# How close would you have to be to the merger of two black holes, for the effects of gravitational waves to be detected without instruments?

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?

• Are you detecting the plunge phase, the inspiral, or what? – Jerry Schirmer Jul 27 '15 at 17:18
• Whichever is easiest to detect. – Florin Andrei Jul 27 '15 at 19:28
• OK, I think I have a lazy, quick way of order of magnitude estimating this thing. I'll put it up tonight or tomorrow. – Jerry Schirmer Jul 27 '15 at 19:41

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!

• In the interest of keeping your answer self-contained, and to prevent link rot, can you include a brief description of what $h$ is? – Emilio Pisanty Sep 18 '15 at 11:01
• 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)? – hyde Feb 13 '16 at 21:04
• @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. – Selene Routley Jul 22 '16 at 2:51
• @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." – Selene Routley Jul 22 '16 at 2:51
• What would be our other concerns? – Jus12 Oct 31 '17 at 6:58