# Can adding mass to a ringed planet cause a huge chain reaction?

• A planetary ring system is most often formed by the breakup of objects within the Roche limit of a planet.
• Higher mass objects exert a greater force on its surrounding material (this is just a generalized statement; I am aware it is much more complicated than that, involving the mass of both objects as well as their distance and several other factors)

This makes me wonder if it is possible under certain circumstances that adding enough mass to a planet with a ring system can cause a massive chain reaction. This process might involve the following steps:

1. A series of large collisions impact the planet, which increases its mass.
2. The objects nearest to the planet in the innermost layers of the ring system experience orbital decay, eventually leading them to crash into the planet.
3. This then adds even more mass to the planet, which causes this pattern to repeat itself until equilibrium is met. (such as a gap existing in the rings, where the nearest part of the ring system remains stable in spite of the added mass, which prevents further orbital decay)

# Can adding mass to a ringed planet cause a massive chain reaction?

I have my doubts about whether this is possible:

• It's possible that the amount of mass added to a planet by the collapse of a portion of a ring system is not large enough to cause a chain reaction
• Perhaps the ring system would simply get a bit closer to the planet to compensate for the added mass

My guess is that it's possible under the right circumstances. Perhaps the innermost part of a ring system lies right outside an area that would exhibit enough atmospheric or electromagnetic drag to cause orbital decay. And maybe the ring system is primarily composed of a dense material such as iron (rather than rock and ice) which could add enough mass to the planet to allow this process to repeat itself.

• Say yes, no, or maybe and provide detailed supporting evidence, links or any other helpful knowledge that pertains to the question

If the answer is yes, this is possible, this could potentially help me to explain the formation of a giant, equatorial gash as is explored in my question How Can I Explain a Giant Equatorial Gash?. However, this question should be treated as an independent and unrelated issue.

• Rings are flimsy ephemeral structures. There is not a lot of mass in them, and they don't last all that long. So, a chain reaction may be or not be, but it won't be massive for sure. – AlexP Dec 2 '19 at 17:18
• Increasing the planets mass significantly by bombardment could well heat the atmosphere to such an extent that the inner rings entered the atmospher creating even more heating. – Slarty Dec 2 '19 at 17:29
• Have you done any research yet on the mass of ring systems relative to the planets they orbit, or on ring systems generally and how they form? That would be a good first step. – Morris The Cat Dec 2 '19 at 17:30
• As noted by AlexP rings are tiny compared to a planet so the situation you describe will not happen. Also the ring material is still exerting a gravitational effect whilst in orbit so it would be just a matter of increasing the density of the system very slightly. – Slarty Dec 2 '19 at 17:34
• @MorrisTheCat It would be a perfectly valid answer. This isn't a totally trivial subject, and the fact that the OP was asking it in the first place suggests that finding that answer isn't totally trivial either. – Starfish Prime Dec 2 '19 at 18:03

It's an interesting scenario. The major problem is that ring systems tend to be quite low-mass in comparison to their parent bodies. For example, measurements by Cassini indicate that in the case of Saturn, the ratio of ring mass to planet mass is $$M_R/M_p\simeq2.7\times10^{-8}$$ (Iess et al. 2019). Even in the notable case of 1SWASP J1407b, whose ring system is arguably close to an accretion disk, we have $$M_R/M_p\simeq6.6\times10^{-6}$$. It should be quite clear that even accreting a substantial portion of the ring system will not significantly change the Roche limit of the planet, which scales as $$d\propto M_p^{1/3}$$, as Starfish Prime has said - in other words, extremely weakly.

Here are the characteristics of a system liable to form a ring system of significant mass:

• A lack of other planets to accrete gas and dust, thereby allowing one planet to accumulate a large system of satellites.
• A highly massive giant planet, with a large Roche limit.
• A young system, meaning there is still plenty of material around to form satellites and rings - or a massive disk similar to that of 1SWASP J1407b.
• A lack of shepherd moons, which would provide a stabilizing effect for the rings even in the event of some catastrophic cascade.
• Possibly an Earth-like satellite capable of being tidally disrupted by the planet.

An interesting side possibility is that of a ring system stabilized by both gravity and the planet's magnetic field, as I discussed in another answer. The regime of stability is determined by a parameter called $$L_*$$, proportional to the planet's angular speed $$\Omega_p$$ and inversely proportional to its mass $$M_p$$. Therefore, if a large object impacted the planet, its mass would increase and its rotation would decrease (by conservation of angular momentum). This could strongly reduce $$L_*$$, bringing it into a regime where the rings are unstable - assuming the mass-to-charge ratio of ring particles is sufficiently small.

Morris the Cat makes an excellent point about particle size - small particles won't result in cratering, and will in fact likely burn up in the atmosphere during reentry. As the distribution of particles in rings is strongly skewed towards smaller particles (I believe it's something like $$n\propto a^{-6}$$, where $$a$$ is the particle radius), you're not going to see many large chunks in the rings. This is especially the case if you want chunks with small mass-to-charge ratios, because it's harder for large collections of particles to maintain significant net charges without separating thanks to the strong electric forces involved.

• The other issue is the individual mass of the particles within the ring system. If the objective is significant impact cratering of the primary, you don't just need a lot of mass in the ring system, the composition of the rings needs to unusually 'chunky' by comparison even with Saturn's B-ring. Otherwise you don't really have impact events as much as you have a very high-velocity sandstorm. – Morris The Cat Dec 2 '19 at 18:22
• @MorrisTheCat Yup, that's a great point. – HDE 226868 Dec 3 '19 at 0:10

Tl;DR: probably no. But it might not even be required for what you want.

The (simple, rigid-body approximation) for the Roche limit is defined as $$d = R_M \sqrt[3]{2{\rho_M \over \rho_m}}$$ where $$R_M$$ is the radius of the primary, and $$\rho_M$$ and $$\rho_m$$ are the densities of the primary and satellite respectively. Given constant densities, the Roche limit will therefore scale proportionallly to the radius of the primary. Assuming a spherical planet, radius scales proportionally to the cube root of the volume $$R_M = \sqrt[3]{3v \over 4\pi}$$. Given a constant density, the volume increases linearly as you add mass, so $$R_M = \sqrt[3]{3M_M \over 4\pi\rho_M}$$ and hence $$d = \sqrt[3]{3M_M \over 2\pi\rho_m}$$.

That means that in order to double your Roche limit at the same density, you need to increase your mass by a factor of 23, which seems like an awful lot.

I suspect (though I'm not about to prove) that there's little chance of having a massy enough inner ring that its fall onto the planet below will appreciably speed up the decay of any other part of the ring... there just can't be enough mass there to do the job.

You could add more mass via collisions with some other massive body, but its quite difficult for a body that's big enough to be interesting to leave most of its mass behind on the planet instead of spraying it off into space (consider the Theia impact which probably gave us the moon). There are multiple other problems there, such as where did the donor body (or bodies) come from? Late in the evolution of a planetary system there shouldn't be too much mass flying around, unless something positively apocalyptic has happened to the outer system (something like a Nemesis event, perhaps). Even if you can find enough mass, its impact is likely to be Quite Dramatic with quite long-lasting effects, making it unclear that you'd end up wit the nice equatorial craters you're after.

I wonder though... I think you might be overcomplicating this. Surely the natural orbital decay of a ring via tidal forces should be enough to create the kind of cratering you're after? It doesn't need to have any other weird and complex trigger; those rings weren't gonna last forever anyway.

• Well, the primary problem with the scenario you're proposing is that ring systems are primarily an attribute of massive gas giants, so no craters. There are some rocky/icy centaurs that have ring systems, but those rings are speculated to be a result of massive tidal disruption of the centaur itself. You could just do a math problem and figure out how many craters times how large an impactor you need per crater to get how much mass you need. I suspect it would be pretty large. – Morris The Cat Dec 2 '19 at 17:53
• @MorrisTheCat the scenario was proposed by the OP, not me. Also, long lived ring systems are things we can see on gas giants, but there's no obvious reason why a body orbiting a rocky world couldn't break up (there's a suggestion it happened to Venus). – Starfish Prime Dec 2 '19 at 17:56
• Ooo, interesting. I mean, at that point I guess the term 'ring system' gets a bit weird since really it's just one phase of a rapid transition from "Satellite" to "Debris Field". – Morris The Cat Dec 2 '19 at 18:03
• @MorrisTheCat yeah, I am perhaps stretching the definition a little there ;-) – Starfish Prime Dec 2 '19 at 18:03