<p>Bodies typically progress outward rather than inward. (See <a href="https://astronomy.stackexchange.com/questions/420/why-is-the-moon-receding-from-the-earth-due-to-tides-is-this-typical-for-other">Why is the Moon receding from the Earth due to tides? Is this typical for other moons?</a> .) The only orbiting bodies that might approach are ones that orbit faster than the main object spins, IOW, closer than synchronous orbit. Even then they could recede if locked into resonance w/ other bodies, <em>eg</em>, moons, further out. (See <a href="https://astronomy.stackexchange.com/questions/1080/does-anyone-know-why-three-of-jupiters-largest-moons-orbit-in-124-resonance">Does anyone know why three of Jupiter&#39;s largest moons orbit in 1:2:4 resonance?</a> .) Deimos and Phobos are approaching Mars though.</p>

<p>Supposing you do have an approaching body, eccentricity and inclination will be damped into a slowly degenerating circular orbit. As the body approaches, the acceleration of the body, through the main body's two tides' net pull, increases roughly as the <strong><em>6th</em></strong> power of distance. (See <a href="http://www.exo.net/~pauld/physics/tides/tidalevolution.htm" rel="nofollow noreferrer">Tidal Evolution of a Planet and its Moon</a>.) <strong><em>And</em></strong> tidal heating will soften the body, allowing even more deformation.</p>

<p>It is a runaway process at some point, and that point may be quite far into the Roche limit. How far would depend on body size, material tensile strength, structure of the body, thermal conductivity, changes with temperature, <em>etc</em>. It would take detailed modelling to describe the process. The catastrophe could start in the most vulnerable locality of the body and spread from there (Ka-Boom!), or involve the whole body concurrently (Squish!). It may not go "boom", but at the end you might be able to observe it in real time.</p>

<p>Another possibility is that the body will start disintegrating at the near end, where the forces are strongest. By conservation of momentum (or would it be energy?), every time a piece leaves, the rest of the body is pushed slightly the other way, sending the remainder slightly higher, delaying the process. This could take quite a while, but there is always a chance that things will destabilize at some point and go into catastrophe.</p>

CC BY-SA 3.0
2015-10-07T19:00:45.443Z
2015-10-07T19:27:58.747Z
2017-04-13T12:59:07.017Z
Eubie Drew
<p>A large moon (the size of a planet) would be modeled by the fluid model, meaning friction and tensile strength are too weak to modify the shape of the moon significantly, shape is determined by rotation, vortices, self-gravitation, and tidal forces.
Smaller moons, like Phobos would likely follow a <a href="https://www.boulder.swri.edu/~bottke/rubble/node2.html" rel="nofollow">rubble pile model</a>.
On circular orbits tidal heating doesn't play a major role.</p>

<p><a href="http://arxiv.org/ftp/arxiv/papers/1409/1409.3858.pdf" rel="nofollow">The fluid model has been studied extensively</a>. The occuring shapes are known as <a href="http://keith.aa.washington.edu/papers/stability.pdf" rel="nofollow">equilibrium figures</a>.
For a full understanding, the parent body should be considered together with the moons, as one system. (Fluid) moons getting too close to the Roche limit gradually deform (tidal heating depends on inner friction), and start to shed mass at some point. There exist solutions with vortices, and vortex-free solutions, depending on the properties of the fluid. The lost mass may either <a href="http://yly-mac.gps.caltech.edu/A_DPS/dps%202011%20/a_dps%202011%20program%20+%20abstracts/pdf/EPSC-DPS2011-1559.pdf" rel="nofollow">form an n-body system</a> outside the Roche limit, or form a ring system, mostly inside the Roche limit.
Closer to the planet, it may either impact, and fuse with the planet to a the overall spheroid of the planet, or - if the planet is already rotating fast, and the mass of the moon was sufficiently high - increase the rotation of the planet, such that it may undergo e.g. the <a href="http://farside.ph.utexas.edu/teaching/336L/Fluidhtml/node39.html" rel="nofollow">Maclaurin</a> - <a href="http://farside.ph.utexas.edu/teaching/336L/Fluidhtml/node40.html" rel="nofollow">Jacobi</a> series, up to the point, that it cannot accrete more mass. <a href="https://hal.archives-ouvertes.fr/jpa-00208894/document" rel="nofollow">There are several more possibilities in detail</a>.</p>

<p>Rubble piles with tensile strength are more likely to undergo sudden shape changes or disruptions than rubble piles without tensile strength. Behaviour of rubble piles without tensile strength depends on friction. The less friction, the closer to the fluid model.
The more tensile strength of the rubble pile, the more it behaves like the ridgid model. Ridgid objects may survive well below the Roche limit for fluid objects, but disrupt suddenly when tidal forces get too strong.</p>

CC BY-SA 3.0
2015-12-06T04:59:42.147Z
2015-12-06T04:59:42.147Z
Gerald
<p>Some cartoon simulations (<a href="https://youtu.be/r_m7VgVSBoM?t=1863">an example</a>) of an object (assume here a large moon with Earth-like density) which crosses the Roche limit of a much more massive giant planet, illustrate a circle suddenly disintegrating and forming a ring. But such a process occurs gradually over geological time scales. I doubt that there would be a single bad day when the whole moon disintegrates (as in <em>-Oh, there Mt. Everest broke off and flew away!</em>)</p>

<p>Wouldn't the tidal tugging cause volcanism and gradually melt the moon as its (somewhat eccentric) orbit spirals inwards across the limit during millions of years?</p>

<p>How would the melting moon deform? Would it really assume an oval shape, elongated towards the primary planet? Since the near side wants to orbit faster than the far side, wouldn't that cause the moon to spin at an accelerated rate, even if it initially was tidally locked? Would the melting, deforming and spinning save it from disintegrating further to within the Roche limit?</p>

<p>Some examples of Roche limit crossings I know of:</p>

<ul>
<li>Comet Shoemaker-Levy 9 may have broken up suddenly because it had
such a high velocity relative to Jupiter.</li>
<li>Phobos will cross its Roche limit to Mars in ~50 million years. It
will hardly be a sudden process. I suppose its very low density and
mass won't allow any volcanism and melting, though.</li>
<li><a href="http://arxiv.org/abs/1307.4080">KOI1843.03</a>, an exoplanet candidate with a density of ~7 g/cm³,
is already inside the Roche limits for its less dense compounds which
it has shed (as I interpret it).</li>
</ul>

CC BY-SA 3.0
2015-10-07T13:08:18.723Z
Related question, without a specific answer, but some good comments.   http://space.stackexchange.com/questions/10113/how-fast-does-roche-limit-disintegration-proceed
userLTK
CC BY-SA 3.0
2015-10-07T18:01:21.953Z
Also, I don't think Shoemaker-Levi 9's relative velocity had anything to do with it's breakup.   Relative velocity matters as it enters the atmosphere, but not as an object passes inside the Roche limit, though, I suppose, if it's traveling super-fast the breakup could be more minimal, but nothing in the solar system travels THAT fast.  Shoemaker had an elongated orbit where it passed inside the Roche Limit, broke up, then traveled a 2 year loop around Jupiter in pieces before crashing into it.   http://ase.tufts.edu/cosmos/pictures/May10%5Cfinal%5Cimages/Fig13_2.jpg
userLTK
CC BY-SA 3.0
2015-12-09T01:35:17.197Z
Recent article suggests that once break-up starts, it could take Phobos only "days to weeks".  http://www.nature.com/news/martian-moon-set-to-form-ring-around-red-planet-1.18852
BowlOfRed
<exoplanet><tidal-forces><roche-limit><phobos>
How does gradual crossing over of the Roche limit transform a planet or moon?
LocalFluff
# How does gradual crossing over of the Roche limit transform a planet or moon?

(Asked by: username_0 on 2015-10-07)

Some cartoon simulations ([an example](https://youtu.be/r_m7VgVSBoM?t=1863)) of an object (assume here a large moon with Earth-like density) which crosses the Roche limit of a much more massive giant planet, illustrate a circle suddenly disintegrating and forming a ring. But such a process occurs gradually over geological time scales. I doubt that there would be a single bad day when the whole moon disintegrates (as in *-Oh, there Mt. Everest broke off and flew away!*)

Wouldn't the tidal tugging cause volcanism and gradually melt the moon as its (somewhat eccentric) orbit spirals inwards across the limit during millions of years?

How would the melting moon deform? Would it really assume an oval shape, elongated towards the primary planet? Since the near side wants to orbit faster than the far side, wouldn't that cause the moon to spin at an accelerated rate, even if it initially was tidally locked? Would the melting, deforming and spinning save it from disintegrating further to within the Roche limit?

Some examples of Roche limit crossings I know of:

* Comet Shoemaker-Levy 9 may have broken up suddenly because it had
  such a high velocity relative to Jupiter.
* Phobos will cross its Roche limit to Mars in ~50 million years. It
  will hardly be a sudden process. I suppose its very low density and
  mass won't allow any volcanism and melting, though.
* [KOI1843.03](http://arxiv.org/abs/1307.4080), an exoplanet candidate with a density of ~7 g/cm³,
  is already inside the Roche limits for its less dense compounds which
  it has shed (as I interpret it).

**Tags:** exoplanet, tidal-forces, roche-limit, phobos

> **Comments:**
> **username_1**: Related question, without a specific answer, but some good comments.   http://space.stackexchange.com/questions/10113/how-fast-does-roche-limit-disintegration-proceed  
> **username_1**: Also, I don't think Shoemaker-Levi 9's relative velocity had anything to do with it's breakup.   Relative velocity matters as it enters the atmosphere, but not as an object passes inside the Roche limit, though, I suppose, if it's traveling super-fast the breakup could be more minimal, but nothing in the solar system travels THAT fast.  Shoemaker had an elongated orbit where it passed inside the Roche Limit, broke up, then traveled a 2 year loop around Jupiter in pieces before crashing into it.   http://ase.tufts.edu/cosmos/pictures/May10%5Cfinal%5Cimages/Fig13_2.jpg  
> **username_2**: Recent article suggests that once break-up starts, it could take Phobos only "days to weeks".  http://www.nature.com/news/martian-moon-set-to-form-ring-around-red-planet-1.18852  

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## 2 answers

### Answer by username_4 on 2015-12-06. Score: 4 | Accepted answer

A large moon (the size of a planet) would be modeled by the fluid model, meaning friction and tensile strength are too weak to modify the shape of the moon significantly, shape is determined by rotation, vortices, self-gravitation, and tidal forces.
Smaller moons, like Phobos would likely follow a [rubble pile model](https://www.boulder.swri.edu/~bottke/rubble/node2.html).
On circular orbits tidal heating doesn't play a major role.

[The fluid model has been studied extensively](http://arxiv.org/ftp/arxiv/papers/1409/1409.3858.pdf). The occuring shapes are known as [equilibrium figures](http://keith.aa.washington.edu/papers/stability.pdf).
For a full understanding, the parent body should be considered together with the moons, as one system. (Fluid) moons getting too close to the Roche limit gradually deform (tidal heating depends on inner friction), and start to shed mass at some point. There exist solutions with vortices, and vortex-free solutions, depending on the properties of the fluid. The lost mass may either [form an n-body system](http://yly-mac.gps.caltech.edu/A_DPS/dps%202011%20/a_dps%202011%20program%20+%20abstracts/pdf/EPSC-DPS2011-1559.pdf) outside the Roche limit, or form a ring system, mostly inside the Roche limit.
Closer to the planet, it may either impact, and fuse with the planet to a the overall spheroid of the planet, or - if the planet is already rotating fast, and the mass of the moon was sufficiently high - increase the rotation of the planet, such that it may undergo e.g. the [Maclaurin](http://farside.ph.utexas.edu/teaching/336L/Fluidhtml/node39.html) - [Jacobi](http://farside.ph.utexas.edu/teaching/336L/Fluidhtml/node40.html) series, up to the point, that it cannot accrete more mass. [There are several more possibilities in detail](https://hal.archives-ouvertes.fr/jpa-00208894/document).

Rubble piles with tensile strength are more likely to undergo sudden shape changes or disruptions than rubble piles without tensile strength. Behaviour of rubble piles without tensile strength depends on friction. The less friction, the closer to the fluid model.
The more tensile strength of the rubble pile, the more it behaves like the ridgid model. Ridgid objects may survive well below the Roche limit for fluid objects, but disrupt suddenly when tidal forces get too strong.


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### Answer by username_3 on 2015-10-07. Score: 2

Bodies typically progress outward rather than inward. (See [Why is the Moon receding from the Earth due to tides? Is this typical for other moons?](https://astronomy.stackexchange.com/questions/420/why-is-the-moon-receding-from-the-earth-due-to-tides-is-this-typical-for-other) .) The only orbiting bodies that might approach are ones that orbit faster than the main object spins, IOW, closer than synchronous orbit. Even then they could recede if locked into resonance w/ other bodies, *eg*, moons, further out. (See [Does anyone know why three of Jupiter's largest moons orbit in 1:2:4 resonance?](https://astronomy.stackexchange.com/questions/1080/does-anyone-know-why-three-of-jupiters-largest-moons-orbit-in-124-resonance) .) Deimos and Phobos are approaching Mars though.

Supposing you do have an approaching body, eccentricity and inclination will be damped into a slowly degenerating circular orbit. As the body approaches, the acceleration of the body, through the main body's two tides' net pull, increases roughly as the ***6th*** power of distance. (See [Tidal Evolution of a Planet and its Moon](http://www.exo.net/~pauld/physics/tides/tidalevolution.htm).) ***And*** tidal heating will soften the body, allowing even more deformation.

It is a runaway process at some point, and that point may be quite far into the Roche limit. How far would depend on body size, material tensile strength, structure of the body, thermal conductivity, changes with temperature, *etc*. It would take detailed modelling to describe the process. The catastrophe could start in the most vulnerable locality of the body and spread from there (Ka-Boom!), or involve the whole body concurrently (Squish!). It may not go "boom", but at the end you might be able to observe it in real time.

Another possibility is that the body will start disintegrating at the near end, where the forces are strongest. By conservation of momentum (or would it be energy?), every time a piece leaves, the rest of the body is pushed slightly the other way, sending the remainder slightly higher, delaying the process. This could take quite a while, but there is always a chance that things will destabilize at some point and go into catastrophe.


---

