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Gravitational waves

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Author Topic: Gravitational waves  (Read 1662 times)
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mccoy
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« Reply #30 on: Feb 20, 2016 09:37 pm »

Guys, it turns out that GWs have a negligibile effect even near to the black holes collision we just witnessed. Someone has calculated that, at a distance of one AU (sun-earth distance) the strain would have been 10-7 that is,  imperceptible. Maybe some very faint sound effect would have been felt. I'm disappointed!!!

Such a titanic clash yields a really tiny effect in terms of gravitational waves. That's why they have been so elusive for decades.

By victor Toth

Quote
A crude formula for the measured strain from the gravitational wave due to a binary star system is given by:
h∼2G2M1M2c4aD,h∼2G2M1M2c4aD,
where G∼6.674×10−11 m3/kg/s2G∼6.674×10−11 m3/kg/s2 is Newton's constant of gravity, M1M1 and M2M2 are the two masses, c=3×108 m/sc=3×108 m/s is the speed of light, aa is the separation between the stars and DD is the distance from the detector.
If you substitute M1=M2=30M⊙M1=M2=30M⊙, a=100 kma=100 km and D=421 MpcD=421 Mpc (after appropriate conversion of units, of course), for a separation of a=100 kma=100 km you get h=3×10−21h=3×10−21, so crude it might be, but the formula is not useless.
And it tells you that the strain is inversely proportional to distance. Which means that  if you were, say, 1 astronomical unit from the source, the strain would have been h∼3×10−7h∼3×10−7. This would have been easily detectable with a desktop experiment. (Very easily, as a matter of fact, as this strain exceed the sensitivity of the Michelson-Morley experiment from 1887 by ten orders of magnitude. Of course Michelson-Morley was not designed for this frequency range, but even so, it would have seen it for sure.)
Not only that, but since the gravitational wave emitted by GW150914 was in the audio frequency range, I suspect that humans would have heard it as the strain, acting as a momentary passing tidal effect, would have stressed their eardrums. That of course assumes that there were either no non-gravitational effects (e.g., deadly radiation from a disturbed accretion disk surrounding the coalescing binary) or the humans were well protected, so they could enjoy the "chirp" instead of having to flee for their lives...
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