at 0:22
• @PM2ring I confirm those numbers. They are also interesting because they represent the maximum radius of a neutron star that you would be able to see the whole surface of in one go. (For the same reason). physics.stackexchange.com/a/350814/43351 Aug 13, 2023 at 11:58

Roughly speaking, for a spinless Schwarzschild black hole, light that gets to a closest approach to the black hole of just a little greater than $$1.5 r_s$$, where $$r_s$$ is the Schwarzschild radius, can be bent through any angle. The closer the closest approach is to $$1.5 r_s$$ the bigger the angle becomes, and the light can even loop around the black hole more than once. A 180 degree deflection is caused when inwardly directed light from far away passes a black hole at a closest approach of $$1.76r_s$$ - see https://physics.stackexchange.com/questions/766132/would-someone-falling-into-or-orbiting-a-black-hole-see-themselves .
Viewing this spectacle from a distance much larger than $$r_s$$, an observer would see the black hole surrounded by a ring of light that is heading towards them after being bent around the black hole. The apparent radius of this ring would be just a little larger than $$3\sqrt{3}r_s/2$$.