Planets orbit stars. Moons orbit planets. But no moons have their own moons (let’s call them submoons). Why is that?

After Juna Kollmeier‘s son Levi asked her this question, she and I tried to figure it out.

Imagine a moon orbiting a planet orbiting the Sun. There is a zone close to the planet in which its gravity dominates over the Sun’s. This is the Hill sphere (although it’s sort of rugby ball-shaped). Any moons must orbit within the planet’s Hill sphere.

Zoom in further and we see the moon’s Hill sphere, where its gravity dominates that of the planet. A submoon must orbit within its moon’s Hill sphere. But that’s not the only requirement for stability. A long-lived submoon must stay far enough away from its moon to avoid being torn to pieces (like comet Shoemaker-Levy 9, which we discussed in relation to the potential origin of ‘Oumuamua). This means that the submoon has to orbit past the Roche limit, so the moon’s Hill sphere must be big enough.

Any submoon still around today must also have survived for billions of years in the face of tides.

Tides are just a consequence of gravity. The side of a moon that is closer to its host planet feels a stronger force of gravity than the far side. This causes a stretching of the moon and creates a tidal “bulge”. The moon’s gravity creates a corresponding bulge on the planet.

A moon’s tidal bulge tries to point at the planet whose gravity is doing the stretching. But in practice it usually doesn’t. Because moons and planets are spinning, a moon’s bulge either points in front of or behind the planet. In the picture above, that would mean that the lines of force would point a little above or below the center of Jupiter.

Tidal bulges couple moons and planets together. Through the bulges, planets and moons trade angular momentum, which changes their orbits and spin rates. These changes happen as energy is dissipated inside the planet and moon. In the most dramatic case energy dissipation can look like this:

Tides usually cause a moon’s orbit to grow and a planet’s spin to slow down. Our Moon’s orbit is currently growing at a rate of about 4 centimeters per year, and Earth’s day is lengthening by a corresponding 2 milliseconds every century. These changes were much faster in the past, when the Moon was closer to the Earth.

Things are more complicated for the case of a submoon orbiting a moon orbiting a planet. There are tidal bulges on the moon generated by both the planet and the submoon. The planet’s gravity affects how the moon spins, which in turn affects the submoon’s orbit. And the energy dissipated inside the moon determines how fast this happens. There are three possible outcomes. Either a) the submoon’s orbit shrinks until it crashes onto the planet, b) the submoon’s orbit expands until it is almost as big as the Hill sphere and it is ejected from the moon, or c) the submoon’s orbit expands or shrinks slowly enough to be able to survive for billions of years.

Juna and I did a simple calculation of this process (using the results from this study). We asked: which moons can host submoons that might survive for billions of years?

The simple answer is: large moons far from their planets can host long-lived submoons. Here are a couple of figures — one each for Jupiter and Saturn — showing where the conditions are right for long-lived submoons in the space of moon size and orbital distance (grey = good for submoons):

As you can see, most of Jupiter and Saturn’s moons are too close to the planet to host submoons. Only Callisto (Jupiter) and Titan and Iapetus (Saturn) are capable of hosting submoons. All of Uranus and Neptune’s moons are likewise too close to their planets to host submoons. If those moons once had submoons, they have since been removed by tides.

Now let’s apply this to Earth and the Kepler-1625b, a giant exoplanet slightly more massive than Jupiter on an Earth-like orbit (although it’s hotter since the central star is more luminous than the Sun). What makes that system interesting is that it hosts the first candidate exomoon. Kepler-1625b-I is an unconfirmed Neptune-sized moon that may be on a relatively wide orbit around the gas giant.

This figure implies that Kepler-1625b-I could indeed potentially host a long-lived submoon. Pushing everything to the extreme, it could in principle host a submoon as large as Ceres! There is plenty of uncertainty, however. First of all, the exomoon itself is both unconfirmed and its properties are still pretty poorly constrained. And taken at face value the exomoon’s orbit is quite odd: it is inclined by about 40 degrees with respect to its host planet’s orbit. While our calculation did not take the inclination into account, it’s not clear that a submoon could be stable at all. I suspect there will be plenty of studies in the coming months of the stability of submoons in this system.

So why don’t Callisto, Titan, Iapetus, and Earth’s Moon actually have submoons? Maybe submoons just don’t form very efficiently. Or maybe submoons do form and then are destroyed. One reason submoons may be destroyed is that, as we saw earlier, tides make moons’ orbits expand. Our own Moon is thought to have been pushed out by tides from within a few Earth radii out to its current position at 60 Earth radii away. Earlier in their histories, many moons were closer to their planets, where submoons could not survive. So, while those moons are on good orbits for submoons today, any submoons they used to have would have been lost long ago. Of course, there are other ways that submoons may be lost, for instance by gravitational jostling between moons (in the same way that moons can be lost during planet-planet interactions; see here).

We now can answer the question we started with: why don’t moons have moons? Tides prevent most moons from having their own moons, because those submoons are lost. There is more to the story for moons that could host submoons but don’t. Those moons may just never have formed submoons, or perhaps submoons did form but were lost by another process. To take the next step: if a submoon system did exist, it probably couldn’t host its own subsubmoons because everything would be squished even closer together, making tides even stronger.

But all is not lost…..

Before we wrap up, let’s perform a thought experiment. Let’s imagine a setup like the Kepler-1625 system but that is friendlier to life. Let’s imagine a gas giant in the habitable zone of its star with a moon more massive than Neptune on a wide orbit. That moon could in principle host a long-lived submoon as large as the Moon, which we will imagine being a potentially habitable “mini-Earth”. It would look like Pandora from Avatar, only that big blue “planet” in the sky would be the host moon of a much more massive Jupiter-like planet. It would look something like this:

A habitable submoon system would be stable. It has a couple of interesting differences compared with a habitable moon system. Its day would be controlled by its orbit around its host moon, not around the planet or the star. For the setup that we’ve imagined — with a mini-Earth submoon orbiting a Neptune-like moon orbiting a mega-Jupiter — the submoon’s orbital period would be anywhere between about half a day and two days. Assuming that the submoon is tidally-locked to the moon, that would make its day about the same length as Earth’s! Habitable submoons would experience very strong tidal forcing from their host moon as well as the planet. Hopefully this wouldn’t preclude habitability, but volcanoes would probably be very common!

Questions? Comments? Words of Wisdom?

More information

A downloadable version of the short paper that Juna Kollmeier and I wrote about submoons.

More on the exomoon candidate Kepler-1625-b-I here, here and here, and more on habitable moons (with a focus on Pandora) here.

Technical references for tides in planet-star-moon systems (here, here and here). Juna and I used these as analogs for planet-moon-submoon systems.