<p>All orbits as you would normally think of them emit gravitational waves. You mention an axially symmetric orbit. A hypothetical rotating rigid hoop would not, since the distribution of mass is not changing over time.</p>
<p>The difference between the gravitational waves produced by neutron stars or black holes vs planets or stars orbiting the galactic center is just a huge difference in degree. From what I have read about the long term future of the universe, on trillion-year timescales, Newtonian interactions between planets lead to them getting ejected before orbits can decay from gravitational waves. (This is a statistical analysis; orbits cannot be forecast nearly that far in detail.)</p>
<p>On the galactic scale, it remains true that energy loss due to gravitational waves is such a weak phenomenon that other effects will determine the ultimate fate of the (by then mostly extinguished) stars. See <a href="https://astronomy.stackexchange.com/a/53780/47607">this link</a> (from the comments - thanks to Sten).</p>
<p>In a sense it is <em>almost</em> true that ordinary orbiting planets, or stars orbiting galactic centers, don't emit gravity waves because the waves they emit are so weak. The energy in the waves has to do with the masses of the bodies and the period of revolution, and longer periods mean less energy. The stately progression of stars around the galactic center are not going to produce very energetic gravity waves.</p>

CC BY-SA 4.0
2023-07-16T21:19:11.057Z
So then, would even galaxies collapse in the very far future due to gravitational waves being emitted by all its components in rotation? (assuming their planets and stars do not get ejected)? @MarkFoskey
vengaq
CC BY-SA 4.0
2023-07-16T22:18:59.827Z
@vengaq Two-body relaxation effects are way more important than gravitational wave emission in galactic contexts; stars will (probably) sink due to dynamical friction with the dark matter long before gravitational waves are relevant. See https://astronomy.stackexchange.com/a/53780/47607
Sten
CC BY-SA 4.0
2023-07-17T11:35:06.037Z
@Sten and if a galaxy did not have dark matter?. Also in your answer you mention that a symmetric "hoop" around a planet would not emit gravitational waves. Would rings around planets (as it happens in Saturn) be examples of this?
vengaq
CC BY-SA 4.0
2023-07-17T13:20:34.463Z
[Wikipedia](https://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity#Gravitational_radiation) has an equation for gravitational radiation power for a simple orbiting system. FWIW, the Earth+Moon orbiting the Sun emits ~201.5 watts, the Jupiter system orbiting the Sun emits ~5284.6 watts, and the Moon orbiting the Earth emits ~7.4 microwatts.
PM 2Ring
CC BY-SA 4.0
2023-07-17T13:31:44.023Z
https://sagecell.sagemath.org/?z=eJyNUsuOglAM3ZPwD90JPvA-yn2YuDQkk7ia5UQMcdBxEnwgZhYT_316L6AuXAyLkp5z2h5asuUF5vAbBgCD9-thMAMuheYCkTHkidAWuR17elHUzRcJpDWKsQRlmjLdUsvj0ZWiZSIxjHFuWvzteto3Ze26CkVdtcKEM_cQfwuDMMhoukqURrmYcB4GG8qFtdoKTI0TXKpiXbrJRHC0qTVMyIUMg3Jzx1nCuNLMqL7gu51LlNYmQW0X1hc8cCpBY3t9Rf4JlAaltV3zDiNhil74WW5htz4df8o6qvgYKjGGYgzlJp65j4WT6yBgCFmOFCueu6QS_kUVMKIk9tIzSVNCN7mLhY8Rhwk1y0WcR3raCeuyudYHx41Ay6nAoVNQIvXUKpdgTLUnmMLZeaQpc8iWlw9_zBVRvLREZkQJoiLPtZdcURuf-uut4mdxQdr75t06KO8XHgZ-B4Q8beOxDKLr_aGJtu2YGfx60SxRuxv8FE1zGcTequit9n_J6pWD7mQPD3fgny667i99_AFP88Lo&lang=sage
PM 2Ring
CC BY-SA 4.0
2023-07-17T13:49:15.507Z
@vengaq The long-term evolution of systems of many stars without dark matter is pretty complicated but is still dominated by two-body energy exchange. People have studied this in the context of globular star clusters, but I'm not enough of an expert on those to say too much about them. I believe they tend to eject stars over time; the energy lost in this evaporation comes from sinking of the heavier stars and the formation and "hardening" of binary systems.
Sten
CC BY-SA 4.0
2023-07-17T22:53:35.750Z
I wonder if one could contrive a highly suppressed scenario. First imagine an equal pair approaching from near opposite directions on hyperbolic trajectories that swing by each other with a close approach in a clockwise direction. That will radiate out of plane I suppose. Then imagine a second pair that do almost the same thing about the same point, but in a mirror symmetric way such that they rotate counter-clockwise and almost graze the first pair. They will probably get deflected out-of-plane as well, but I wonder if the dipole radiation can be suppressed and the quadrupole be much weaker?
uhoh
CC BY-SA 4.0
2023-07-16T14:46:25.820Z
2023-07-17T00:07:33.590Z
2023-07-17T00:07:33.590Z
Mark Foskey
<p>In principle, all orbits in the universe should progressively decay due to the emission of gravitational waves. However, does this always happen? Are there any kind of orbits that do not decay as they do not emit gravitational waves? Perhaps if the orbit is perfectly axially symmetric with an even distribution of mass?...</p>

CC BY-SA 4.0
2023-07-16T13:46:27.363Z
What do you mean by a perfectly axially symmetric orbit?
ProfRob
CC BY-SA 4.0
2023-07-16T17:03:51.973Z
Electrons orbiting a nucleus do not emit gravitational waves, but that is because they don't actually orbit.  They are in a quantum superposition of distributions (wave functions).  Also, some orbits may not decay even as they emit gravitational waves because there could be tidal friction that is increasing orbital energy.
eshaya
CC BY-SA 4.0
2023-07-17T13:12:53.107Z
Might be helpful https://physics.stackexchange.com/questions/33132/do-rotating-bodies-emit-gravitational-waves
Daddy Kropotkin
CC BY-SA 4.0
2023-07-17T22:54:05.077Z
Oh this is *such a beautiful and answerable question!* It will no doubt bring forth very interesting answers, so +1
uhoh
<orbit><astrophysics><orbital-mechanics><gravitational-waves><mass>
Do all orbits emit gravitational waves?
vengaq
# Do all orbits emit gravitational waves?

(Asked by: username_0 on 2023-07-16)

In principle, all orbits in the universe should progressively decay due to the emission of gravitational waves. However, does this always happen? Are there any kind of orbits that do not decay as they do not emit gravitational waves? Perhaps if the orbit is perfectly axially symmetric with an even distribution of mass?...

**Tags:** orbit, astrophysics, orbital-mechanics, gravitational-waves, mass

> **Comments:**
> **username_1**: What do you mean by a perfectly axially symmetric orbit?  
> **username_2**: Electrons orbiting a nucleus do not emit gravitational waves, but that is because they don't actually orbit.  They are in a quantum superposition of distributions (wave functions).  Also, some orbits may not decay even as they emit gravitational waves because there could be tidal friction that is increasing orbital energy.  
> **username_3**: Might be helpful https://physics.stackexchange.com/questions/33132/do-rotating-bodies-emit-gravitational-waves  
> **username_4**: Oh this is *such a beautiful and answerable question!* It will no doubt bring forth very interesting answers, so +1  

---

## 1 answers

### Answer by username_5 on 2023-07-16. Score: 3

All orbits as you would normally think of them emit gravitational waves. You mention an axially symmetric orbit. A hypothetical rotating rigid hoop would not, since the distribution of mass is not changing over time.

The difference between the gravitational waves produced by neutron stars or black holes vs planets or stars orbiting the galactic center is just a huge difference in degree. From what I have read about the long term future of the universe, on trillion-year timescales, Newtonian interactions between planets lead to them getting ejected before orbits can decay from gravitational waves. (This is a statistical analysis; orbits cannot be forecast nearly that far in detail.)

On the galactic scale, it remains true that energy loss due to gravitational waves is such a weak phenomenon that other effects will determine the ultimate fate of the (by then mostly extinguished) stars. See [this link](https://astronomy.stackexchange.com/a/53780/47607) (from the comments - thanks to username_6).

In a sense it is *almost* true that ordinary orbiting planets, or stars orbiting galactic centers, don't emit gravity waves because the waves they emit are so weak. The energy in the waves has to do with the masses of the bodies and the period of revolution, and longer periods mean less energy. The stately progression of stars around the galactic center are not going to produce very energetic gravity waves.

> **Comments:**
> **username_0**: So then, would even galaxies collapse in the very far future due to gravitational waves being emitted by all its components in rotation? (assuming their planets and stars do not get ejected)? @MarkFoskey  
> **username_6**: @username_0 Two-body relaxation effects are way more important than gravitational wave emission in galactic contexts; stars will (probably) sink due to dynamical friction with the dark matter long before gravitational waves are relevant. See https://astronomy.stackexchange.com/a/53780/47607  
> **username_0**: @username_6 and if a galaxy did not have dark matter?. Also in your answer you mention that a symmetric "hoop" around a planet would not emit gravitational waves. Would rings around planets (as it happens in Saturn) be examples of this?  
> **username_7**: [Wikipedia](https://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity#Gravitational_radiation) has an equation for gravitational radiation power for a simple orbiting system. FWIW, the Earth+Moon orbiting the Sun emits ~201.5 watts, the Jupiter system orbiting the Sun emits ~5284.6 watts, and the Moon orbiting the Earth emits ~7.4 microwatts.  
> **username_7**: https://sagecell.sagemath.org/?z=eJyNUsuOglAM3ZPwD90JPvA-yn2YuDQkk7ia5UQMcdBxEnwgZhYT_316L6AuXAyLkp5z2h5asuUF5vAbBgCD9-thMAMuheYCkTHkidAWuR17elHUzRcJpDWKsQRlmjLdUsvj0ZWiZSIxjHFuWvzteto3Ze26CkVdtcKEM_cQfwuDMMhoukqURrmYcB4GG8qFtdoKTI0TXKpiXbrJRHC0qTVMyIUMg3Jzx1nCuNLMqL7gu51LlNYmQW0X1hc8cCpBY3t9Rf4JlAaltV3zDiNhil74WW5htz4df8o6qvgYKjGGYgzlJp65j4WT6yBgCFmOFCueu6QS_kUVMKIk9tIzSVNCN7mLhY8Rhwk1y0WcR3raCeuyudYHx41Ay6nAoVNQIvXUKpdgTLUnmMLZeaQpc8iWlw9_zBVRvLREZkQJoiLPtZdcURuf-uut4mdxQdr75t06KO8XHgZ-B4Q8beOxDKLr_aGJtu2YGfx60SxRuxv8FE1zGcTequit9n_J6pWD7mQPD3fgny667i99_AFP88Lo&lang=sage  
> **username_6**: @username_0 The long-term evolution of systems of many stars without dark matter is pretty complicated but is still dominated by two-body energy exchange. People have studied this in the context of globular star clusters, but I'm not enough of an expert on those to say too much about them. I believe they tend to eject stars over time; the energy lost in this evaporation comes from sinking of the heavier stars and the formation and "hardening" of binary systems.  
> **username_4**: I wonder if one could contrive a highly suppressed scenario. First imagine an equal pair approaching from near opposite directions on hyperbolic trajectories that swing by each other with a close approach in a clockwise direction. That will radiate out of plane I suppose. Then imagine a second pair that do almost the same thing about the same point, but in a mirror symmetric way such that they rotate counter-clockwise and almost graze the first pair. They will probably get deflected out-of-plane as well, but I wonder if the dipole radiation can be suppressed and the quadrupole be much weaker?  

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