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When looking at a black hole the ability to see ourselves is compromised by the small window for the light trajectory to come back to us. The light from the Earth that is bent by (almost) 180° and that comes back to Earth occupies a very narrow solid angle.

Could one make things easier by opening up the angle (so it's less than 180°) by sending out a telescopic probe right angle from Earth to increase that window to better see ourselves?

enter image description here

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    $\begingroup$ The better spot for the telescope is on the opposite side of the black hole, not at 90 degrees. (This was used in MACHO searches.) Have you tried any ray-tracing simulations, or searched for the analytical expressions for the light deflection? $\endgroup$ – benjimin Jan 12 '16 at 13:11
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The problem with your proposal is the distance to the black hole. Even if a black hole is only one light year away, then a telescope probe that changes the angle of return for the image of the earth by even one degree would have to be quite far from Earth. How far? If the Earth-telescope distance looks like a 1° angle "as seen from the black hole", then it's about 1/57th of a light year or about 1100 au away. That is well outside the solar system. So no - I don't think it will help.

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In practicality, there is no way you'd be able to get a clear enough picture to actually see the Earth in the refracted light at all. The only way we can presently detect black holes is that they consume stars. If my memory serves correctly, one of the first black holes was actually found when they watched a star be consumed by the black hole. The entire event only took up about 9 pixels on the Hubble Space Telescope, though.

Even with the James Webb telescope in development, there's no way you're going to get a clear enough image. Trying to use a black hole's gravitational lensing to see the planet is a bit like proposing to shoot a gigantic mirror several light years into space so we can see ourselves in the past. I'm sorry to be a buzzkill, but there is simply no way you can collect enough detail in a digital image to see the Earth in the gravitational lensing of any celestial object.

I'm not entirely certain of what you're asking, but if you want to see the planet in as much detail as possible, it's definitely easiest to simply use an Earth-orbiting satellite. Whatever lensing you need done is easily accomplished by using glass or reflective plates instead.

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    $\begingroup$ Once video games where 2 bits to start now they are at 256 bit. 8 pixels is just a start. $\endgroup$ – Muze the good Troll. Jan 1 '16 at 12:22
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    $\begingroup$ We can barely see the black hole itself right now. Even if it will one day be possible to see the earth in the gravitational lensing of a black hole, it'd be a waste of time. Again, whatever lensing you need done can be done with glass or reflective plates. In addition, the lensing increases as distance to the event horizon decreases, so the image would be bent. $\endgroup$ – Sanix25 Jan 1 '16 at 15:55

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