<p>In his video, Anton Petrov is referring to <a href="https://arxiv.org/abs/2303.14546" rel="nofollow noreferrer">this paper</a>. The main idea of the paper is not new. In some situations, rotation governed by the triaxial and tidal torques is unstable -- and periods of sporadic rotation and even wobble are possible.</p>
<p>[&quot;The triaxial torque&quot; is a jargon term for &quot;the torque caused by the permanent dynamical triaxiality&quot;.]</p>
<p>One of the mechanisms causing instability and chaos will be easy to understand if we recall that a triaxial body librates in longitude around any spin-orbit state, not only about the synchronous one. E.g. Mercury is librating about the 3:2 spin state. Now, if the dynamical triaxiality is sufficiently large, the magnitudes of longitudinal libration about different spin-orbit states may overlap -- and that will result in a stochastic walk over spin states. This is just one easy-to-visualise mechanism leading to chaotic rotation. Rotation may also become unstable w.r.t. latitudinal libration -- which will cause wobble and perhaps even flips.</p>
<p>Whether a rotator falls within a chaotic zone -- is a delicate problem requiring accurate modeling. In <em><a href="https://arxiv.org/abs/2303.14546" rel="nofollow noreferrer">Ibid.</a></em>, a mathematical inaccuracy is easily discernable. Their equation (4) is derived within the CTL (constant time lag) tidal model, i.e., under the assumption that the quadrupole Love number divided by the tidal quality factor, <span class="math-container">$k_2/Q$</span>, scales linearly in the forcing frequency. Right after that, the authors switch to the CPL (constant phase lag) tidal model, one assuming <span class="math-container">$k_2/Q =$</span> const.   Without an accurate check based on a right expression for the tidal torque, it is impossible to say if this oversight is fatal.</p>
<p>Another problem with this paper is that it does not say a word on the employed values of the dynamical triaxiality. Also, to calculate the tidal torques acting on the TRAPPIST-1 planets, the authors are using <a href="https://www.google.com/search?q=trappist%201%20planets" rel="nofollow noreferrer">a model</a> developed for TRAPPIST-1e. The model endows the planet with both an atmosphere and an ocean. I am not sure if this model is applicable to planet e (or to b or to d), because it ignores these planets' violent past. <a href="https://iopscience.iop.org/article/10.3847/1538-4357/aab845" rel="nofollow noreferrer">Calculation</a> shows that during their initial tidal spin-down these planets were captured into a 3:2 or higher spin-orbit resonance, like Mercury. Being very close to the star, they then underwent a thermal runaway caused by tidal overheating. This made them hot and plastic, so their rheology changed, and for this reason they slipped out of the higher resonance and continued their slow-down towards synchronism. I am not sure if after this episode they can sustain a water ocean. Most volatiles are probably gone.</p>
<p>Generally, a <em>bona fide</em> model of stochastic rotation must include calculation of the tidal dissipation rate. When a body gets captured in a nonsynchronous spin state, the tidal bulge is running around the circumference, and the heating rate increases by orders of magnitude. This changes the rheology, making the body more viscous. As a result of this, the quality factor is reduced greatly, and the triaxiality is no longer sustained -- which sets a limit on the duration of such periods.</p>
<p>To conclude, while the mathematical model needs some attention (and, probably needs to be redone completely), and while its applicability to TRAPPIST-1 inner planets is discussable, the central idea is correct. Sporadic rotation is possible, at least in principle.</p>

CC BY-SA 4.0
2023-04-21T01:59:49.820Z
2023-04-22T12:27:39.960Z
2023-04-22T12:27:39.960Z
Michael_1812
<p>This <a href="https://www.youtube.com/watch?v=SJWKExj7-IA" rel="noreferrer">Youtube video</a> by Anton Petrov shows research<sup>1</sup> claiming that tidally-locked planets orbiting the same star in tight orbits may interfere with one another and one planet may cause the other to &quot;flip&quot; its side facing the parent star: A tidally locked planet may face the same side to its star for a few hundred millenia before flipping and facing its other side to the star. This is said to happen to planets around M-type stars, which have their planets in close proximity to the star (hence the tidal locking) and the planets are in tight orbits hence gravitationally acting on one another.</p>
<p>No such planets exist in our solar system. However, we can search for equivalent examples involving planets and their moons instead of stars and their planets. In our solar system, Jupiter and Saturn for instance have several moons that are tidally-locked to them. Europa, a moon of Jupiter, experiences tidal flexing from Jupiter and the other moons. It is known that libration does occur, but does the observation confirm that the moons may have flipped their side facing the planet? Do we have a geological evidence such as increased geological activity that cannot be explained otherwise?</p>
<p>EDIT: The term &quot;Catastrophic&quot; in this video refers to the effect of flipping on life evolving on such planets. My question does not tackle that issue.</p>
<hr />
<p><sup>1</sup> arXiv <a href="https://arxiv.org/abs/2303.14546" rel="noreferrer">Day 'N' Nite: Habitability of Tidally Locked Planets with Sporadic Rotation</a></p>

CC BY-SA 4.0
2023-04-20T18:13:41.827Z
The moons' spins are well-aligned with their orbital spins, so no?
AtmosphericPrisonEscape
CC BY-SA 4.0
2023-04-20T18:21:58.403Z
@AtmosphericPrisonEscape My understanding is that the flipping is in on the same axis as the other moon's orbits. That means the moon's far side (relative to the planet) faces the planet, as if "turning its back to it" and not flipping north-and-south as if "upside-down".
Christmas Snow
CC BY-SA 4.0
2023-04-20T19:49:17.303Z
That would require angular momentum to come from somwehere and a insufficient tidal lock.
AtmosphericPrisonEscape
CC BY-SA 4.0
2023-04-20T23:58:45.270Z
Different but slightly related: [Is Venus in some way tidally locked to... Earth?](https://astronomy.stackexchange.com/q/36488/7982) I would guess that this kind of catastrophic moon-flipping would be pretty unlikely unless at least one of the moons were both pretty massive (referenced to the primary planet's mass) and pretty non-spherical (in other words, have some large low-order gravitational moments beyond monopole)
uhoh
<orbit><orbital-mechanics><tidal-locking>
Eyeball planets experiencing "catastrophic" flips
Christmas Snow
# Eyeball planets experiencing "catastrophic" flips

(Asked by: username_0 on 2023-04-20)

This [Youtube video](https://www.youtube.com/watch?v=SJWKExj7-IA) by Anton Petrov shows research1 claiming that tidally-locked planets orbiting the same star in tight orbits may interfere with one another and one planet may cause the other to "flip" its side facing the parent star: A tidally locked planet may face the same side to its star for a few hundred millenia before flipping and facing its other side to the star. This is said to happen to planets around M-type stars, which have their planets in close proximity to the star (hence the tidal locking) and the planets are in tight orbits hence gravitationally acting on one another.

No such planets exist in our solar system. However, we can search for equivalent examples involving planets and their moons instead of stars and their planets. In our solar system, Jupiter and Saturn for instance have several moons that are tidally-locked to them. Europa, a moon of Jupiter, experiences tidal flexing from Jupiter and the other moons. It is known that libration does occur, but does the observation confirm that the moons may have flipped their side facing the planet? Do we have a geological evidence such as increased geological activity that cannot be explained otherwise?

EDIT: The term "Catastrophic" in this video refers to the effect of flipping on life evolving on such planets. My question does not tackle that issue.

---

1 arXiv [Day 'N' Nite: Habitability of Tidally Locked Planets with Sporadic Rotation](https://arxiv.org/abs/2303.14546)

**Tags:** orbit, orbital-mechanics, tidal-locking

> **Comments:**
> **username_1**: The moons' spins are well-aligned with their orbital spins, so no?  
> **username_0**: @username_1 My understanding is that the flipping is in on the same axis as the other moon's orbits. That means the moon's far side (relative to the planet) faces the planet, as if "turning its back to it" and not flipping north-and-south as if "upside-down".  
> **username_1**: That would require angular momentum to come from somwehere and a insufficient tidal lock.  
> **username_2**: Different but slightly related: [Is Venus in some way tidally locked to... Earth?](https://astronomy.stackexchange.com/q/36488/7982) I would guess that this kind of catastrophic moon-flipping would be pretty unlikely unless at least one of the moons were both pretty massive (referenced to the primary planet's mass) and pretty non-spherical (in other words, have some large low-order gravitational moments beyond monopole)  

---

## 1 answers

### Answer by username_3 on 2023-04-21. Score: 3

In his video, Anton Petrov is referring to [this paper](https://arxiv.org/abs/2303.14546). The main idea of the paper is not new. In some situations, rotation governed by the triaxial and tidal torques is unstable -- and periods of sporadic rotation and even wobble are possible.

["The triaxial torque" is a jargon term for "the torque caused by the permanent dynamical triaxiality".]

One of the mechanisms causing instability and chaos will be easy to understand if we recall that a triaxial body librates in longitude around any spin-orbit state, not only about the synchronous one. E.g. Mercury is librating about the 3:2 spin state. Now, if the dynamical triaxiality is sufficiently large, the magnitudes of longitudinal libration about different spin-orbit states may overlap -- and that will result in a stochastic walk over spin states. This is just one easy-to-visualise mechanism leading to chaotic rotation. Rotation may also become unstable w.r.t. latitudinal libration -- which will cause wobble and perhaps even flips.

Whether a rotator falls within a chaotic zone -- is a delicate problem requiring accurate modeling. In *[Ibid.](https://arxiv.org/abs/2303.14546)*, a mathematical inaccuracy is easily discernable. Their equation (4) is derived within the CTL (constant time lag) tidal model, i.e., under the assumption that the quadrupole Love number divided by the tidal quality factor, $k\_2/Q$, scales linearly in the forcing frequency. Right after that, the authors switch to the CPL (constant phase lag) tidal model, one assuming $k\_2/Q =$ const. Without an accurate check based on a right expression for the tidal torque, it is impossible to say if this oversight is fatal.

Another problem with this paper is that it does not say a word on the employed values of the dynamical triaxiality. Also, to calculate the tidal torques acting on the TRAPPIST-1 planets, the authors are using [a model](https://www.google.com/search?q=trappist%201%20planets) developed for TRAPPIST-1e. The model endows the planet with both an atmosphere and an ocean. I am not sure if this model is applicable to planet e (or to b or to d), because it ignores these planets' violent past. [Calculation](https://iopscience.iop.org/article/10.3847/1538-4357/aab845) shows that during their initial tidal spin-down these planets were captured into a 3:2 or higher spin-orbit resonance, like Mercury. Being very close to the star, they then underwent a thermal runaway caused by tidal overheating. This made them hot and plastic, so their rheology changed, and for this reason they slipped out of the higher resonance and continued their slow-down towards synchronism. I am not sure if after this episode they can sustain a water ocean. Most volatiles are probably gone.

Generally, a *bona fide* model of stochastic rotation must include calculation of the tidal dissipation rate. When a body gets captured in a nonsynchronous spin state, the tidal bulge is running around the circumference, and the heating rate increases by orders of magnitude. This changes the rheology, making the body more viscous. As a result of this, the quality factor is reduced greatly, and the triaxiality is no longer sustained -- which sets a limit on the duration of such periods.

To conclude, while the mathematical model needs some attention (and, probably needs to be redone completely), and while its applicability to TRAPPIST-1 inner planets is discussable, the central idea is correct. Sporadic rotation is possible, at least in principle.


---

