New Horizons will soon reach Pluto, and is expected to find new moons and possibly a ring system. Could it find a moon of a moon? Or a moon with rings? Or, is that impossible? Is there anywhere else in the solar system that could have moons with moonlets?
As we search for an answer, we will find out about why our Moon finds it hard keep a satellite at all, even just for a few years, and why an early satellite released by Apollo 16 unexpectedly crashed into the Moon. Also we’ll chase up an intriguing puzzle about Saturn’s moon Rhea.
Let’s start with our own Earth / Moon system. Why is the Moon’s orbit stable – and why can’t our Moon have moonlets, or can it?
MOON NEVER ABLE TO CATCH UP WITH ITS OWN TIDES
The Moon spirals outwards because of the lag in the tides. If the tides could respond instantly, so that you get the highest tides when the Moon is exactly overhead, then the tides would have no noticeable tidal effects on the orbit of the Moon.
Also, if the Earth’s surface never changed shape at all, like a steel bearing, say, again there would be no tidal drag. But for something as big as the Earth of course that is totally impossible, no natural material is as strong as that.
But instead, the tides lag just a bit behind the Moon in its daily apparent motion across the sky from East to West. That’s what it seems like to us. But from the point of view of the Moon, the tides are always a bit ahead of the Moon in its orbit around the Earth from West to East, and it never quite manages to catch up.
Drawing credit Andrew Buck This is the view from above the North pole. For someone on the globe at the equator at the top of the picture next to the arrow, East is to left of this picture, West is to right and North is out of the picture, pointing towards us.
Shows how the tides lag. The Earth is spinning right to left (from West to East). The Moon is orbiting in the same direction but much more slowly.
From our vantage point on the rotating Earth, we see the Moon traveling from East to West, rising and setting like the sun (though every day it rises and sets nearly an hour later in the day, because of its eastward drift against the night sky, see for example moon rise and set times for New York).
So from our vantage point, the tides seem to lag behind the Moon – the Moon passes overhead first, and the highest tides follow later on in the day.
But as far as the Moon is concerned, the tides keep ahead of it, on the more rapidly spinning Earth, and it never quite manages to catch up with them.
You get tides in the solid Earth, tiny tides, raise the land by about 30 cms or so. These are much more regular than sea tides. And you can measure the lag by satellite. It’s about 0.12 to 0.13 degrees.
Sea tides along coastlines lag much more, due to resonances in the oceans. The average tidal lag is six hours. So, often you find you get low tide when the Moon is at its zenith, the opposite of what you’d expect. See Currents and Tides. (This depends on local coastal conditions – sea tides are extremely complex depending on the coast, seas, islands, underwater features etc. There are many places with one high tide a day and other places with more than two high tides a day).
OUR MOON’S OUTWARD SPIRAL
These tidal forces pull the Moon in the direction in which it is orbiting. Which pulls it into higher and higher orbits around the Earth. Surprisingly this forward pull on the Moon in its orbit causes it to slow down rather than speed up, the opposite of what you’d expect intuitively. While at the same time it gradually slows down the Earth’s spin rate.
Aside about orbital mechanics
Orbital mechanics is a bit unintuitive sometimes. If you have a rocket in low orbit around the Earth, same height as the ISS, say, or lower – and you want to get it up to the much higher geostationary orbit, you accelerate in the direction of its orbit around the Earth.
You’d think it would make it orbit more quickly, but no, even though you accelerate constantly in the direction of motion around the Earth, it actually slows down relative to Earth. A satellite in GEO moves at 3.07 km/sec relative to the Earth while the ISS in its lower orbit moves at around 7.66 km/sec
So, even the Moon’s orbit is not totally stable, it keeps changing like that, getting slower and higher.
Eventually – as the Earth slows down in its spin, then (if it survives the sun going red giant that is) then the Earth and Moon become synchronous like Pluto and Charon each facing the other but at a huge distance apart.
And then – if they survive the Red Giant phase of our sun a billion or so years into the future, then over immense periods of time, under influence of the tidal effect of the sun, the system continues to evolve further. There are differing ideas about what happens next, one possibility is that the rotation speeds up again, Moon spirals in – the whole system losing energy in the process and eventually the Moon hits the Earth, at which point the Earth is spinning rapidly much as it did when the Moon first formed.
Anyway. so even the Sun / Earth / Moon system is not stable long term but is evolving and eventually either the Moon would hit the Earth or the Earth would lose the Moon over really huge timescales.
But it is stable over the billions of years that have elapsed so far.
The Moon spirals outwards because its orbital period, the lunar month, is longer than the Earth day. If the month was shorter than an Earth day it would spiral inwards.
MOONLETS OF THE MOON WOULD SPIRAL INWARDS UNDER INFLUENCE OF TIDES
A moonlet orbiting the Moon has to orbit really close to it, as the “Hill sphere”, the furthest away it can get and not be captured by the Earth is just 60,000 miles above the surface). So our moonlet will orbit far faster than the Moon’s 28 day rotation period. Typically, it orbits the Moon every couple of hours or so.
This movement will set up tiny tides in the Moon, through the gravitational tug of the satellite. And those in turn will pull back at the satellite. But this time they pull backwards on its orbit, instead of forward, because the tides can’t keep up with the motion of the satellite around the Moon and lag behind it.
So that then has the effect that the satellite gets faster and faster (same paradoxical thing as before, pulling backwards on the moonlet this time pulls it into a lower orbit with a faster period) spiraling in towards the Moon and eventually hits it.
However, tidal effects are less for small objects. As you can imagine, the tides raised by a tiny moonlet, say of a few tens of meters diameter, or an artificial satellite are tiny, and have little effect on their orbit.
So though if you do a web search you’ll find many posts and even articles by people saying that the reason the Moon hasn’t got natural satellites is because of tidal effects – actually that’s not the main reason at all.
There is another effect that makes it really hard for the Moon to capture a satellite. Our Moon would be unable to keep most natural satellites, however small, for more than a year or two usually, and sometimes it can’t keep it for more than a month. That can’t be anything to do with tides.
THE REAL REASON WHY LUNAR SATELLITES AND MOONLETS CRASH INTO THE MOON
This was first discovered in April 24, 1972. The Apollo 16 astronauts tried to put a small satellite called PFS-2 into lunar orbit to orbit every 2 hours. An earlier satellite PFS-1 was released by Apollo 15 and had been orbiting the Moon just fine for eight months. And they were in similar orbits originally, ranging from 55 to 76 miles above the surface.
But – to their surprise, PFS-2 rapidly changed the shape of its orbit. Within two and a half weeks, it was swooping down to within 6 miles of the surface. After a while it backed away again to 30 miles from the surface, but eventually, only 35 days after it was released, it hit the Moon.
The real reason that moonlets can’t form around our Moon are because of the Mascons – the concentrations of mass on the Moon.
As the satellites orbit the Moon their orbits are tugged one way and then the other by the Mascons, and these keep changing the shape of the orbits. They don’t make them spiral down – it’s not a tidal effect. Instead make them more or less elliptical. And eventually, in most orbits around the Moon the orbits become so elliptical they intersect the surface of the Moon and the moonlet crashes.
“FROZEN ORBITS” OF THE MOON
Some orbits are more stable. PSF-1 lasted for a year and a half, before it hit the Moon.
And there are a few “frozen orbits” where a spacecraft can orbit the Moon indefinitely. So those are good for mission planners who want to orbit the Moon for a long time without using a lot of fuel. But would be hard for a natural satellite to get into them.
I got this from the NASA page: Bizarre Lunar Orbits where they say
“There are actually a number of ‘frozen orbits’ where a spacecraft can stay in a low lunar orbit indefinitely. They occur at four inclinations: 27º, 50º, 76º, and 86º”
With moonlets of moons, the tidal effect isn’t that important over short timescales. And after all even the Moon’s orbit is not stable indefinitely, over billions of years.
So depending on the shape of the moon, I think a moon could have stable moonlets for at least some period of time..
So let’s look at this a bit closer
SOME ASTEROIDS HAVE MOONS TOO
Some asteroids have satellites and some even have two satellites. These are sometimes referred to as Moonlets. In this answer, I thought I’d use that word throughout for moons of moons as well, to help keep track of which is which in the discussions.
This is Ida, first asteroid found to have a moon, with its tiny moon Dactyl. Photo taken by Galileo spacecraft in 1993
The consensus seems to be that Dactyl was probably formed in the same event that created Ida, about 1.5 billion years ago. Unfortunately, Galileo passed Ida almost exactly in the plane of Dactyl, which made it almost impossible to pin down an orbit for it exactly.
As you can see, it is irregular in shape, and rather like the Moon, the orbits of Dactyl are complicated. Depending on your assumptions, you can end up with a chaotic orbit that never repeats exactly and lasts for 1.5 billion years. Or you may find with other assumptions that it escapes within a year, or impacts on Ida. Or you can find it is in a resonant orbit that repeats pretty much exactly throughout that time. See the long term dynamics of Dactyl’s orbit for techy details with plots of example orbits.
This is 87 Sylvia, the first asteroid found to have more than one satellite, its second satellite was discovered in 2004.
ASTEROID WITH RINGS
An asteroid can also have a ring system as well. This was a spectacular discovery in 2014 of the Rings of Chariklo. The images are thin and would be really bright to the naked eye if you were standing on the asteroid.
An artist’s view of the rings surrounding the asteroid Chariklo, which is only 125 kilometers in radius, and the rings are around 400 km in radius.
Credit: Lucie Maquet
So, that suggests we can widen the question and ask, not just, can a moon have moonlets – can it have rings also?
WHAT IF WE HAD SYLVIA WITH ITS TWO SATELLITES IN ORBIT AROUND EARTH INSTEAD OF THE MOON?
Suppose that, somehow instead of our Moon, we had 87 Sylvia, orbiting at the distance of the Moon. Would it be stable?
It’s easy to find out, as you just need to calculate the Hill radius, and there’s a simple formula for that (this is for the simplest case of a circular orbit; the formula is a little more complex for an elliptical orbit). I’ll indent all the calculations here, to make them easy to skip if you aren’t interested in the details:
where r is the radius of the Hill sphere, a is the semi-major axis of the moon’s orbit, m is the mass of the moon and M is the mass of the planet.
So, in case of 87 Sylvia, orbiting at the distance of the Moon, then m=1.478×10^19 kg.
M = mass of the Earth = 5.97219 × 10^24 kg
a = distance of Moon (semi-major axis) = 384,400 km
so r = 384,400*(1.478×10^19/(3*5.97219 × 10^24))^(1/3)
= 3605 km.
(BTW its diameter is 286 km).
So its Hill radius of Sylvia, if we had it in place of our Moon, is 3605 km.
Sylvia’s moon Remus orbits at 706.5 km, and Romulus orbits at 1357 km, both well within its Hill sphere. So the system would be stable if it was located in place of our Moon.
SHOWS THAT YOU CAN HAVE A MOONLET OF A MOON AT LEAST IN THEORY
So – it is clear that you can have a moonlet of a moon. If our Moon was replaced by Sylvia it would be stable over long periods of time just like Sylvia itself.
So – the main thing is – not whether they can exist – but if they can possibly form in our solar system. For instance how would an asteroid be captured around a planet, and do so without losing its moonlet? Or might the capture process (say a collision) actually create a moonlet?
WHAT ABOUT A MOONLET OF A MOON AROUND VENUS?
Could there be a tiny asteroid with a moonlet in orbit around Venus for instance, undiscovered? It seems an obvious place to look, similar size to the Earth.
If it rotated as fast as the Earth it could easily hold onto a moon as big as ours. But it has an veru slow rotation period, only once every 243 Earth days. So there is no way it can have a moon far enough away to spiral outwards rather than inwards. The tidal effects of Venus on any moon will always pull it inwards.
Even if it was hit by a big body that created a Moon like ours in the early solar system, then – long ago it would have spiraled in and hit the surface of Venus. Some planetary scientists think that exactly that might have happened
But a smaller moon could have survived for billions of years, because tidal effects lead to much slower rates of decay of the orbit for smaller moons. The researches calculated that Venus would need to have a moon less than a few kilometers in diameter to survive right up to today.
There was a search in 2009, which surveyed it down to 0.3 Km and didn’t find any moons. Page on ciw.edu in any case a moon that small would be low mass (far smaller than 87 Sylvia and have a tiny Hill sphere.
WHERE TO LOOK FOR MOONLETS OF MOONS
I suppose it depends how these moons form. If they form by collision, what you want is a tiny moon orbiting a long way away from a planet, and then hit by another moon so that a cloud of debris flies into space and then forms a moonlet about it.
The asteroid moonlets may well be just loosely clumped together piles of boulders, as may be the asteroids themselves also, these tiny ones like Ida and Dactyl – with such low gravity they don’t need to be held together strongly, may be more like loose rubble piles.
So if you have a place with lots of collisions happening, seems a place to look for moonlets.
So that’s something that could well happen I think some distance away from any of the larger planets.
SATURN AS A GOOD PLACE TO LOOK WITH SO MUCH DEBRIS IN ORBIT AROUND IT
If the moonlets form by collision, then you want a planetary system where there is a good chance of moons to hit each other or materials to hit the moons. And for that – well I’d say the Saturn system is a good bet. If we do find a moon with a moonlet, maybe we’ll find it there?
Here is one of the moons of Saturn, Prometheus
Saturn’s Rings and Moons are Solar System Antiques
It’s got numerous moons. So is quite promising. But none of them have confirmed moonlets, yet discovered, sadly. But it does get quite close. First the co-orbital moons:
It does have co-orbital moons Epimetheus and Janus.
This is not a double moon though it may seem so from this photograph.
Instead, they are co-orbiting and swap orbits. It is what can happen to what would otherwise be a moonlet of a moon, when the Hill sphere is too small to include both objects. So I think it is worth going into, it also helps to explain what the Hill sphere is all about.
Suppose for instance that Epimetheus is on the inside, as happens every 8 years, and Janus on the outside. Then Epimetheus is orbiting just 30 seconds per orbit faster than Janus. So it gradually gets further and further ahead of Janus until, four years later, it starts to catch up with Janus from behind.
When it does that, then Epimetheus pulls backwards at Janus – which causes it to go faster and drop into a lower orbit. Meanwhile Janus pulls forward at Epimetheus causing it to go slower and into a higher orbit. So then they swap places. Now Janus is on the inside, and Epimetheus is on the outside, and Janus will gradually speed away and so it goes on like that, swapping positions every four years. See Epimetheus (moon)
This gives a rough idea of how it works:
The main difference is that in that video, the green one is much heavier so its orbital radius doesn’t change. In the Saturn system, whenever the white one moves inwards in its orbit, the green one moves outwards, and vice versa. But otherwise it is just the same.
Here is another view this time in 3D, using rotating frame:
More about it here: The Orbital Dance of Epimetheus and Janus. That page includes a short video taken by the Cassini orbiter in 2005. It shows Janus and Epimetheus at the moment they change orbits (though it’s taken from within the plane of the orbits, and by a spacecraft which is itself also orbiting, so it is not so easy to see what is going on).
Here BTW is a simulation of four moons co-orbiting, something which could happen theoretically though no examples known, this is in rotating frame
HORSESHOE ORBITS – THE CASE OF EARTH AND CRUITHE
It’s related to the idea of a “horseshoe orbit”, like the much more complex orbit of 3753 Cruithnewhich is in a “bean shaped orbit” relative to Earth.
Or in a rotating frame, from Earth’s perspective
But something you don’t see in that animation, that “bean” is also gradually drifting around relative to Earth until it catches up with Earth from behind, similarly to Janus and Epimetheus – and then when that happens, then the Earth and 3753 Cruithne do a similar swap except this time because of the difference of size, 3753 Cruithne moves over half a million kilometers while Earth moves just 1.3 centimetres.
Nevertheless that swap will move the Earth outwards a bit, enough so that your year is a little longer from then onwards, until next time the swap happens. Then it swaps back again and the process repeats. The whole process takes around 770 years.
So anyway you can get co-orbiting moons, though they are rare.
WHAT ABOUT OTHER MOONS OF SATURN?
Saturn has numerous moons, wikipedia lists 62 so far. Outermost is Fornjot (moon) orbiting at a distance of 24,504,879 km from Saturn.
At six kilometers in diameter, it’s a little small, though many NEOs are smaller than that and have moonlets.
But let’s take the case of Phoebe (moon), the outermost moon of any size. It is also prograde – rotating Saturn in opposite direction to the planet’s rotation. And has a fast rotation period of 9 h 16 min 55.2 secs
m=8.292*10^18 kg (mass of Phoebe)
M = mass of the Saturn=5.68319 × 10^26 kg
a = semi-major axis of Phoebe= 12,955,759 km
so r = 12,955,759 *(8.292*10^18/(3*5.68319 × 10^26))^(1/3)
= 21950.5 km.
It is highly non spherical
But on the other hand it is really tiny, radius only 100 km. It’s not like an orbit at say 15,000 km away is close to its surface and going to be diverted into elliptical orbits as happens with the Moon. And Ida is very irregular also and has a moonlet.
So, could it have a tiny moonlet, orbiting up to 20,000 km away or so? Would it have been spotted if it had one?
Another obvious place to search is Titan.
m = 1.3452×10^23 kg (mass of Titan)
M = mass of the Saturn=5.68319 × 10^26 kg
a = semi-major axis of Titan= 1,221,870 km
so r = 1,221,870 *(1.3452×10^23/(3*5.68319 × 10^26))^(1/3)
= 52,406 km.
Its radius is 2,576 km. So a Hills radius of 75,582 km gives a fair bit of room for a tiny moonlet.
Since it is also highly spherical that might seem promising.
But it is tidally locked with Saturn, with a slow rotation of 15.945 days, and another factor that could count against moonlets, it may have a subsurface ocean which could lead to stronger tidal effects.
Still it would seem promising for a tiny moonlet or ring. Though I’ve not seen any suggestion that it could have moonlets or rings.
ONE OF THE MOST PROMISING PLACES TO LOOK, RHEA
One promising candidate is Saturn’s moon Rhea, its second largest moon and a long way from the planet, and at one time it was thought to have a ring system, with most of it within its Hill sphere. If this was true, it would be the only moon known with a ring system, which you could think of as lots of really tiny moonlets.
Artist’s impression of the rings of Rhea
And this shows where it is relative to the rings and the other moons – a long way out though not as far as Titan:
Sadly, later observations to try to confirm this found no evidence of any ring system. “A very sad story”: No rings for Rhea after all
But the jury is still out as to whether it has a ring system that somehow eluded discovery – or at least maybe did in the past, because it has these intriguing blue marks all around its equator, which may be the marks of de-orbiting ring material:
If Rhea does have a ring system, then just like Saturn it might have a shepherding moonlet outside of it helping to keep the material in place around the moon.
Rhea is a particularly good candidate because it is a near spherical moon (so not got the problem of irregular shape) – so if it doesn’t have Mascons like the Moon, orbits could be very stable around it. And though tidally locked with Saturn with a period of 4 days, it is not likely to have significant tidal effects on a tiny moonlet unless it has an underground ocean.
Let’s do our Hill sphere calculation for Rhea for completeness
m=2.306518×10^21 kg (mass of Rhea)
M = mass of the Saturn=5.68319 × 10^26 kg
a = semi-major axis of Phoebe= 527,108 km
so r = 527,108*(2.306518×10^21/(3*5.68319 × 10^26))^(1/3)
= 5829.7 km.
So its Hill sphere radius is 5829.7 km
Rhea’s radius is 763.8 km.
Rotation period (synchronous so same as orbital period) 4.518212 days
So anyway – whether Rhea does turn out to have a ring system or not, and whether or not it turns out to have a shepherding moonlet, in the modeling they did for the ring system, they did work out the physics of it all and showed that such a system could be stable over the duration of the solar system.
So the answer is a definite YES, in theory, moons can have moonlets, and even rings!
None are known for sure yet, but there is a distinct possibility that Rhea at least might still, some day, be proved to have a tiny moonlet or even a sparse ring system.
WHAT ABOUT THE PLUTO SYSTEM
This is topical with New Horizons doing a flyby mid July 2015. Might it discover a moonlet of a moon?
It would seem quite promising if moonlets are created by collision, since it’s moving rapidly in the Kelper belt and gets hit often with high speed collisions, and has many moons already discovered.
Also its many moons may have formed from a ring system, like Saturn, and it may still have rings. This is result of one recent simulation into the possibility of rings of Pluto.
Ring System Around Pluto?
Notice that the binary system in the middle clears out the central part of the ring, but beyond that, the orbits are circular.
First colour image of Pluto and Charon taken by New Horizons.
Let’s do our Hill sphere calculation for Charon first
m = 1.52×10^21 kg (mass of Charon)
M = mass of the Pluto =1.30900 × 10^22 kilograms
a = semi-major axis 17,536 km
so r = 17,536*( 1.52×10^21/(3*1.30900 × 10^22))^(1/3)
= 5931.9 km.
So its Hill sphere radius is 5931.9 km.
Charon’s radius is 603.5.
Rotation period 6 d, 9 h, 17 m
So its Hill sphere radius is 5829.7 km
Rhea’s radius is 763.8 km.
Rotation period (synchronous so same as orbital period) 4.518212 days
It’s an almost exact clone in terms of Hill sphere.
So it would seem that if Rhea can have a ring system, possibly even a moonlet to shepherd it, then Charon could too, at least on the basis of its Hill sphere radius. Though I can’t find any suggestion of this as a possibility in the articles I read.
Let’s also try Hydra, Pluto’s outermost of its known moons:
m = 4.2×10^17 kg (mass of Hydra)
M = mass of the Pluto =1.30900 × 10^22 kilograms
a = semi-major axis 64,749 km
so r = 64,749*( 4.2×10^17/(1.30900 × 10^22))^(1/3)
= 1426.6 km.
So its Hill sphere radius is 1426.6 km.
Hydra’s radius is 61 to 167 kilometers
Rotation period unknown
It is similar in size to Ida, possibly larger. And Ida’s moon Dactyl was only 90 kilometres away from the parent asteroid when it was photographed. Its orbit is unknown, so could be elliptical or circular.
But since then many asteroids have been found to have moons, at various orbits from less than a kilometer to over a thousand of kilometers from the parent. Even the most distant in that table, thePetit Prince asteroid of Eugenia – first moon of an asteroid to be discovered from Earth – has an orbit of 1184 as its semi-major axis so could just fit inside the Hill sphere radius of Hydra.
So, it would seem that Hydra could easily have a moonlet like Ida, in theory at least.
It has several other tiny Moons now known, Kerberos and Styx have been added to the list.
What about binary moonlets, a pair of moonlets both around the same size as each other?
You get binary asteroids, with two moonlets the same size, more or less.
This is an artist’s impression of the binary asteroid 90 Antiope.
Adaptive optics image of 90 Antiope taken by the W. M. Keck Observatory in 2000
Some binary asteroids are really tiny. Here are
Radar images of 1937 UB (Hermes) taken in 2013
This time the two moonlets are a really tiny 300–450 meters. (Since neither is noticeably bigger than the other I think have to call them both moonlets).
And the separation of the two is only 1200 meters (1.2 km).
In the case of asteroids, then about 15% of the Near Earth asteroids are binary. various mechanisms suggested, and – they seem like processes that could also apply to moons with a large Hill sphere, if there are other objects around that could hit them. Including – major impacts with an asteroid where the main body breaks apart into several parts, which then collect together to make several bodies in place of the original single body. Or an impact that doesn’t break the body apart completely but ejects enough material from a crater so that some of it in the cloud of material created gathers together to form a single moon that ends up in orbit around it. See this paper on Binary and Multiple systems of asteroids.
So again, by analogy with asteroids that often have moonlets, Pluto with its complex moon system, and situation where it is subject to high velocity incoming debris from material in the Kuiper belt, perhaps for fun, I can venture a wild speculation that Horizons might just find a double moon or a moon with a moonlet :).
Perhaps it may spot a tiny moonlet of Charon – or else – that one of the outermost moons is a binary moon.
It is just a fun idea :). I haven’t seen any speculations about this either way. Do say if you know of anything about this possibility. Is there anything that makes it unlikely?
What do you think, do you think there is a chance that some of the moons in our solar system, such as Saturn’s Rhea, might have undiscovered moonlets or rings? Do you think there is any chance that Pluto’s system could have a moon with a moonlet or a ring of some kind?
As usual if you spot any errors in any of this be sure to say, or anything that needs to be corrected. Thanks!
From my answer to the Quora question, “Do moons have moons”