Can a moon have a moon?
If so, what would we call such an object?
And do we know of any moons out there
that could possibly pull this off?
A few years back my research team discovered
Kepler 1625b-i, the first exomoon candidate.
But what made the candidate particularly
astonishing was the enormous size.
A Neptune-like moon orbiting a super Jupiter-mass planet.
Still to date, we don't know
whether the candidate was real or not
because Kepler suffered a mechanical failure
preventing it from re-observing the star.
Nevertheless though, just last year
and right here in the Cool Worlds lab,
we found the second exomoon candidate, Kepler 1708b-i.
Once again, the object was rather startling, though,
a mini Neptune-size moon, this time,
around a Jupiter-size planet.
Even though these objects remain unconfirmed,
they have sparked plenty of discussion
and one question I've received again and again
is could these moons have their own moons?
Now since Kepler 1625b-i is a Neptune-size moon,
then the temptation is to compare it to Uranus and Neptune.
Both of which, of course, have dozens
of satellites around them
and so, by extension, submoons
might seem quite promising then.
But, of course, Uranus and Neptune are planets,
which means they must have had a very different history
than that of Kepler 1625b-i.
Perhaps efficiently so that we really
shouldn't expect to find anything in orbit.
Probably the simplest thing we can say
without any controversy,
is that at least for a small satellite,
yes, it is possible to put that in orbit of a moon
because, hey, we've already done it.
In fact, we've been doing it since the 1960s.
In March 1966, the Soviet mission, Luna 10,
became the first of now many vehicles
to successfully orbit the moon.
In fact, completing over 460 orbits
before the mission was terminated.
But whilst that was indeed a satellite,
it wasn't a natural satellite nor indeed a long-lived one.
And of course we have to admit
that by astronomical standards,
those were just tiny objects.
So the question remains.
How large of a moon can sustainably orbit
around another moon?
To figure this out, let's take a step back
and ask even if these moons
somehow form their own satellites,
let's call them submoons for the moment,
would those submoons survive for billions of years?
It's one thing to make a submoon,
it's another thing to hold onto it.
A smaller body in orbit of a larger body
can be lost through two basic processes.
They either get too close or too far apart.
If they get too close, then the smaller body
can get tidally ripped apart or even just
crash together in a dramatic encounter.
On the other hand, if they drift too far apart,
then the gravitational tug of other bodies
in the system can disrupt the pair.
Now for a moon orbiting a planet,
their primary other source of gravity
is the star which the pair orbit
and the threshold distance of which the star
will essentially steal away the moon
defines the so-called Hill sphere,
one of the most important concepts in orbital dynamics.
If a moon drifts outside of this region,
which technically isn't a perfect sphere,
then it will be lost.
Or, in fact, usually even about half
of the Hill radius is often sufficient.
Now, the reason why this inner and outer distance
matters so much is because the orbits of moons
gradually evolve over time.
Every moon in the Solar System
is slightly changing its orbit each and every day.
Nothing has permanence.
Our own Moon exemplifies this,
moving away from us by four centimeters every year.
But why? Because of one word, tides.
The Moon raises tides on the Earth,
giving us two high tides per day.
This happens because the Moon's gravitational influence
is slightly different across the Earth's surface,
gently massaging the oceans
towards the sublunar and antilunar positions,
causing this bulging effect.
Now, since the Earth rotates once every 24 hours,
which is much quicker than the Moon's revolution,
then this bulge can be thought of
as trying to overtake the Moon.
But then it gets pulled back
through the gravity of the Moon again.
This effectively slows the Earth down,
gradually reducing its spin over time.
However, since the Earth-Moon system,
like any other pair of objects,
has to conserve angular momentum,
then the slowing down of the Earth demands
an increase elsewhere in the system,
Like a skater sticking its legs out to slow down,
the Earth can be thought of as sticking its moon out,
pushing the Moon away into an ever wider orbit.
If we could make the Moon more massive,
then this process would happen even quicker,
because the tides raised on the Earth would be greater.
But make the moon too heavy,
and the recession rate becomes so fast
that the Moon will escape the Hill sphere
in just a few billion years or less,
thus defining an unstable moon.
So look, really, you can put any sized moon
around any sized planet and be okay,
at least in the short term.
But if you want stability for billions of years,
then very large moons become precarious,
because of their very rapid tidal migration rates.
And I should also note that these motions
don't always have to be a recession.
The Moon would actually slowly fall into the planet
if the Earth was spinning slower
than the Moon's revolution rate, a lunar month.
It would be an understatement
to say that the film, Moonfall,
did not accurately portray this on the big screen.
This process of migrating in or out,
also known as tidal acceleration,
is the primary limiting factor
as to how big of a moon a planet can hold onto.
And so by the same token,
it is also the primary limiting factor
as to how large of a submoon a moon can hold onto.
In the same way that a planet has a Hill sphere around it
where it's gravity dominates over that of the star
allowing for moons, a moon also has a smaller Hill sphere
around it where its gravity dominates
over that of the planet, allowing for submoons.
But merely residing within the moon's Hill sphere
is not suffice, the submoon must also be small enough
that it can stay there for billions of years.
Too big and the tides that it raises upon the moon
will cause the submoon to exit that region too expediently.
Much of the theory of moon tidal evolution
was worked out decades ago, especially
in a classic paper by Barnes and O'Brien in 2002.
And so, starting from this,
one can really just reuse that theory
but just switch over the labels to apply this to submoons.
And that's exactly what Kollmeier and Raymond did
back in 2019, shortly after we announced Kepler 1625b-i.
So let's take a look at their results
and start with Saturn as an interesting test case.
In this figure, we're assuming
that the submoon is pretty small,
just 10 kilometers in size as a fiducial example.
On the X and Y axes, the authors
are varying the properties of their host moon.
Specifically, the X-axis varies the distance
between Saturn and the moon
and the Y-axis changes the size of that moon.
Kollmeier and Raymond find that any moons
above this line could hold onto a 10 kilometer submoon
so this seems good news.
Indeed this result should make sense.
The further away the moon is from Saturn,
the larger its Hill sphere will be,
because Saturn's gravity diminishes at larger distances.
We can also change the submoon
from 10 kilometers in size to 20 kilometers,
which gives us this dash line,
or five kilometers, giving us this dotted line.
So far, this is pretty generalized,
but now let's add Saturn's actual
real moons onto this diagram.
Titan, which is by far the biggest moon around Saturn,
is certainly in the running for holding onto a submoon,
but really, it's her less famous brethren, Iapetus,
that steals the show as the best submoon host.
In fact, according to this model,
Iapetus should be able to hold onto a submoon
up to a respectable 195 kilometers in size,
which is about the size of Mimas.
Now looking at the other Solar System planets,
Callisto around Jupiter and the Moon around the Earth
are also capable of holding onto small submoons,
but neither displace Iapetus as the submoon king,
at least in theory.
Now Iapetus does not have any known submoons,
nor indeed do Callisto, Titan or the Moon.
So does this therefore establish
that submoons are impossible?
Well, not quite, because remember that moons
are constantly changing in their orbits.
So it's quite possible that these moons
start out their lives closer to their planets,
had smaller Hill spheres around them
as a result of that and then consequently
lost their submoons fairly expediently,
so we just don't see them today.
In fact, Kollmeier and Raymond highlight
that Iapetus may, in fact, already be presenting us
with clues about a previous submoon.
You see, Iapetus has this interesting ridge
running along its equator,
which largely remains a mystery in planetary science.
In 2011, it was suggested that something
may have smashed into Iapetus,
forming a temporary submoon as well as a ring of debris.
Over time, the submoon may have evolved
outwards and eventually escaped,
just as we've been discussing in this video,
but the ring of debris instead
may have reigned inwards, forming the Ridge.
Submoons in the Solar System are certainly fun to imagine,
but the prospects of submoons become much more interesting
when we look out to these new giant exomoon candidates
that we've recently discovered,
things like Kepler 1625b-i.
In this case< the moon is estimated to be capable
of holding onto a much more formidable submoon
of similar size to the dwarf planet, Ceres.
Of course, such a submoon would still be too small
to be detectable with current technology, even with JWST.
But if these giant exomoon candidates are real,
then that suggests there should be more of them
out there in the cosmos and perhaps then,
there are even better submoon hosts,
just waiting to be found.
So could we imagine an even more suitable submoon host?
One extreme case we can consider
is taking Jupiter around the Sun,
but making it 10 times more massive,
a super Jupiter planet,
yet not heavy enough to be quite a brand off.
Now imagine that we put a Neptune-like moon around it,
similar to Kepler 1625b-i,
but parked much further out at 800 planetary radii,
which would still be within half
of a Hill radius away from the planet.
Okay, so fa, so good.
That Neptune-like moon would be plenty stable out there.
Now we could put a pretty big submoon around that moon.
Let's go for an Earth-size one for fun.
Such a submoon is perfectly stable as long as the moon host
is at least 100 planetary radii away from the planet,
which, of course, is true,
because we chose 800 for that number.
So to recap, we have a Sun-like star
that has a super Jupiter-like planet
that has a Neptune-like moon that has an Earth-like submoon
and so one question we might ask
is could that Earth-like submoon itself have a moon?
So I don't know what we'd call that.
It's kinda ridiculous.
A moon-moon-moon, a sub-submoon, you tell me.
The Neptunian moon here has a Hill radius
of 276 Neptune radii,
so let's park our submoon at 130 to be safe.
And by placing it like that, our submoon
would have its own little Hill radius around it
of 135 Earth radii, plenty of space
for a sub-submoon, it would seem.
Putting something at the outer limit of about half of that
for stability is that 60 Earth radii
that would allow for a maximum sub-submoon
of something like 50 kilometers in radius.
Not too shabby, a good size for an asteroid-based, perhaps.
So initial calculations do indeed suggest
that yes, you can have moons of moons
and perhaps you can even have moons of moons of moons.
Although you need some fairly
well-chosen parameters to pull that off.
However, one issue is that the current calculations
allow for the submoons orbit to evolve, but not the moon
and that's really not realistic,
because we know that moons tidally migrate as well.
Anyone looking for a good research project here
could perhaps revisit these calculations,
accounting for that motion, which would undoubtedly
reduce the range of submoons further,
but I doubt it would be enough to make them impossible.
I'm happy to offer any tips if you take that up.
So if we do find one of these things one day,
what should we call them?
I've been using the phrase submoon in this video,
but others have suggested moon-moon
or perhaps we might even imagine moon-squared or moon-cubed.
But another suggestion might be just to drop
the word moon altogether because it's confusing
and after all, we don't call moons subplanets
or planet-planets so why are we doing that here?
I'm sure you have some ideas.
Please do let me know down below
in the comments what you think.
As a final thought, these calculations remind us
that wholly astronomical objects
might yet be lurking amongst the stars.
I think that this underpins why astronomy,
despite being the oldest of sciences,
still captivates us like none other.
For even today, we've barely scratched
the surface of what await us out there.
Submoons, quark star, cosmic strings and much,
much more that we've likely never even imagined.
For many, I know that these unknowns can feel frustrating.
Perhaps we might wish that we had been born
at a time when all had been found.
But for me, I think it's worth cherishing
that we get to live in an age of discovery,
in a time where our imagination can still wonder.
So until next time.
Stay thoughtful, stay curious.
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Thank you so much for watching, everybody.
If you enjoyed this and wanna support
my research team's hunt for exoplanets, exomoons,
and, hey, maybe even submoons and sub-submoons as well,
then be sure to click the link up above
where you can become a donor to my research team
at Columbia University, just like our latest two donors
who I want to personally thank.
That is Lee Deakin and Ryan Provost.
Thank you so much for your support.
So thanks again for watching
and see you around the galaxy.
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