# Why are there gaps in the size distribution of solar system moons?

Looking at the moons natural satellites in the solar system, the larger ones appear to fall in a few groups of sizes.

Eyeballing the above picture, there appear to be a bunch of big moons (the Galilean Jupiter moons, Titan, the Moon, Triton), then some medium sized moons around Saturn and Uranus, and then some smaller moons such as Enceladus and Miranda.

If I take a look at those moons on the list of solar system bodies ordered by size, there indeed appear to be significant gaps between those size groups. There is a gap between Triton (1353 km radus) and Titania (789 km radus) of 72%, and between Tethys (533 km radus) and Enceladus (252 km radius) of 111%. Including other solar system objects in the comparison does not change the gap between the big and medium moons much, Pluto and Eris join the 'large' group and Haumea joins the 'medium' group. The gap between medium and small moons is also not changed much if we include the other cis-Neptunian objects (Ceres joins the mediums, Pallas and Vesta the smalls). There is however a large number of transneptunian objects in this gap, although most of them don't have a well constrained size.

So is there an explanation for why these gaps in the size distribution of moons (and many other solar system objects) exist? Or is it just a random accident from the formation of the solar system?

• Could the gaps be random? Can you show, perhaps using something like a Kolmogorov–Smirnov test, that the distribution fails to match a simple power law? Commented Dec 28, 2023 at 1:33
• Sure, they could be random, that is exactly the question I'm asking. I'm not acquainted with the Kolmogorov-Smirnov test, but I might look into that. Commented Dec 30, 2023 at 14:06

I doubt that the assumption of this question holds: I took the sizes from all (named) bodies of the solar system I could find, put them into a table and plotted the cumulative size distribution. It does not show the alleged difference, regardless whether I plot all bodies or only the moons of the planets:

One might argue to find a change of slope at around 1000 km (thus bodies smaller than ~1000km are relative more numerous than larger bodies), and another around 40km (which is probably both, an observation bias (not all bodies of 10m and above are known) and a selection bias as my selection taken from wikipedia is not complete here - and I didn't find quickly an easy access to a more comprehensive list - any hint for an accessible, more complete list with corresponding data very welcome). You can find the data table and the the source to this plot in my github repo.

Looking only at the moons of the planets, the distribution looks similar, but the smaller sizes seems better sampled, thus the kink at 40km is not so pronounced and at a smaller value around 10km:

• In your second plot there ARE two gaps - one at 1000 km and the other at 400 km - exactly as suggested by the OP. The first sentence of your answer is just as statistically untested as the original question. If you really want to test it then you do a Monte Carlo using a smooth model of the cumulative distribution and then ask the question - how often do gaps of $\sim 0.2 dex$ occur when you simulate a population of moons similar to that of the Solar System drawn from that distribution. Commented Dec 29, 2023 at 18:12
• I love these plots. I agree with @ProfRob that the significance of the 400 km and 1000 km gaps could be tested with Monte Carlo simulation of a power law distribution. Commented Dec 30, 2023 at 0:19
• FWIW, I have a log-log plot of the observed main belt asteroid size distribution here: astronomy.stackexchange.com/a/49425/16685 Commented Dec 30, 2023 at 13:17
• I don't assume there are statistically significant gaps in the sizes of moons, I'm just observing that there are these gaps and asking for an explanation. Chance is a possible explanation/answer to my question. Commented Dec 30, 2023 at 14:47

As discussed in the answer by @planetmaker, it is not clear whether there are significant gaps in the size distribution or not.

But even if there are significant gaps, they may not be evidence of any overarching moon-formation laws. This is because the satellite systems result from so many different processes and histories. Some may have been formed in circumplanetary disks (Jupiter, Saturn, Uranus), the Moon may have formed from a giant impact on the Earth, and Charon may have formed from a collisional process intermediate between giant impact and capture. Triton was captured, but it may have disrupted Neptune's original satellite system in the process. Saturn's rings may have been created by the disruption of the former satellite "Chrysalis," and the circumplanetary disks of the giant planets may have produced earlier satellites that migrated and fell into the central planets.

• Why would there be significant gaps if there were just lots of random things going on? Commented Dec 30, 2023 at 3:23
• I didn't ask about overarching/universal moon formation laws, I asked about explanations for these gaps. I'm very happy with explanations involving details of the formation of our specific solar system. And them being random is also an explanation of course. Commented Dec 30, 2023 at 14:41

I would definitely agree that, before a discussion as to mechanisms for this disparity, you would need to statistically prove that there is a disparity that needs to be accounted for and cannot be explained by random chance. Additionally, the protoplanetary disk around the young sun was not uniform, and I do not think it right to directly compare the different moons in drastically different parts of the solar system.

In light of this, I will attempt to address two of the points you mentioned.

(1) Neptune and Uranus' Moons
Neptune and Uranus are fairly similar in mass, so it would make logical sense that their moons would be fairly similar as well. And, for the most part, I'd argue they are. The difference is that Triton is likely a captured object and did not form alongside Neptune.

(2) Saturn's Moons
I feel less inclined to account for this discrepancy without statistical work as the masses are within an order of magnitude, especially considering Saturn's system is so dynamic (it's rings are only around 400 million years old at most, for example).

I hope this helps a bit!

• In what sense are Neptune and Uranus' moons similar? Not in size distribution. Neptune has one large moon that's probably captured while Uranus has four medium moons, and then both have a bunch of small moons. Commented Dec 30, 2023 at 14:45