Assortments of Thought

Moons and Rings of the Cosmos

Posted on: March 3rd, 2015

Other than all the stars, the Moon and the planets classically held attention and commanded wonder, whenever a civilization gazed into the heavens. Of course this was largely because so little was known of outer space, about what else was up there besides what could clearly be seen, but it shouldn’t be denied that the planets of our own solar system are indeed magnificent. And now, while we unfortunately have to rely as yet on artists’ conceptions to visualize them, the recent multitudes of exoplanets found have, along with theoretical considerations, yielded even more diverse and wondrous planets to inspire us. Yet moons and rings are presumably integral parts of planetary systems as well, and while moons at least are virtually certain to exist alongside and beyond many of the planets of our galaxy’s systems, their small sizes have presumably kept them invisible as yet to our instruments and detection methods. Even so, we might hazard that “large” planets nearly always have moons and rings, while “small” ones have them much less so; that most moons are “very small”, except that “large” planets typically have a few “larger” but still non-gaseous ones; that extensive rings are less common, and only ever exist around “large” planets; that most moons lack atmospheres, yet a fair number of systems have at least one atmospheric moon; and that non-unitary planets and moons are comparatively rare, as are moons or rings of moons. To see why these conjectures might be true, let us consider what, in terms of moons, rings, and non-unitary bodies, planetary systems in our galaxy and across all the cosmos might be like.

Definitions and Background

To begin, it’s helpful to specify precisely what we mean by “planet”, “moon”, “ring”, and “non-unitary body” (we should also note that we’ll use terms like “large” and “small” to refer to volume and, when we actually use quotes, volume in a relative sense–explicitly specifying mass when we mean mass instead), and then to consider how planetary systems form and evolve overall. Indeed, no official definitions exist for the aforementioned terms aside from that of “planet” (confined at that to planets within our own solar system), and besides, for our purposes here, we want to define things a little more uniquely (“non-unitary body” isn’t even a standard term). That being said then, a “planet” is an object, other than a star, that directly orbits a star or group of stars; which is the most massive of any objects sharing its orbit; and which has at most only a “few” other objects “close” to its orbit at any given time. (Any less massive objects could be, for instance, like the trojan asteroids that follow Earth and other planets in our own system in their orbits, while such “few” objects could be, for instance, passing asteroids or comets.) A “moon”, meanwhile, is an object which orbits any object in a system other than a star, and which is not part of a ring. A “ring”, in turn then, is a collection of objects, irregardless of size, which “densely” share an orbital region around any object within a system, but that are so numerous that they “fill out” this region, leaving no “breaks”. Finally, a “non-unitary body” is any two or more objects in a system, necessarily of the same type, that orbit about a common point, but without other objects of the same type between this point and the objects. (Like trinary stars, for instance, where all three orbit a common point, as opposed to those where one orbits the other two.) Finally then, for our purposes here, all other known types of objects, if need be, will simply be referred to by common terms like “asteroid” or “comet”, without further specification.

Now while these definitions of “planet”, “moon”, “ring”, and “non-unitary body” are pretty straightforward, it’s interesting to note a few of their implications. One is that while a star may orbit another star, a would-be planet that orbits a planet must instead be a moon. (Only two or more planets orbiting about a common point–a non-unitary planet–are in fact planets.) Another is that planets must orbit stars–although in reality, many planets exist outside of systems, orbiting galactic centers directly. (See the Wikipedia article “Rogue Planet“; since we’re interested in moons and rings within systems, we’ve defined “planet” and such only within that context.) Also, for instance, moons may themselves have moons (as may asteroids and such, something we won’t otherwise get into); the distinction may blur between members of a ring and a collection of several moons; and, the asteroid belt in our own system for example is, in fact, a ring. This last implication is perhaps the most surprising and odd, although considering how our own planetary system formed, I think it’s reasonable to say that rings may encircle objects other than planets, including stars. The others aren’t so unexpected; they simply show the grey area between planets and moons in practice, and between moons and components of rings. (I’ve even seen the term “moonlet” used in reference to comparatively “large” parts of rings, or even just to “very small” moons; see, for instance, the Wikipedia article “Moonlet“.) In any case, any classification of objects within planetary systems is necessarily approximate; we just need something fairly solid to go on, particularly something that applies to all currently-conceivable planetary systems.

When pondering moons and rings then, our questions center on whether some types of planets have them more often than others; how big or extensive, respectively, moons and rings typically are; and whether moons commonly have atmospheres to any appreciable degree–all matters of which we’ll be able to answer in part by considering what we know of how planetary systems form and evolve. Meanwhile, the consideration of non-unitary bodies arises naturally, because the processes that give rise to them are also one way that planets can obtain moons. Abstracting then from the suspected history of our own system (see the Wikipedia article “Formation and Evolution of the Solar System“, sec.s 2 & 3), a planetary system begins with a sphere of raw material; hydrogen and helium for the most part and, if forming later than earlier stars which have already distributed heavier elements to the cosmos, then such heavier elements as well. The ongoing interaction between gravity, gas pressure, magnetic fields, and rotation flattens the sphere into a disc, and begins the formation of star(s) at the center. As the star(s) go on to fuse hydrogen and become “true” stars (taking up the bulk of the material in the disc), meanwhile, planets begin to form. Tiny fragments of material now in orbits around the star(s) start to fuse together, although the heat of the star(s) forces only compounds with high melting points to be available “close” to the star(s) (rocky materials like metals and such), while any and all material “far” from the star(s) remains available for planets there (rocky, plus icy materials like water, ammonia, and methane–to follow astronomical parlance–plus gases, namely hydrogen and helium). Hence “small”, rocky planets form “close” to the star(s) and “large”, icy/rocky or icy/rocky/gaseous planets “far” from the star(s), simply because the rocky planets have so little material available to them; too little to provide much mass, and, in turn, too little mass to snag great quantities of hydrogen and helium. Of course, it’s essential to note that this whole process is very chaotic over millions of years, meaning for instance that planets may migrate from their initial orbits to others, and that much material may never be incorporated into planets, instead becoming asteroids, comets, or perhaps being ejected from the system altogether.

However it all progresses, moons and rings begin to form in ways very akin to those of planets, or else as byproducts of the chaotic evolution of the system–a chaos which may also yield non-unitary bodies. Abstracting once more from our own system’s suspected history (see the Wikipedia articles “Formation and Evolution of the Solar System,” sec.s 4 & 5.2, and “Planetary Ring“), “large” planets acquire material discs of their own of which portions may fuse to form moons, or else remain apart to ultimately form rings. Meanwhile, collisions during the evolution of a planet–whether between objects in orbit, or between such objects and the planet itself–may create either moons or rings, or else a planet may gravitationally capture a moon. Moons may also “fall” towards a planet over time, thus breaking up to form a ring. Finally, non-unitary bodies may form out of the chaos as well, although this is more speculative, considering, for instance, that very few non-unitary bodies exist in our own system. We do know that among stars, at least four of every five in the observable universe are non-unitary (see the introduction of the article “Binary Star Systems: Classification and Evolution” by the Space.com staff), and that our own system contains a binary asteroid and a binary Kuiper belt object (see the introduction of the Wikipedia article “Double Planet“), with Pluto and its “moon” Charon arguably being a binary body as well. At the very least then, it’s clear that either upon formation, by subsequent collisions, or from gravitational capture, non-unitary bodies may form in systems. In summary then, planets, moons, rings, non-unitary bodies, and all other such objects form from discs of material via, essentially, the fusing and colliding of portions within it.

How Moons, Rings, and Non-Unitary Bodies are Distributed

To our central questions now, however, the first is how, precisely, are moons, rings, and non-unitary bodies distributed? And the answer, most reasonably, is that “large” planets nearly always have moons and rings both, while “small” planets have them much less abundantly and less frequently, with non-unitary planets and moons having formed from non-unitary processes being the rarest of all. To address the easiest conclusion first, we know that “large” planets acquire material discs of their own during formation, from which moons or rings will result. In fact in general, abstracting from what Eric Loberg of the Museum of the Rockies’ Taylor Planetarium explains (see the video “An Explanation of Why Some Planets Have More Moons Than Others Do” at classroom.Synonym.com), “large” planets have the most moons because of their greater masses; the sheer amount of material available during formation for planet and moons alike, but also their enhanced ability to snag passing asteroids and comets and such, although being close to their star(s) can result in the star(s) stripping them of moons or rings. Based on this then, we can comfortably conclude that “large” planets that’ve never been “close” to their star(s) almost always have moons and rings, and that such planets aren’t necessarily even only icy/rocky/gaseous ones at that. For any planet massive enough to acquire great quantities of hydrogen and helium (the two least-massive gases) is surely adept at capturing moons as well, and this reasonably extends even to the largest of rocky or icy/rocky planets that’re otherwise not quite massive enough to acquire hydrogen and helium. (Though where the cut-off is for rocky and icy/rocky planets isn’t clear. Of course, granted, it probably isn’t a sharp cut-off regardless.) Presumably then, that all four of Jupiter, Saturn, Uranus, and Neptune in our own system have rings and many moons isn’t coincidental; it’s the extremely probable outcome for a system’s “large” planets.

The extent of moons or rings around “small” rocky or icy/rocky planets, however, is much more difficult to reason out, although there’s reason to believe that such moons and rings are less common in frequency, and particularly less in abundance as well. Part of the difficulty is that no one as yet knows how the Earth got its moon, so potentially, for moons of “small” planets, a distinct process of formation exists (besides capture or collision) that we aren’t privy to. Nonetheless, we do have a few things to go on. Even “small” planets can capture moons, as Mars did by snatching two from the asteroid belt (see, for instance, Loberg’s video “An Explanation of Why Some Planets Have More Moons Than Others Do“), so if we assume that asteroid belts are common across planetary systems, then it’s reasonable to think that at least some of the rocky and icy/rocky planets in systems often have at least one moon. (And as to the feasibility of systems with rocky or icy/rocky planets often having at least one asteroid belt, see the endnote.) Further, it’s thought that several million years from now, in our own system, Mars will acquire a ring from the break-up of its current moon Phobos (see the Wikipedia article “Planetary Ring,” sec. 1, para. 9). Hence there’re at least two obvious ways in which one or more “small” planets in a system can acquire a limited number of moons (one way for rings), and what’s more, there’s reason to believe that such moons are fairly common, even if much less abundant than moons around “large” planets.

As for moons or rings around “small” planets by other means, it’s reasonable to venture that they’re more unusual, as are, incidentally, non-unitary planets in systems. The basis for this is simply that planets form from many, many fragments fusing together, and unless this process is disturbed (leaving a ring around a star), an extraordinary event is probably required to produce anything other than a unitary planet. As it’s long been hypothesized that our own moon formed from a collision between the early Earth and a third-party body (the giant impact hypothesis), so too might a moon form around a rocky or icy/rocky planet in general. Yet collisions are an inherent feature of the violent, chaotic formation of all systems, and unless ones happen at just the right times and places, the end results will inevitably be unitary planets. (Meanwhile, assuming most rings around rocky or icy/rocky planets form from “falling” moons, then rings are even less common than the moons that occasionally give rise to them–comparatively rare.) Interestingly, the giant impact hypothesis for the Moon’s formation has largely been disproven by now, because recent chemical analyses between the Earth’s material and the Moon’s have shown that the Earth and Moon were originally one; the chemical signatures that a third-party body having collided with the early Earth would have produced are simply not there. While this leaves no explanation for why the Earth-Moon system has such high angular momentum, or, in a sense, rotates so fast (see the Wikipedia article “Origin of the Moon“), at least it seems clear that in whatever way non-unitary bodies form, that’s how the Earth and the Moon formed. (Presumably, the Moon simply lacked the mass for it and the Earth to orbit about a common point, and hence rather than a non-unitary planet, a planet-with-a-moon formed instead.)

Finally then, consideration of how common non-unitary planets are will simultaneously shed light on how common moons are that arise from non-unitary processes, and, in fact, such non-unitary processes are probably comparatively rare. Ironically, we know from experimental observation that non-unitary stars, as previously noted, are quite abundant in the galaxy (see the introduction of the Space.com article “Binary Star Systems: Classification and Evolution“). Yet non-unitary bodies, or planets and moons which arose from non-unitary processes, are not common at all in our own system (of course we as yet lack the means to observe them in other systems), and not only can we argue why theoretically, we can even set an upper bound on the probability of a non-unitary process playing out for a particular object in general. Basically, whereas stars form from spinning, condensing material at the center of discs, planets form from the fusing of orbiting materials. While a soon-to-be-star can easily fragment into two or more if material begins to pool in several spots (see the news article “New Studies Give Strong Boost to Binary-Star Formation Theory,” by NRAO at Astronomy.com), again, planets (and moons forming around “large” planets, incidentally) form from orbiting materials smashing into and fusing together along “curves of orbit”, leaving a tendency to form unitary bodies that is not readily, permanently disrupted. As such, non-unitary bodies and, in general, objects resulting from non-unitary processes are probably comparatively rare.

Indeed, let’s say that the probability of a non-unitary process playing out for a given body is 25%. Considering our own system then, let’s exclude Pluto-Charon and any binary asteroids and such (on the basis of them being “leftovers”, likely, whose development to completion was halted), plus all our moons (since we can’t be entirely sure which ones aren’t just captured asteroids, Kuiper belt objects, or comets or such). Then, with eight planets and a 25% chance of each forming in a non-unitary process, there was only a 0.75^8 + (0.75^7)(0.25) = 13.3% chance that our system would have ended up with either only one or else no non-unitary processes having played out … except that considering the Earth and the Moon, one apparently did. If we assume that our system isn’t one of the roughly one-in-ten then (according to our assumption) in which two or more non-unitary processes didn’t play out, then the probability of a non-unitary process for a given body must be something less than 25% (though granted, possibly as low as nearly 0%; we as yet lack the empirical evidence to refine this at all). Then, since some non-unitary processes yield non-unitary planets but others yield planets-with-moon(s), the chance of a planet-with-moon(s) must, at best, be something even less than 25% per planet. Hence also not knowing how many rocky and icy/rocky planets a system typically has (so as to specifically focus now on such planets getting moons by non-unitary processes; “large” planets are replete with moons regardless), as just a rough guess, say there’re typically three such planets per system and a 10% chance apiece for forming one or more moons by a non-unitary process. Then, on average, just a little under three of every ten systems have at least one rocky or icy/rocky planet with such moon(s) (1 – 0.90^3), making them (and non-unitary planets) not rare in an absolute sense, but still rare in comparison to moons obtained by capture.

The Sizes of Moons and Rings

Now to our second central question, we have, of what sizes are moons, and how extensive are rings? And the answer to the first part, most likely, is that moons around “small” planets are always even smaller, and that most moons around “large” planets are quite small as well, except that most “large” planets do have at least a handful of bigger ones. Also, in the sense of being icy/rocky/gaseous, “large” moons, while perhaps not completely absent in the cosmos, generally don’t exist. (We’ll consider the extensiveness of rings shortly.) To see why for all of this, we really only have to refer back to how systems form and evolve, and to realize that more massive bodies are not at all likely to orbit less massive ones, simply because their proportionately-stronger gravitational influences would force the less massive bodies to orbit them instead. Thus rocky or icy/rocky planets, necessarily “small” for having only limited material from which to form, can’t have “large” moons, simply because of their own sizes. (Note though that we assume an approximate mass-volume equivalency here, on the grounds that rocky or icy/rocky planets and their moons are expected to be of a similar density). Any moons to form from non-unitary processes or collisions (between the planet and a third-party body, or between two or more pre-existing moons) must simply result in extra, smaller objects, while even setting aside the fact that a more massive body won’t orbit a less massive one, rocky and icy/rocky planets just don’t have the gravitational power to capture “large” moons. And, interestingly, since the fragments throughout a system’s evolution that never become fused with others to form rocky or icy/rocky planets, moons, or cores of icy/rocky/gaseous planets presumably always remain small, even as adept as “large” planets are at capturing such fragments for moons, such moons should always be “very small” as well.

Comparatively “large” moons should nonetheless commonly exist around “large” planets though, just with limits on size that, incidentally, almost certainly preclude icy/rocky/gaseous ones. This is because “large” planets acquire material discs of their own from which moons may form, except that with a “large” planet initially taking so much material for itself that could otherwise have gone to these discs, there’s simply not much left for moons. Granted, without much space around even a “large” planet, in comparison to star(s), to provide stable orbits for “several” moons, at least the material that’s available to moons should be funneled into only a “few”, making those “few” larger. Even so though, we can’t reasonably expect them to be “large”, again, just because the material around a “large” planet is so limited in amount; and, certainly, in comparison to that around a star. In particular then, as for icy/rocky/gaseous moons forming, even if we assume that moons commonly become massive enough to acquire hydrogen and helium of their own, given that they’re around “large” planets that’ve already taken so much of it to begin with–planets which clearly have the gravitational advantage at taking even more–such moons just aren’t at all likely to ever actually acquire much for themselves. Of course then, around “very large” planets, we expect the largest moons of all (from the extra material available to them), but however large a moon gets, hydrogen and helium is presumably never truly available to it for it to go on and become icy/rocky/gaseous.

Finally, regarding the extensiveness of rings, the answer, most likely, is that rings comparable to those of Saturn are not particularly rare, although not all systems have rings to such extents. We as yet lack the evidence to say for sure, however as to how extensive rings form, it seems clear that “large” moons are first necessary. This is because only the collisions between or orbital degradations of “large” moons can be expected to produce all the material necessary to form extensive rings (third-party bodies not gravitationally-bound would presumably never leave so much material behind), or else to have the gravitational influences necessary to prevent portions of the material disc around a planet from forming into additional moons. Hence only “large”, icy/rocky/gaseous planets can reasonably be expected to have extensive rings, because only “large” planets ever have “large” moons. (“Small” planets, with much less abundant, “very small” moons at best, don’t commonly have rings at all.) Further though, more extensive rings probably form principally from the break-up of “large” moons, because collisions between such moons would need to be just right so as to thoroughly break the moons up, while even “large” moons may not be massive enough for their gravitational influences to keep substantial portions of material discs apart as rings. (So whereas, for instance, Jupiter is believed to have kept the asteroid belt apart–see the Wikipedia article “Asteroid Belt,” sec. 2.1–even “large” moons are far, far less massive in comparison, and so may be incapable of causing rings to form within the material discs of their planets.) Hence while nearly all “large” planets have rings, more extensive rings probably depend mostly on the break-up of “large” moons, and, as such, while not being particularly rare, are nevertheless not present in many planetary systems either.

Atmospheres

Now to our third and final central question (we’ll address how often moons have moons of their own or rings afterwards, as a sub-question of our first that simply merited the other discussions up to and including this point), we have, how frequently do moons have atmospheres to any appreciable degree? And the answer here, most likely, is that such moons are probably fairly common, perhaps occurring in at least half of all planetary systems, although this is more speculative than our previous conclusions. The problem is that theoretical and intuitive considerations seem to suggest that atmospheric moons aren’t rare, yet we as yet have little to go on that’s certain or absolute. (We don’t even know how the one moon in our own system that has a substantial atmosphere got it, namely Saturn’s moon Titan.) To begin with what we do know (or at least highly suspect), we know that moons are abundant in planetary systems, but that most are “very small” (including being of little mass), with virtually none being icy/rocky/gaseous. We also know that any celestial body needs to be of at least a certain mass before it can retain an atmosphere, particularly an atmosphere composed of more massive molecules than those of hydrogen or helium. Lastly, we can probably safely assume that rocky and icy/rocky moons in general possess the materials from which they might gain atmospheres (avoiding the questions of precisely which materials they might have, potentially yielding what kinds of atmospheres); that moons are at best only a little less safe than planets are from many, many impacts during a system’s evolution; and that with planetary migrations, moons forming at one distance from star(s) may subsequently end up elsewhere. Consequently, we have the theoretical and intuitive basis to imagine that atmospheric moons, while far from abundant across systems, are nonetheless fairly common.

Indeed, moons can at least begin to acquire atmospheres from either the release of gases or other materials from within them, or from the delivery of materials via impacts (possibly among even more processes), and the high likelihoods of impacts to moons, planetary migrations, and then the fact that rocky and icy/rocky moons presumably already have suitable materials to result in gases, suggests that atmospheric moons should be common. Of course, most moons, being “very small”, are comparatively low in mass as well, meaning most moons simply aren’t massive enough to support atmospheres regardless. But for the “large” moons in systems, presumably most either have surface ices that can change to gases to form an atmosphere, or else materials within that could end up coming to the surface (for instance by volcanic eruptions, or even just through fissures in the surface), while all moons can have material brought to them via impacts. The only doubt then, is just how often any of these processes play out in such a way that a moon actually acquires an atmosphere. One idea, which Peter Tyson suggests in his essay “How to Get an Atmosphere” at NOVA’s website (sec. “A Moon With Atmosphere”), is that to acquire an atmosphere from the release of gases within a moon, the moon in question needs to be close enough to its planet such that tidal forces keep it geologically active. Since moons are naturally spaced in varying distances from a planet (in stable orbits), it doesn’t seem so improbable then that systems might often have a “large” moon that just happens to be “close enough” to its planet such that gases eventually form an atmosphere, having been released from its interior due to geological activity maintained by tidal forces.

Further, as already suggested, impacts throughout a system’s evolution are common and inevitable, while planetary migrations are perhaps fairly common as well, and, in fact, such impacts or migrations can, respectively, deliver atmospheric materials to moons, and move moons to places in systems that allow icy materials to become gaseous. Indeed, it remains unknown why, in our own system, Titan has an atmosphere while Jupiter’s “large” moons don’t (particularly Ganymede and Callisto), and yet we do now know, from chemical analysis, that the nitrogen in Titan’s atmosphere came from the outer reaches of our system (see the news article “Titan’s Building-Blocks Might Pre-Date Saturn” at the Jet Propulsion Laboratory’s website), strongly suggesting delivery via impacts. And, in an interview at NASA’s website (see “Saturn’s Moon Titan: Planet Wannabe“), Jonathan Lunine has earlier suggested the possibility that Titan, being farther from the Sun than Jupiter’s moons, was cold enough such that ices became trapped in its interior, which then (again, perhaps due to it’s closeness to Saturn, per Tyson’s NOVA essay) yielded at least part of its atmosphere. Incidentally, while this does bring up the distance between a moon and its star(s) as an issue, keeping in mind that planets may readily migrate during a system’s development, the suggestion is that even if a moon needs to be initially “distant” from a system’s star(s) in order to begin getting an atmosphere in this way, thanks to planetary migration, such a moon could ultimately end up anywhere in the system. So, if a moon ends up sufficiently close to its system’s star(s), then even the tidal forces suggested by Tyson perhaps wouldn’t be needed to create the atmosphere, because the heat from the star(s) might change the ices into gases, allowing them to seep up from below the surface (not to mention that the surface itself would likely be icy beforehand as well).

Overall then, so many common processes can make moons atmospheric that it almost seems the only real challenge to moons becoming so is that most are of insufficient mass, and hence incapable of holding atmospheres regardless. Otherwise, with “large” moons comparatively rare yet still common in systems, it would seem that atmospheric moons must be fairly common as well, albeit around “large” planets only. Granted, if atmospheric moons were extremely common, then in our own system, moons like Ganymede and Callisto would probably have atmospheres similarly to Titan. When we consider reasons why they don’t though, what’s interesting is that of reasons we can think of, the reversal of at most two would have permitted them to have had atmospheres after all. For instance, maybe they’re too far from Jupiter to be geologically active (per Tyson’s idea in his NOVA essay); maybe they formed too close to the Sun to be sufficiently icy (per Lunine’s remarks in his NASA interview); maybe impacts never delivered the right materials to them; or maybe Jupiter didn’t end up closer to the Sun (and of course it didn’t), so they didn’t either. Now certainly, reasons other than these that we’re not as yet privy to might account for the lack of atmospheres around Ganymede and Callisto; yet our potential reasons all involve common and plausible processes, and if at most two or, for some reasons, even just one of these processes had played out differently, Ganymede and Callisto would almost certainly have atmospheres today. (In particular, if either had been impacted by the “right” objects, and had perhaps subsequently ended up closer to the Sun; or, if either had ended up closer to Jupiter, and had perhaps formed farther from the Sun.) Hence atmospheric moons should be common around “large” planets in systems, except that precisely how common, we can’t quite say. We’ll imagine at least one in every two systems then, although again, this number is highly speculative, with little to precisely support it.

Moons or Rings Around Other Moons

Lastly, to re-visit the distribution of moons and rings plus everything else covered up to this point, we may ask, how prevalent are moons and rings around other moons? And the answer here, most likely, is that they’re very rare but not entirely absent from systems, and when moons of other moons do occur, they’re always “very small”, rocky or icy/rocky, and non-atmospheric. Indeed, as Fraser Cain discusses in his Universe Today article “Can Moons Have Moons?“, the problem with moons of moons is that the gravitational influences between a planet and its moons mean that any would-be moon of a moon would be unstable (that is, have an unstable orbit), unless, perhaps, the planet was massive and its moon “distant” from it. It appears then that while, for instance, moons orbit planets orbiting stars, it’s the extreme mass of stars and the distances between planets and to their star(s) that make this possible. Whereas, planets usually have moons orbiting much closer, relatively, both to each other and to the planet, and aren’t proportionately massive enough to enable moons to stably orbit any of their moons. We should also keep in mind that aside from whether a moon could stably orbit another moon (calculations show, for instance, that Saturn’s moon Rhea could stably support a moon, and that it may or may not currently have rings; see the Wikipedia article “Natural Satellite,” sec. “Satellites of Satellites”), the even greater difficulty would be a moon keeping a moon throughout the progression of its planet’s chaotic development.

Finally though, wherever moons or rings of moons may exist in the cosmos, our conclusions to this point should apply to them. Hence, for instance, yet another reason that moons seldom have moons or rings is that moons, being “small” rocky or icy/rocky bodies, don’t readily obtain either, any more than “small” planets do. Also then, any moons of moons must be “very small”, certainly not atmospheric. It would seem then that any moons or rings of moons would be most notable simply because of their existence, and would otherwise be fairly unremarkable.

Possibilities and Conclusions

One overall conclusion we may finally reach then is that perhaps disappointingly, our own system, in terms of its moons and rings, is pretty typical. All of it’s “large” planets have multiple moons and rings, but only a few moons of which are themselves “large”, and only one set of rings that’s extensive. Also, moons around its “small” planets are scarce, with a couple captured but only one that formed from a non-unitary process, while rings around its “small” planets are totally absent. Further, our system has no icy/rocky/gaseous moons, and while one moon does have an extensive atmosphere, none of the others, even the other “large” ones, do. Finally, none of its moons have moons of their own, although one may possess rings (see the Wikipedia article “Natural Satellite,” sec. “Satellites of Satellites”). Indeed then, results such as these are predicted by our earlier conclusions: that nearly all “large” planets have moons and rings, including a few “large” moons and not uncommonly a more extensive set of rings; that there’s often at least one “small” planet with a handful of captured moons, while objects resulting from non-unitary processes exist in perhaps three of every ten systems at best; that virtually no icy/rocky/gaseous moons exist; and that atmospheric moons occur in perhaps one of every two planetary systems. What the galaxy and perhaps all the cosmos looks like in terms of moons and rings then actually comes out somewhat uninteresting (assuming we are at all correct in our conclusions), for it seems we have a little of everything.

It’s actually quite certain, however, that we don’t have “a little of everything”, and that there’re probably some pretty cool objects awaiting our direct observation. The reason is simply that planets and moons can differ in ways that we haven’t dwelt on, either because they don’t fundamentally change our conclusions, or else because they’re as yet too speculative. For instance, rocky planets and moons can differ based on precisely which elements made up the material discs from which they formed, such that planets may exist with abundant diamond on and erupting from the surface, for instance, and with lakes, rivers, or seas of tar and methane and such (see the Wikipedia article “Carbon Planet“). Or, icy/rocky planets and moons, having formed “far” from their star(s), may subsequently migrate closer in, melting the ices and forming objects where oceans aren’t just a light covering on top of land, but are rather the vast bulk of the object (see the Wikipedia article “Ocean Planet“). In fact, it’s interesting that whereas the traditional division of planets is rocky or gaseous (what we’ve been referring to as rocky or icy/rocky/gaseous), more properly (in common terms), it’s rocky, gaseous, or icy. And, whereas rocky and gaseous objects generally retain their forms no matter how far or close they end up to their star(s), icy objects are primarily solid when “far”; liquid when “close”; and even gaseous when “closer”, except not gaseous as the term typically means (composed of hydrogen and helium), but instead, composed of gaseous forms of water, ammonia, and various other ices. None of these types of planets and moons are radically different from what our own system has (at least in principle), except that in common terms, they’re quite unique, and should be exciting to eventually see.

Further, perhaps the seeming typicality of our own system is nonetheless more than it currently seems. For instance, although Jupiter’s moon Europa is probably the most famous for likely possessing a sub-surface water ocean, several icy/rocky moons of the outer planets in our system are presently thought to have such oceans (see, for instance, the article “‘Death Star’ Ocean? Seven Moons That Could Host Huge Hidden Liquid Reservoirs,” by Elizabeth Howell at Universe Today), and given just how typical such moons presumably are across systems, it’s likely that sub-surface oceans are quite abundant throughout the cosmos’ moons at large. Of course, if such oceans are only ever simple oceans, then maybe they’re not such a big deal, and are just as banal everywhere else as they may be here. But if instead, say, they frequently harbor microbial life, then they may even be quite significant in the distribution of life in the universe, a topic otherwise far, far beyond our present scope. Although our conclusions suggest then a disappointing typicality of our own system’s moons and rings, there’s no reason to fear that nothing “new” or really exciting is out there, because despite our conclusions here, certain possibilities and exciting objects are still plausible.

Perhaps in closing then, we should simply acknowledge that while astronomers and physicists are ultimately working to account for everything in the universe (a task we just indulged in ourselves, at least with respect to moons and rings), until they do, there may yet things out there that’ll truly amaze us, and likely even shake up our expectations a bit. And lastly, if we recall that despite our own working definition of the term, planets commonly exist outside of systems too (see the Wikipedia article “Rogue Planet“), then we may even wonder as well what kinds of moons or rings these planets typically have. (Of course, granted, ones that’re presumably little different from those within systems except for the lack of light, but still.) The cosmos is indeed magnificent, including all the planets, moons, rings, non-unitary bodies, asteroids, comets, and various other celestial bodies that sprinkle the otherwise vast emptiness of it. Such give it form where, otherwise, there wouldn’t be anything at all, not least of all being, I suppose, our own little planet upon which we all as yet dwell … continuing to progress in our lives, yet still finding time to ponder the heavens just as we always have, since our time immemorial.

Endnote:

Regarding asteroid belts in planetary systems with rocky or icy/rocky planets, in our own system, it was Jupiter’s influence that prevented the asteroid belt from fusing into one or more planets (see the Wikipedia article “Asteroid Belt,” sec. 2.1), plus Jupiter, Saturn, and Neptune’s influences that made the Kuiper belt what it is today (per the “currently most popular model”; see the Wikipedia article “Kuiper Belt,” sec. 2, para.s 3 & 4). Furthermore, it’s believed that Uranus and Neptune originally formed between Jupiter and Saturn (later migrating outward), because the materials that came together in forming them would otherwise have been too distant from the Sun to have done so (see the Wikipedia article “Ice Giant,” sec. 2.1). Hence it’s clear that “large” icy/rocky/gaseous planets in a system can cause asteroid belts to form, but it’s also clear that the ratio of icy/rocky/gaseous planets to rocky ones almost certainly varies considerably between systems. Specifically then, the issue is that a star’s (or group of stars’s) energy output must be neither too great nor weak in relation to its gravitational force, or else either the region in which ices are available for icy/rocky/gaseous planets to form will be small or non-existent, or else the the region where rocky planets can form will be so.

Fortunately though, “small” icy/rocky planets can form alongside “large” icy/rocky/gaseous ones, so even if systems with both rocky and icy/rocky/gaseous planets turn out to be rare, plenty of systems still ought to have “large” planets that can cause asteroid belts to form close to “small” ones. Indeed, the majority of stars in our own galaxy at least seem to be only half-or-less as massive as the Sun (see the introduction to the Wikipedia article “Red dwarf“), and according to the mass-luminosity relation (see the introduction to the Wikipedia article “Mass-Luminosity Relation“), a star half-or-less as massive should be only one sixteenth-or-less as luminous. While mass isn’t the same as gravitational force, it’s directly proportional (to the product of the masses of two objects), so it seems that the majority of stars definitely have a region for icy/rocky/gaseous and icy/rocky planets to form, even if not necessarily a region for rocky ones to do so. (In fact, observations suggest that while only one in fifty such systems have a planet of Jupiter’s mass, about one in three have a planet of Neptune’s mass; see the article “Red dwarf“, sec. 2, para. 1. Unknown as yet however is how many of these systems have icy/rocky planets too, although with such systems being of little overall mass to begin with, it’s reasonable to think that such planets should be common, forming once the little hydrogen and helium there was has been taken.) Further, of course, systems with star(s) comparable in mass to our own Sun are plentiful outside of the majority too; systems where rocky, icy/rocky/gaseous, and icy/rocky planets should all commonly coexist.

Although only roughly figured then, the conclusion is that asteroid belts should be common across planetary systems, along with handfuls of moons that the “small” icy/rocky or rocky planets in such systems capture from them.

References:

Cain, F: “Can Moons Have Moons?,” Feb. 24th, 2014, at Universe Today as of March 3rd, 2015
[http://www.universetoday.com/109666/can-moons-have-moons/].

Howell, E: “‘Death Star’ Ocean? Seven Moons That Could Host Huge Hidden Liquid Reservoirs,” Oct. 17th, 2014, at Universe Today as of March 3rd, 2015
[http://www.universetoday.com/115373/death-star-ocean-seven-moons-that-could-host-huge-hidden-liquid-reservoirs/].

Jpl.nasa.gov: “Titan’s Building Blocks Might Pre-Date Saturn,” June 23rd, 2014, at the website of the Jet Propulsion Laboratory as of March 3rd, 2015
[http://www.jpl.nasa.gov/news/news.php?release=2014-200].

Loberg, J.E: “An Explanation of Why Some Planets Have More Moons Than Others Do,” video, at classroom.Synonym.com as of March 3rd, 2015
[http://classroom.synonym.com/explanation-planets-moons-others-17654.html].

Lunine, J: “Saturn’s Moon Titan: Planet Wannabe,” interview by Astrobiology Magazine, Aug. 20th, 2004, at the website of NASA as of March 3rd, 2015
[http://www.nasa.gov/mission_pages/cassini/whycassini/Saturns_Moon.html].

NRAO: “New Studies Give Strong Boost to Binary-Star Formation Theory,” Jan. 2nd, 2014, at Astronomy.com as of March 3rd, 2015
[http://www.astronomy.com/news/2014/01/new-studies-give-strong-boost-to-binary-star-formation-theory].

Space.com Staff: “Binary Star Systems: Classification and Evolution,” Aug. 23rd, 2013, at Space.com as of March 3rd 2015
[http://www.space.com/22509-binary-stars.html].

Tyson, P: “How to Get an Atmosphere,” April 4th, 2006, at the website of NOVA as of March 3rd, 2015
[http://www.pbs.org/wgbh/nova/space/how-to-get-an-atmosphere.html].

en.Wikipedia.org: “Asteroid Belt,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Asteroid_belt].

en.Wikipedia.org: “Carbon Planet,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Carbon_planet].

en.Wikipedia.org: “Double Planet,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Double_planet].

en.Wikipedia.org: “Formation and Evolution of the Solar System,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Formation_and_evolution_of_the_Solar_System].

en.Wikipedia.org: “Ice Giant,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Ice_giant].

en.Wikipedia.org: “Kuiper Belt,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Kuiper_belt].

en.Wikipedia.org: “Mass-Luminosity Relation,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation].

en.Wikipedia.org: “Moonlet,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Moonlet].

en.Wikipedia.org: “Natural Satellite,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Natural_satellite].

en.Wikipedia.org: “Ocean Planet,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Ocean_planet].

en.Wikipedia.org: “Origin of the Moon,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Origin_of_the_Moon].

en.Wikipedia.org: “Planetary Ring,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Planetary_ring].

en.Wikipedia.org: “Red dwarf,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Red_dwarf].

en.Wikipedia.org: “Rogue Planet,” at Wikipedia as of March 3rd, 2015
[http://en.wikipedia.org/wiki/Rogue_planet].

©2015, D.S. Applemin. All rights reserved.

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