The sun bends the trajectory of light slightly. And a black hole will bend the trajectory entirely. This is all dependent on the proximity to the source of gravity. For a given angle, is there some minimum mass required to bend light light at least that much?
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1How much is "noticeably" ? Voting to Close as Primarily Opinion Based. – Abhimanyu Pallavi Sudhir Dec 16 '13 at 03:32
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2@DIMension10 yeah the word "noticeably" is under-defined but you can answer the spirit of the question without defining noticeably. – Brandon Enright Dec 16 '13 at 03:49
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4The question also suffers from not having done even any cursory research. Check the Wikipedia page on gravitational lensing and find a precise mathematical answer for any value of "shift" you care to look at. Why did you ask other people to do this work for you? Lazy questions are never good questions. – dmckee --- ex-moderator kitten Dec 16 '13 at 03:51
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Related http://physics.stackexchange.com/questions/90591/calculating-the-size-of-the-lensing-sphere-of-a-black-hole – John Rennie Dec 21 '13 at 09:49
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I believe you've already spotted the answer to your question with this sentence:
And a black hole will shift the trajectory entirely. This is all dependent on the proximity to the source of gravity.
You can "shift light" (bend its trajectory) as much as you want with as little mass as you want using a black hole. Just let the light get arbitrarily close to the event horizon. There isn't any (practical) lower limit on the mass of a black hole so there isn't any particular mass required to bend light. Just huge densities which will cause the curvature of space needed.
Brandon Enright
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Yep! Everything that has mass warps space a tiny bit and therefor causes light to bend. – Brandon Enright Dec 18 '13 at 16:01