Gravitational Chirp Death Zone
LIGO detected the gravitational waves from a black-hole merger. One hole was 39 solar masses, the other was 26, together they made a 62-solar-mass black hole; the 3 solar mass difference turned into gravitational radiation in about a tenth of a second. That’s a powerful chirp; it outpowered all the stars in the universe. One estimate was 10^24 sunpowers; that’s a trillion trillion, or 1.6 moles of stars!
So I wondered how close your spaceship would have to be to the black holes for the chirp to kill you. Here are my calculations:
Diameter of proton = 8.77 * 10^-16 m
1/10000 of that = how far LIGO mirror moved = 8.77 * 10^-20 m
Length of LIGO antenna = 4 * 10^3 m
Ratio of those lengths = 2.19 * 10^-23
Gravitational radiation goes by an inverse-square law. Also:
sqrt(2.19 *10^-23) = 4.68 * 10^-12
so I presume that anything closer, by that factor, to the black hole merger experienced gravitational-wave distortions on the order of the length of the object itself. Anything that close gets pounded like pizza dough; squashed flat in alternating perpendicular directions, 25 times in 0.1 seconds. That sounds like a death-zone to me. All bones broken, total ship-systems malfunction, planets explode, etc. CHIRP!
4.68* 10^-12 times 1.3 billion light-years = 0.006 light-years = 2.16 light-days.
OK, I’m staying at least that far away! But we’re not out of the woods yet. Note the supermassive black holes at the centers of Milky Way and Andromeda Galaxies. In a few billion years these galaxies will merge to form Milkomeda, and then their black holes will merge and chirp. How loud?
Mass of Milky Way black hole = 4.1 * 10^6 suns
Mass of Andromeda black hole = 2.3 * 10^8 suns
The recent black hole merger involved 29 and 36 suns. Assume that ‘our’ black hole does most of the radiating; the ratio of it to 29 suns is about 141,379; so I assume that the energy will be greater by that proportion.
Assuming inverse-square law, the death-chirp zone is greater by a factor of sqrt(141379) = 376
376 * 0.006 light-years is about 2.25 light years.
OK, again I’m keeping my distance. But I wasn’t planning to go there anyway.
*Phew*. Frankly I was worried; my first, inaccurate, calculation had the death-chirp span Milkomeda. Frying when the Sun goes supergiant has some dignity; but death by chirp is an insult.