<p>The answer is yes.</p>
<p>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 <span class="math-container">$1.5 r_s$</span>, where <span class="math-container">$r_s$</span> is the Schwarzschild radius, can be bent through any angle. The closer the closest approach is to <span class="math-container">$1.5 r_s$</span> 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 <span class="math-container">$1.76r_s$</span> - see <a href="https://physics.stackexchange.com/questions/766132/would-someone-falling-into-or-orbiting-a-black-hole-see-themselves">https://physics.stackexchange.com/questions/766132/would-someone-falling-into-or-orbiting-a-black-hole-see-themselves</a> .</p>
<p>Viewing this spectacle from a distance much larger than <span class="math-container">$r_s$</span>, 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 <span class="math-container">$3\sqrt{3}r_s/2$</span>.</p>

CC BY-SA 4.0
2023-08-13T11:19:06.917Z
also related in Physics SE: [Could a trajectory around a large mass ever deflect by more than 180 degrees due to general relativistic effects?](https://physics.stackexchange.com/q/467144/83380) (thought it asks about a particle's trajectory rather than light)
uhoh
CC BY-SA 4.0
2023-08-14T15:34:51.897Z
The movie *Interstellar* famously paid for actual astrophysicists to do a real physics simulation of light paths to generate the famous black hole image that looks like it's wearing a hat, which shows how you can see every part of the accretion disc due to the bizarre light bending that's going on.  It's not exactly a companion star's light but I think it does a good job of showing that no matter which direction it comes from, the light can reach you where you are. Of course the amount of light that reaches any given observer would be tiny compared to the incident light.
Darth Pseudonym
CC BY-SA 4.0
2023-08-14T17:27:27.190Z
OK, now I want someone to create a video of life on a planet orbiting at 1 AU around a G2 star orbiting a super massive black hole at 1.76 r_s, where r_s is about 4 AU (or 1 AU is about 1/4 r_s). (The black hole would need to have a mass of a little over 200,000,000 solar masses.) Bah, just realized that the hypothetical planet would be _well_ outside the star's Hill sphere. I'll have to dream up another example...
Ben Hocking
CC BY-SA 4.0
2023-08-12T23:31:10.830Z
2023-08-13T07:15:48.270Z
2023-08-13T07:15:48.270Z
ProfRob
<p>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?</p>

CC BY-SA 4.0
2023-08-12T23:29:14.157Z
Related: https://astronomy.stackexchange.com/a/49874/16685 Also see https://physics.stackexchange.com/a/766180/123208
PM 2Ring
CC BY-SA 4.0
2023-08-13T00:22:52.660Z
Oops! I just fixed a typo in the `b` value for 180° deflection in that Physics.SE answer. https://i.sstatic.net/LsG0C.png Here are more precise values of those parameters: b = 2.678479315370894344, delta = 0.080403104017578404, r = 1.760308981575963230
PM 2Ring
CC BY-SA 4.0
2023-08-13T11:58:57.067Z
@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).  https://physics.stackexchange.com/a/350814/43351
ProfRob
<black-hole><gravitational-lensing>
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?
Jack R. Woods
# 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?

(Asked by: username_0 on 2023-08-12)

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?

**Tags:** black-hole, gravitational-lensing
> **Comments:**
> **username_1**: Related: https://astronomy.stackexchange.com/a/49874/16685 Also see https://physics.stackexchange.com/a/766180/123208  
> **username_1**: Oops! I just fixed a typo in the `b` value for 180° deflection in that Physics.SE answer. https://i.sstatic.net/LsG0C.png Here are more precise values of those parameters: b = 2.678479315370894344, delta = 0.080403104017578404, r = 1.760308981575963230  
> **username_2**: @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).  https://physics.stackexchange.com/a/350814/43351  

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## 1 answers

### Answer by username_2 on 2023-08-12. Score: 19 | Accepted answer

The answer is yes.

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 $3\sqrt{3}r\_s/2$.

> **Comments:**
> **username_3**: also related in Physics SE: [Could a trajectory around a large mass ever deflect by more than 180 degrees due to general relativistic effects?](https://physics.stackexchange.com/q/467144/83380) (thought it asks about a particle's trajectory rather than light)  
> **username_4**: The movie *Interstellar* famously paid for actual astrophysicists to do a real physics simulation of light paths to generate the famous black hole image that looks like it's wearing a hat, which shows how you can see every part of the accretion disc due to the bizarre light bending that's going on.  It's not exactly a companion star's light but I think it does a good job of showing that no matter which direction it comes from, the light can reach you where you are. Of course the amount of light that reaches any given observer would be tiny compared to the incident light.  
> **username_5**: OK, now I want someone to create a video of life on a planet orbiting at 1 AU around a G2 star orbiting a super massive black hole at 1.76 r_s, where r_s is about 4 AU (or 1 AU is about 1/4 r_s). (The black hole would need to have a mass of a little over 200,000,000 solar masses.) Bah, just realized that the hypothetical planet would be _well_ outside the star's Hill sphere. I'll have to dream up another example...  

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