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As moons orbit planets, they get squashed by uneven gravitational forces acting on them. Does this make a moon emit gravitational waves?

user438383
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  • @user438383 about the proposed edit, they DO get cyclicly squashed and "unsquashed" so I've voted to reject it. – uhoh Apr 11 '23 at 23:40

2 Answers2

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Yes, but the effect is tiny

Tim Rias (in a comment below) calculates it to be $10^{-18}$ Watts. (see a paper about doing a similar calculation for neutron stars)

Bodies that have spherically asymmetric acceleration in a gravitational field will emit gravitational waves. Hence if a mosquito does a loop-the-loop it emits gravitational waves. In practice, the energy in such waves will be negligible.

The moon weighs more than a mosquito, and if it is squashed (in a non-spherically symmetric fashion) then the motion of mass in its gravitational field will necessarily result in some gravitational radiation.

But the energy released in such motions will be negligible, in comparison to the heating effect, and consequent blackbody electromagnetic radiation. It will also be negligible in comparison to the gravitational radiation already emitted by the Earth-moon system as a result of the orbit. The acceleration of the moon by the Earth is much greater that the acceleration of matter on the moon by tides.

We are able to detect only the most extreme gravitational waves, those which result from black hole collisions. I'd bet that we will never detect gravitational waves from any solar system object.

James K
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    If an elderly but distinguished scientist says that something is possible, he is almost certainly right; but if he says that it is impossible, he is very probably wrong. - Arthur C. Clarke. – planetmaker Apr 11 '23 at 11:38
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    Eg, "For the Earth-Sun system, this works out to be about 196 watts of power." https://physics.stackexchange.com/a/412990/123208 – PM 2Ring Apr 11 '23 at 12:55
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    @planetmaker Is James K an elderly but distinguished scientist? Does the quote apply to him. Anyway, from all that I have read, gravitational waves are very weak except for those produced by super energetic events. – M. A. Golding Apr 11 '23 at 16:58
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    @M.A.Golding. Were you reading the work of elderly but distinguished scientists? – Mad Physicist Apr 11 '23 at 19:41
  • I stumbled on the second sentence of your answer. Could you kindly explain what a "spherically symmetric acceleration" is? My best guess is a spherical body, whose individual parts accelerate as $$ \mathbf{r}'' = f(r,t) \mathbf{e}_r $$, is that correct? – LLlAMnYP Apr 12 '23 at 06:38
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    The phrase "The moon weighs more than a mosquito" is just begging for an xkcd-style "[citation needed]". – Spratty Apr 12 '23 at 14:34
  • @PM2Ring That number refers to the GWs generated by the changing orbital quadrupole moment. The amount of GWs generated due to the changing quadrupole moment of the Earth due to tidal deformations, is many orders of magnitude smaller. – TimRias Apr 17 '23 at 17:20
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    If I did not make a mistake putting numbers in https://arxiv.org/pdf/0709.1915.pdf, the power produced in gravitational waves due to tidal deformation of the Moon is something like $10^{-18}$ Watt. – TimRias Apr 17 '23 at 18:22
  • Thanks Tim, I've incorporated that value into my answer, with credit, of course. – James K Apr 17 '23 at 19:56
  • @Tim Indeed! I assumed that the reader would realise that the GW power emitted by tidal deformation would be many orders of magnitude smaller than my Sun-Earth example, but I suppose I should've said that explicitly... – PM 2Ring Apr 17 '23 at 22:34
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While JamesK's answer works hard and goes to great effort to emphasize that the effect is really small, so as to dismiss the effect as (humorous hat tip to Douglas Adams):

The effect is small, You just won't believe how vanishingly, sub-microscopically, mind-bogglingly small it is. I mean, you may think it's a short way down the road to the chemist's, but that's just peanuts to this.

But I think we should stop and think the other way for a moment.

Space is ringing with a quadrillion-zillion-billion voices! Everything makes gravitational waves, and the distortion of space is a tapestry of reality.

It reminds me of Herman Hesse's Siddhartha_ and the sound of the river.

“Siddhartha listened. He was now completely and utterly immersed in his listening, utterly empty, utterly receptive; he felt he had now succeeded in learning how to listen. He had heard all these things often now, these many voices in the river; today it sounded new. Already he could no longer distinguish the many voices, could not distinguish the gay from the weeping, the childish from the virile; they all belonged together, the yearning laments and the wise man’s laughter, the cry of anger and the moans of the dying; they were all one, all of them interlinked and interwoven, bound together in a thousand ways. And all of this together—all the voices, all the goals, all the longing, all the suffering, all the pleasure, everything good and everything bad—all of it together was the world. All of it together was the river of occurrences, the music of life. And when Siddhartha listened attentively to this river, to this thousand-voiced song, when he listened neither for the sorrow nor for the laughter, when he did not attach his soul to any one voice and enter into it with his ego but rather heard all of them, heard the whole, the oneness—then the great song of the thousand voices consisted only of a single word: Om, perfection.”

The more sensitive we make instruments, and the wider and more diverse ranges of frequencies those future instruments are optimized for, the more we will learn about the universe!

Just to get the ball rolling:

uhoh
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    +1 for the beautiful quote. Astronomy is science, philosophy and art. – Ritesh Singh Apr 12 '23 at 02:45
  • Your "space is ringing with" point suggests an analogy: There are sounds being created constantly all around the world. But except for extremely loud sounds, only nearby sounds can be heard even by extremely sensitive microphones. – Barmar Apr 12 '23 at 16:01
  • @Barmar theres a big difference between the way sound pressure in air and gravitational wave strain decrease with distance. First of all, sound pressure drops as $1/r^2$ whereas gravitational wave strain drops much more slowly as $1/r$. Second, sound has has an exponential attenuation in air, it is damped, there are losses in air - sound converts to heat. This doesn't happen with gravitational waves. Third, there are objects around - we don't always have completely unobstructed line-of-sight to sources of sound. – uhoh Apr 13 '23 at 00:48
  • Fourth, over long distances air is "lumpy" in temperature and density and has turbulence, so sound can be scattered away from line-of-sight trajectories. Elephants have a way of avoiding some of these loss mechanisms of sound pressure level in air, they produce low-frequency noises between 1 to 20 Hertz, known as infrasounds, that help them keep in touch over distances as large as 10 kilometers. You and I can't talk over 10 kilometers, but that only our limited experience. – uhoh Apr 13 '23 at 00:54
  • Basically, gravitational wave astronomy is still in its infancy. There are a huge amount of vibrations out there coming from modest and relatively small phenomena that are theoretically detectable if the right detection system is built. Think of how astronomy changed after optical telescopes were first invented and then grew to what they are today in number, variety and locations (including space).That same explosion in information is going to happen for gravitational waves science. – uhoh Apr 13 '23 at 00:59