<p>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:
<a href="https://i.sstatic.net/jDggm.png" rel="noreferrer"><img src="https://i.sstatic.net/jDggm.png" alt="Size distribution of the named solar system bodies" /></a></p>
<p>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 <a href="https://en.wikipedia.org/wiki/List_of_Solar_System_objects_by_size#" rel="noreferrer">taken from wikipedia</a> 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 <a href="https://github.com/planetmaker/pytools/tree/master/solarsystem" rel="noreferrer">my github repo</a>.</p>
<p>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:
<a href="https://i.sstatic.net/H4npG.png" rel="noreferrer"><img src="https://i.sstatic.net/H4npG.png" alt="Size distribution of planets' moons in the solar system" /></a></p>

CC BY-SA 4.0
2023-12-29T18:12:09.623Z
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.
ProfRob
CC BY-SA 4.0
2023-12-30T00:19:48.713Z
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.
giardia
CC BY-SA 4.0
2023-12-30T13:17:01.400Z
FWIW, I have a log-log plot of the observed main belt asteroid size distribution here:  https://astronomy.stackexchange.com/a/49425/16685
PM 2Ring
CC BY-SA 4.0
2023-12-30T14:47:46.343Z
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.
JanKanis
CC BY-SA 4.0
2023-12-29T14:22:42.333Z
2023-12-29T14:22:42.333Z
planetmaker
<p>As discussed in the answer by @planetmaker, it is not clear whether there are significant gaps in the size distribution or not.</p>
<p>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 <a href="https://en.wikipedia.org/wiki/Charon_(moon)#Formation" rel="nofollow noreferrer">formed from a collisional process</a> 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 &quot;<a href="https://en.wikipedia.org/wiki/Chrysalis_(hypothetical_moon)" rel="nofollow noreferrer">Chrysalis</a>,&quot; and the circumplanetary disks of the giant planets may have produced earlier satellites that migrated and fell into the central planets.</p>

CC BY-SA 4.0
2023-12-30T03:23:05.750Z
Why would there be significant gaps if there were just lots of random things going on?
ProfRob
CC BY-SA 4.0
2023-12-30T14:41:19.563Z
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.
JanKanis
CC BY-SA 4.0
2023-12-30T00:39:09.273Z
2023-12-30T00:39:09.273Z
giardia
<p>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.</p>
<p>In light of this, I will attempt to address two of the points you mentioned.</p>
<p>(1) Neptune and Uranus' Moons <br>
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.</p>
<p>(2) Saturn's Moons <br>
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).</p>
<p>I hope this helps a bit!</p>

CC BY-SA 4.0
2023-12-30T14:45:59.487Z
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.
JanKanis
CC BY-SA 4.0
2023-12-29T05:42:52.623Z
2023-12-29T05:42:52.623Z
Erika Dunning
<p>Looking at the <s>moons</s> natural satellites in the solar system, the larger ones appear to fall in a few groups of sizes.</p>
<p><a href="https://i.sstatic.net/Myp8m.jpg" rel="noreferrer"><img src="https://i.sstatic.net/Myp8m.jpg" alt="The Not-Planets, published by the Planetary Society, https://www.planetary.org/space-images/the-not-planets" /></a></p>
<p>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.</p>
<p>If I take a look at those moons on the list of <a href="https://en.wikipedia.org/wiki/List_of_Solar_System_objects_by_size#Objects_with_radius_over_400_km" rel="noreferrer">solar system bodies ordered by size</a>, 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.</p>
<p>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?</p>

CC BY-SA 4.0
2023-12-28T01:33:09.457Z
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?
John Doty
CC BY-SA 4.0
2023-12-30T14:06:50.727Z
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.
JanKanis
<solar-system><natural-satellites><size><radius>
Why are there gaps in the size distribution of solar system moons?
JanKanis
# Why are there gaps in the size distribution of solar system moons?

(Asked by: username_0 on 2023-12-28)

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

[![The Not-Planets, published by the Planetary Society, https://www.planetary.org/space-images/the-not-planets](https://i.sstatic.net/Myp8m.jpg)](https://i.sstatic.net/Myp8m.jpg)

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](https://en.wikipedia.org/wiki/List_of_Solar_System_objects_by_size#Objects_with_radius_over_400_km), 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?

**Tags:** solar-system, natural-satellites, size, radius
> **Comments:**
> **username_1**: 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?  
> **username_0**: 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.  

---

## 3 answers

### Answer by username_2 on 2023-12-29. Score: 5

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:
[![Size distribution of the named solar system bodies](https://i.sstatic.net/jDggm.png)](https://i.sstatic.net/jDggm.png)

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](https://en.wikipedia.org/wiki/List_of_Solar_System_objects_by_size#) 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](https://github.com/planetmaker/pytools/tree/master/solarsystem).

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:
[![Size distribution of planets' moons in the solar system](https://i.sstatic.net/H4npG.png)](https://i.sstatic.net/H4npG.png)

> **Comments:**
> **username_3**: 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.  
> **username_4**: 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.  
> **username_5**: FWIW, I have a log-log plot of the observed main belt asteroid size distribution here:  https://astronomy.stackexchange.com/a/49425/16685  
> **username_0**: 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.  

---

### Answer by username_4 on 2023-12-30. Score: 1

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](https://en.wikipedia.org/wiki/Charon_(moon)#Formation) 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](https://en.wikipedia.org/wiki/Chrysalis_(hypothetical_moon))," and the circumplanetary disks of the giant planets may have produced earlier satellites that migrated and fell into the central planets.

> **Comments:**
> **username_3**: Why would there be significant gaps if there were just lots of random things going on?  
> **username_0**: 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.  

---

### Answer by username_6 on 2023-12-29. Score: 0

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!

> **Comments:**
> **username_0**: 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.  

---

