# Energy deposition in planet Earth due to gravitational waves

The gravitational wave detected by the LIGO observatory acted on planet Earth streching and shrinking it a little bit. I assume that not all of this action was fully elastic and that some energy of the gravitational wave was lost by the passage through planet Earth.

Are there some scientific estimates of how much energy was deposited in planet Earth by this gravitational wave?

Are there estimates how much energy is in total deposited by gravitational waves in planet Earth per year?

• cool question.. – Fattie Sep 26 '16 at 14:29
• I think its about 1.21 jigawatts – Dean Sep 27 '16 at 10:35
• This is a good question, but honestly, not easily answered. Unless someone here specifically studies gravitational waves, I think you're going to be hard pressed to find an answer without significant research. That being said, the closest thing I could find that may help is this paper. They discuss the momentum imparted to test particles by gravitational waves. Specifically look at (the daunting) equation 25. With enough work, you could probably work out how to calculate what you want to know. – zephyr Sep 28 '16 at 14:53
• I suppose some geologist or physicist can calculate how much energy is lost in rocks if you compress and decompress the Earth by $10^{-15}$ meters a few times. I would think that most materials are highly elastic at these tiny levels of compression, perhaps immeasurably so. – eshaya Oct 7 '16 at 20:23

The measured event was two black holes merging with a total mass loss of $3 M_{\odot}$. While the distance for that event was calculated to $1.3*10^9 ly$.
$$E_{Earth} = \pi r_{Earth}^2*\frac{m_{conv}c^2}{4\pi r_{dist}^2}$$ $$E_{Earth} \approx (6378km)^2*\frac{3M_{\odot}*c^2}{4*(1.3*10^9years*c)^2}$$ $$E_{Earth} \approx 4.0*10^{13}m^2*\frac{5.7*10^{30}kg}{6.72*10^{33}s^2}$$ $$E_{Earth} \approx 3.39 * 10^{10}J$$
So the maximum amount of energy passing through earth would have been roughly $34 GJ$. That is about the kinetic energy of three Boeing 747 in flight - or neglectable on a planetary scale.