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Replace strain by distortion
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Steve Linton
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Part of the answer is easy. The strain measured in that event was about $0.25\times 10^{-21}$. That is an object $1m$ long would be squeezed by $0.25\times 10^{-21} m$ in one direction and stretched by the same amount in the orthogonal direction.

The strain drops off linearly with distance from the black hole, so to achieve a straindistortion of 1mm in something the size of the Earth (ie about $8\times 10^{-11}$ it would need to be about $5\times 10^{10}$ times closer, so about $0.03$ light years away, or about 2000 AU. Two 30 solar mass plus black holes at that distance would have disrupted the solar system quite a bit before they collided.

To achieve a straindistortion of 1mm in something the size of a human they would need to be another factor of $6\times 10^6$ closer, so about $\mathrm{30000 km}$, closer than geostationary orbit. In this case we would certainly have bigger problems than the gravity waves.

What I don't know how to calculate is the energy absorbed by the Earth, or a human, in one of these scenarios. I suspect it would not be all that much, at least from the wave.

Added later: this answer gives the total energy passing through the Earth (about 34GJ with the black holes at their current distance) but offers no ideas for how much is absorbed. This would increase according to the inverse square law if the black holes were closer.

Part of the answer is easy. The strain measured in that event was about $0.25\times 10^{-21}$. That is an object $1m$ long would be squeezed by $0.25\times 10^{-21} m$ in one direction and stretched by the same amount in the orthogonal direction.

The strain drops off linearly with distance from the black hole, so to achieve a strain of 1mm in something the size of the Earth (ie about $8\times 10^{-11}$ it would need to be about $5\times 10^{10}$ times closer, so about $0.03$ light years away, or about 2000 AU. Two 30 solar mass plus black holes at that distance would have disrupted the solar system quite a bit before they collided.

To achieve a strain of 1mm in something the size of a human they would need to be another factor of $6\times 10^6$ closer, so about $\mathrm{30000 km}$, closer than geostationary orbit. In this case we would certainly have bigger problems than the gravity waves.

What I don't know how to calculate is the energy absorbed by the Earth, or a human, in one of these scenarios. I suspect it would not be all that much, at least from the wave.

Added later: this answer gives the total energy passing through the Earth (about 34GJ with the black holes at their current distance) but offers no ideas for how much is absorbed. This would increase according to the inverse square law if the black holes were closer.

Part of the answer is easy. The strain measured in that event was about $0.25\times 10^{-21}$. That is an object $1m$ long would be squeezed by $0.25\times 10^{-21} m$ in one direction and stretched by the same amount in the orthogonal direction.

The strain drops off linearly with distance from the black hole, so to achieve a distortion of 1mm in something the size of the Earth (ie about $8\times 10^{-11}$ it would need to be about $5\times 10^{10}$ times closer, so about $0.03$ light years away, or about 2000 AU. Two 30 solar mass plus black holes at that distance would have disrupted the solar system quite a bit before they collided.

To achieve a distortion of 1mm in something the size of a human they would need to be another factor of $6\times 10^6$ closer, so about $\mathrm{30000 km}$, closer than geostationary orbit. In this case we would certainly have bigger problems than the gravity waves.

What I don't know how to calculate is the energy absorbed by the Earth, or a human, in one of these scenarios. I suspect it would not be all that much, at least from the wave.

Added later: this answer gives the total energy passing through the Earth (about 34GJ with the black holes at their current distance) but offers no ideas for how much is absorbed. This would increase according to the inverse square law if the black holes were closer.

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Steve Linton
  • 10.3k
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  • 49

Part of the answer is easy. The strain measured in that event was about $0.25\times 10^{-21}$. That is an object $1m$ long would be squeezed by $0.25\times 10^{-21} m$ in one direction and stretched by the same amount in the orthogonal direction.

The strain drops off linearly with distance from the black hole, so to achieve a strain of 1mm in something the size of the Earth (ie about $8\times 10^{-11}$ it would need to be about $5\times 10^{10}$ times closer, so about $0.03$ light years away, or about 2000 AU. Two 30 solar mass plus black holes at that distance would have disrupted the solar system quite a bit before they collided.

To achieve a strain of 1mm in something the size of a human they would need to be another factor of $6\times 10^6$ closer, so about $\mathrm{30000 km}$, closer than geostationary orbit. In this case we would certainly have bigger problems than the gravity waves.

What I don't know how to calculate is the energy absorbed by the Earth, or a human, in one of these scenarios. I suspect it would not be all that much, at least from the wave.

Added later: this answer gives the total energy passing through the Earth (about 34GJ with the black holes at their current distance) but offers no ideas for how much is absorbed. This would increase according to the inverse square law if the black holes were closer.

Part of the answer is easy. The strain measured in that event was about $0.25\times 10^{-21}$. That is an object $1m$ long would be squeezed by $0.25\times 10^{-21} m$ in one direction and stretched by the same amount in the orthogonal direction.

The strain drops off linearly with distance from the black hole, so to achieve a strain of 1mm in something the size of the Earth (ie about $8\times 10^{-11}$ it would need to be about $5\times 10^{10}$ times closer, so about $0.03$ light years away, or about 2000 AU. Two 30 solar mass plus black holes at that distance would have disrupted the solar system quite a bit before they collided.

To achieve a strain of 1mm in something the size of a human they would need to be another factor of $6\times 10^6$ closer, so about $\mathrm{30000 km}$, closer than geostationary orbit. In this case we would certainly have bigger problems than the gravity waves.

What I don't know how to calculate is the energy absorbed by the Earth, or a human, in one of these scenarios. I suspect it would not be all that much, at least from the wave.

Part of the answer is easy. The strain measured in that event was about $0.25\times 10^{-21}$. That is an object $1m$ long would be squeezed by $0.25\times 10^{-21} m$ in one direction and stretched by the same amount in the orthogonal direction.

The strain drops off linearly with distance from the black hole, so to achieve a strain of 1mm in something the size of the Earth (ie about $8\times 10^{-11}$ it would need to be about $5\times 10^{10}$ times closer, so about $0.03$ light years away, or about 2000 AU. Two 30 solar mass plus black holes at that distance would have disrupted the solar system quite a bit before they collided.

To achieve a strain of 1mm in something the size of a human they would need to be another factor of $6\times 10^6$ closer, so about $\mathrm{30000 km}$, closer than geostationary orbit. In this case we would certainly have bigger problems than the gravity waves.

What I don't know how to calculate is the energy absorbed by the Earth, or a human, in one of these scenarios. I suspect it would not be all that much, at least from the wave.

Added later: this answer gives the total energy passing through the Earth (about 34GJ with the black holes at their current distance) but offers no ideas for how much is absorbed. This would increase according to the inverse square law if the black holes were closer.

Part of the answer is easy. The strain measured in that event was about $0.25\times 10^{-21}$. That is an object $1m$ long would be squeezed by $0.25\times 10^{-21} m$ in one direction and stretched by the same amount in the orthogonal direction.

The strain drops off linearly with distance from the black hole, so to achieve a strain of 1mm in something the size of the Earth (ie about $8\times 10^{-11}$ it would need to be about $5\times 10^10$$5\times 10^{10}$ times closer, so about $0.03$ light years away, or about 2000AU2000 AU. Two 30 solar mass plus black holes at that distance would have disrupted the solar system quite a bit before they collided.

To achieve a strain of 1mm in something the size of a human they would need to be another factor of $6\times 10^6$ closer, so about $30000 km$$\mathrm{30000 km}$, closer than geostationary orbit. In this case we would certainly have bigger problems than the gravity waves.

What I don't know how to calculate is the energy absorbed by the Earth, or a human, in one of these scenarios. I suspect it would not be all that much, at least from the wave.

Part of the answer is easy. The strain measured in that event was about $0.25\times 10^{-21}$. That is an object $1m$ long would be squeezed by $0.25\times 10^{-21} m$ in one direction and stretched by the same amount in the orthogonal direction.

The strain drops off linearly with distance from the black hole, so to achieve a strain of 1mm in something the size of the Earth (ie about $8\times 10^{-11}$ it would need to be about $5\times 10^10$ times closer, so about $0.03$ light years away, or about 2000AU. Two 30 solar mass plus black holes at that distance would have disrupted the solar system quite a bit before they collided.

To achieve a strain of 1mm in something the size of a human they would need to be another factor of $6\times 10^6$ closer, so about $30000 km$, closer than geostationary orbit. In this case we would certainly have bigger problems than the gravity waves.

What I don't know how to calculate is the energy absorbed by the Earth, or a human, in one of these scenarios. I suspect it would not be all that much, at least from the wave.

Part of the answer is easy. The strain measured in that event was about $0.25\times 10^{-21}$. That is an object $1m$ long would be squeezed by $0.25\times 10^{-21} m$ in one direction and stretched by the same amount in the orthogonal direction.

The strain drops off linearly with distance from the black hole, so to achieve a strain of 1mm in something the size of the Earth (ie about $8\times 10^{-11}$ it would need to be about $5\times 10^{10}$ times closer, so about $0.03$ light years away, or about 2000 AU. Two 30 solar mass plus black holes at that distance would have disrupted the solar system quite a bit before they collided.

To achieve a strain of 1mm in something the size of a human they would need to be another factor of $6\times 10^6$ closer, so about $\mathrm{30000 km}$, closer than geostationary orbit. In this case we would certainly have bigger problems than the gravity waves.

What I don't know how to calculate is the energy absorbed by the Earth, or a human, in one of these scenarios. I suspect it would not be all that much, at least from the wave.

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Steve Linton
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