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Assume two black holes in the most common size range, spiraling into each other until they merge. The event releases significant amounts of energy via gravitational waves, which warp the space-time.

If the distortion is powerful enough, it would get noticed in daily life, or perhaps even detected by the proprioceptors in the human body.

How close, as an order of magnitude estimate, would you have to be to the merger to perceive it like that, without any instrument?

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  • $\begingroup$ Are you detecting the plunge phase, the inspiral, or what? $\endgroup$
    – Zo the Relativist
    Commented Jul 27, 2015 at 17:18
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    $\begingroup$ Whichever is easiest to detect. $\endgroup$
    – Florin Andrei
    Commented Jul 27, 2015 at 19:28
  • $\begingroup$ OK, I think I have a lazy, quick way of order of magnitude estimating this thing. I'll put it up tonight or tomorrow. $\endgroup$
    – Zo the Relativist
    Commented Jul 27, 2015 at 19:41

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The gravitational distortion at a distance $r$ from gravitational waves due to a radiating system of mass $M$ with typical speeds of $v$ is roughly \begin{equation} h\approx \frac{GM}{c^2} \times \frac{1}{r} \times \left(\frac{v}{c}\right)^2 \end{equation} see e.g. http://www.tapir.caltech.edu/~teviet/Waves/gwave.html for an explanation.

So let's say that roughly at the merger speeds are close to the speed of light, so that \begin{equation} h\approx r_{sch}/ r \end{equation}

the average black hole is roughly $~20$ miles, so to get a ~$1$% distortion in lengths observable by human senses, $r\approx 2,000$ miles.

If a merger of two black holes is happening at this distance, gravitational waves would be our least concern.

This also illustrates how feeble gravitational waves are!

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    $\begingroup$ In the interest of keeping your answer self-contained, and to prevent link rot, can you include a brief description of what $h$ is? $\endgroup$
    – Emilio Pisanty
    Commented Sep 18, 2015 at 11:01
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    $\begingroup$ How do you recon 1% distortion is detected by human senses? Why not 0,5% or 2%? Another question, assuming there's not accretion disk, no infalling matter, what worse effects would there be at that distance, assuming stable orbit (which is possible that far, I think)? $\endgroup$
    – hyde
    Commented Feb 13, 2016 at 21:04
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    $\begingroup$ @hyde I agree that the 1% is probably waaaay more than would be needed to feel it. However, Ali's good answer has given you the technique needed to answer this question more accurately, so I think it falls to those of us who disagree with the exact figures to do our own research and to plug our criterion into Ali's method. I'm guessing that a 1% distortion with sub millisecond rise time would at the very least shred the vascular system of complex animals and thus kill every mammal on Earth instantly and that, probably a strain of $10^{-6}$ is detectable. $\endgroup$
    – Selene Routley
    Commented Jul 22, 2016 at 2:51
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    $\begingroup$ @hyde So the answer changes to 20 million miles: about a quarter of an AU. I don't think this is far enough to change the spirit of Ali's answer: "If a merger of two black holes is happening at this distance, gravitational waves would be our least concern." $\endgroup$
    – Selene Routley
    Commented Jul 22, 2016 at 2:51
  • $\begingroup$ What would be our other concerns? $\endgroup$
    – Jus12
    Commented Oct 31, 2017 at 6:58

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