<p>It was <a href="https://mathshistory.st-andrews.ac.uk/Extras/Maxwell_Saturn/" rel="noreferrer">Maxwell (1859)</a> who showed that Saturn's rings must be made of a host of independent particles and cannot be described in terms of a fluid disc.</p>
<blockquote>
<p>The final result, therefore, of the mechanical theory is, that the only system of rings which can exist is one composed of an indefinite number of unconnected particles, revolving round the planet with different velocities according to their respective distances.</p>
</blockquote>
<p>Since the essence of an accretion disc, its dynamics and stability, are entirely based on a fluid description (gas pressure, viscosity etc.) Saturn's rings are  not similar to an accretion disc.</p>
<p>Theoretical work by <a href="https://ui.adsabs.harvard.edu/abs/2005ApJ...626L..61O/abstract" rel="noreferrer">Ohtsuki (2005)</a> suggested that large particles rotate slowly (as slow as 10% of their orbital rate) with their spin vector aligned with their orbital angular momentum vectors. Smaller particles should rotate up to 100 times faster and with essentially random spin vectors.</p>
<p>The observational picture from Cassini is summarised by <a href="https://ui.adsabs.harvard.edu/abs/2006P%26SS...54.1167S/abstract" rel="noreferrer">Spilker et al. (2006)</a>. The observations suggest that there are large particles with a spin rate slower than their orbital period and an increasing number of smaller , more rapidly rotating particles. Unfortunately, the paper is paywalled, so I have no more details than are in the abstract.</p>

CC BY-SA 4.0
2024-12-30T16:00:52.380Z
reading this [extract](https://mathshistory.st-andrews.ac.uk/Extras/Maxwell_Saturn/) i cannot understand the difference between mostly smaller than sand particles arranged in a ring, and a low density gas or fluid having very large mean free path. might be another question though. btw thanks, and for the links +1
user721108
CC BY-SA 4.0
2024-12-30T16:05:07.277Z
Thank you for the link - I was looking for one. I have included the relevant sentences now I think. @user721108  A disc as you describe would not be an *accretion* disc since there is no obvious way to transport angular momentum outwards to allow mass transfer inwards.
ProfRob
CC BY-SA 4.0
2024-12-31T08:56:42.147Z
@user721108 the interaction between particles in a fluid is quite different from that in a loose cloud of solid particles. Do NOT assume that just because a bucket of fine sand in some scenarios behaves like a liquid, all systems of solid particles to. In this case fluid dynamics don't apply, each particle in the ring system is subject to Newtonian physics individually (generating an n-body system, but probably most of the particles can be simplified to only being influenced by the planet when it comes to gravity because of the force difference).
jwenting
CC BY-SA 4.0
2024-12-31T13:26:05.517Z
I'm wondering if the OP may have meant a [protplanetary disk](https://en.wikipedia.org/wiki/Protoplanetary_disk). Wikipedia is inconsistent in the nomenclature: The PPD article claims they should not be confused while the AD article lists PPDs as a type of AD..
Peter - Reinstate Monica
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2024-12-31T15:01:16.740Z
@Peter-ReinstateMonica yes I was thinking about protoplanetary disk. thanks for pointing out ( i thought stellar accretion disk was the stuff gathering around a single star, forming planetoids, my bad , edited ) sorry about the confusion, hope/guess this does not change the answer
user721108
CC BY-SA 4.0
2024-12-30T14:15:49.473Z
2024-12-30T16:04:24.157Z
2024-12-30T16:04:24.157Z
ProfRob
<p>For context this question is related to this one: <a href="https://astronomy.stackexchange.com/questions/6183/why-do-most-of-the-planets-rotate-counterclockwise-i-e-the-same-way-the-sun">Why do (most of) the planets rotate counterclockwise, i.e. the same way the Sun does?</a></p>
<p>More specifically to <a href="https://astronomy.stackexchange.com/a/41456/57209">this answer</a> that involves gaseous drag and ballistic coefficient of various clumps' size, and the fact that larger chunks already cleaned up or swept out debris on their shrinking orbital path. (which is quite convincing reasoning for counter-intuitive rotation of planets around the Sun in my opinion)</p>
<p>Knowing Cassini brought lots of data regarding <a href="https://science.nasa.gov/mission/cassini/science/rings/" rel="nofollow noreferrer">Saturn rings</a> I failed to find info regarding rotational observation, mostly direction of rotation, of mountain sized chunks.</p>
<p>I wonder if this was observed and mostly if those hypothetical rotation direction of chunks inside the rings can be considered like a small scale protoplanetary disk model ?</p>
<p>From what I understand which might be wrong, the closer an object orbits its parent body, the more likely it is to be synchronous, like Pan or Daphnis. Yet for smaller objects, I have no clue if this is valid.</p>
<p>Question is : regarding rotation of objects, does it make sense to think about planetary rings as something equivalent to
<em>or a small scale model of</em> much larger and somewhat unrelated objects that are protoplanetary disks?</p>

CC BY-SA 4.0
2024-12-31T13:09:09.313Z
In other words, are you wondering whether new moons will form?
Peter - Reinstate Monica
CC BY-SA 4.0
2024-12-31T15:25:30.747Z
@Peter-ReinstateMonica i was wondering if large chunks in rings rotate like planets, same direction as their revolution around the sun. and if planetary rings could be considered alike protoplanetary disk, regarding mechanisms/ collisions, interferences initiating that rotation.
user721108
CC BY-SA 4.0
2024-12-31T15:38:16.993Z
because if there's a correlation between the two i'd rather trust rings as a model (that do exist now, evolving and observable next door) rather than a protoplanetary simulation of early solar system, with all due respect to simulations
user721108
CC BY-SA 4.0
2024-12-31T15:43:13.663Z
If you don't trust simulations there are a few proper observable protoplanetary disks out there, as seen on the Wikipedia page. Get a comfortable chair, get your popcorn out and be witness of the creation of worlds! Just don't fall asleep, you may miss it! ;-)
Peter - Reinstate Monica
<rotation><accretion-discs><saturn-rings>
Do Saturn rings behave like a small scale model of protoplanetary disk?
user721108
# Do Saturn rings behave like a small scale model of protoplanetary disk?

(Asked by: username_0 on 2024-12-30)

For context this question is related to this one: [Why do (most of) the planets rotate counterclockwise, i.e. the same way the Sun does?](https://astronomy.stackexchange.com/questions/6183/why-do-most-of-the-planets-rotate-counterclockwise-i-e-the-same-way-the-sun)

More specifically to [this answer](https://astronomy.stackexchange.com/a/41456/57209) that involves gaseous drag and ballistic coefficient of various clumps' size, and the fact that larger chunks already cleaned up or swept out debris on their shrinking orbital path. (which is quite convincing reasoning for counter-intuitive rotation of planets around the Sun in my opinion)

Knowing Cassini brought lots of data regarding [Saturn rings](https://science.nasa.gov/mission/cassini/science/rings/) I failed to find info regarding rotational observation, mostly direction of rotation, of mountain sized chunks.

I wonder if this was observed and mostly if those hypothetical rotation direction of chunks inside the rings can be considered like a small scale protoplanetary disk model ?

From what I understand which might be wrong, the closer an object orbits its parent body, the more likely it is to be synchronous, like Pan or Daphnis. Yet for smaller objects, I have no clue if this is valid.

Question is : regarding rotation of objects, does it make sense to think about planetary rings as something equivalent to
*or a small scale model of* much larger and somewhat unrelated objects that are protoplanetary disks?

**Tags:** rotation, accretion-discs, saturn-rings
> **Comments:**
> **username_1**: In other words, are you wondering whether new moons will form?  
> **username_0**: @Peter-ReinstateMonica i was wondering if large chunks in rings rotate like planets, same direction as their revolution around the sun. and if planetary rings could be considered alike protoplanetary disk, regarding mechanisms/ collisions, interferences initiating that rotation.  
> **username_0**: because if there's a correlation between the two i'd rather trust rings as a model (that do exist now, evolving and observable next door) rather than a protoplanetary simulation of early solar system, with all due respect to simulations  
> **username_1**: If you don't trust simulations there are a few proper observable protoplanetary disks out there, as seen on the Wikipedia page. Get a comfortable chair, get your popcorn out and be witness of the creation of worlds! Just don't fall asleep, you may miss it! ;-)  

---

## 1 answers

### Answer by username_2 on 2024-12-30. Score: 16 | Accepted answer

It was [Maxwell (1859)](https://mathshistory.st-andrews.ac.uk/Extras/Maxwell_Saturn/) who showed that Saturn's rings must be made of a host of independent particles and cannot be described in terms of a fluid disc.

> The final result, therefore, of the mechanical theory is, that the only system of rings which can exist is one composed of an indefinite number of unconnected particles, revolving round the planet with different velocities according to their respective distances.

Since the essence of an accretion disc, its dynamics and stability, are entirely based on a fluid description (gas pressure, viscosity etc.) Saturn's rings are not similar to an accretion disc.

Theoretical work by [Ohtsuki (2005)](https://ui.adsabs.harvard.edu/abs/2005ApJ...626L..61O/abstract) suggested that large particles rotate slowly (as slow as 10% of their orbital rate) with their spin vector aligned with their orbital angular momentum vectors. Smaller particles should rotate up to 100 times faster and with essentially random spin vectors.

The observational picture from Cassini is summarised by [Spilker et al. (2006)](https://ui.adsabs.harvard.edu/abs/2006P%26SS...54.1167S/abstract). The observations suggest that there are large particles with a spin rate slower than their orbital period and an increasing number of smaller , more rapidly rotating particles. Unfortunately, the paper is paywalled, so I have no more details than are in the abstract.

> **Comments:**
> **username_0**: reading this [extract](https://mathshistory.st-andrews.ac.uk/Extras/Maxwell_Saturn/) i cannot understand the difference between mostly smaller than sand particles arranged in a ring, and a low density gas or fluid having very large mean free path. might be another question though. btw thanks, and for the links +1  
> **username_2**: Thank you for the link - I was looking for one. I have included the relevant sentences now I think. @user721108  A disc as you describe would not be an *accretion* disc since there is no obvious way to transport angular momentum outwards to allow mass transfer inwards.  
> **username_3**: @user721108 the interaction between particles in a fluid is quite different from that in a loose cloud of solid particles. Do NOT assume that just because a bucket of fine sand in some scenarios behaves like a liquid, all systems of solid particles to. In this case fluid dynamics don't apply, each particle in the ring system is subject to Newtonian physics individually (generating an n-body system, but probably most of the particles can be simplified to only being influenced by the planet when it comes to gravity because of the force difference).  
> **username_1**: I'm wondering if the OP may have meant a [protplanetary disk](https://en.wikipedia.org/wiki/Protoplanetary_disk). Wikipedia is inconsistent in the nomenclature: The PPD article claims they should not be confused while the AD article lists PPDs as a type of AD..  
> **username_0**: @Peter-ReinstateMonica yes I was thinking about protoplanetary disk. thanks for pointing out ( i thought stellar accretion disk was the stuff gathering around a single star, forming planetoids, my bad , edited ) sorry about the confusion, hope/guess this does not change the answer  

---

