# Can 3 planets rotate around each other like this?

I was wondering if three planets can rotate around each other so that:

• Two of the planets are smaller and rotate around each other

• Both of the smaller planets rotate around another, bigger planet.

It's a bit hard to explain, so I made a (low-quality, just illustrative, using Mercury, Venus and Earth like planets) animation using GIMP and Blender:

Is this possible (not exactly like in the animation, of course)?

• If it is possible, I will be impressed. Even more impressed if i can understand the mechanics behind it. Sep 1 '16 at 17:57
• This seems like the same basic concept as Moons of Moons of Moons. Sep 1 '16 at 18:08
• Relevant reading on Wikipedia: three-body problem. "Historically, the first specific three-body problem to receive extended study was the one involving the Moon, the Earth and the Sun." It becomes a four-body problem (which degenerates to a n-body problem) if you also add a central star.
– user
Sep 1 '16 at 20:18
• The Sun, Pluto, and Charon form a 3-body system like this. Sep 1 '16 at 20:35
• the big one is the sun, the medium one is the earth, the small one is the moon. Sep 2 '16 at 2:37

In theory, yes, this is possible. In practice, it would be a rare thing to encounter, just because the laws of nature can be fickle and somewhat unpredictable. I'm going to call the planet your animation shows as Earth as PB1 (Planetary Body 1). I'm also going to call the Mars one PB2, and the Moon one PB3.

There are some important bits, though:

• The Roche Limit: In short, the Roche Limit describes how close two planets can get before gravitational forces tear one or the other apart. Obviously, this mostly applies to PB2 and PB3, but also applies to PB1 and the paired PB2+PB3 system.
• The distance between PB1 and PB2+PB3 must be sufficiently large, so that PB2+PB3 stay in their orbits around each other. This allows us to say that the TB2+TB3 system acts like one big planetary body. I'll call this hypothetical planet of equal mass "J".
• Once the "J" system is sufficiently far away, the PB1+J system can be modeled just like any planet with a satellite. In fact, J can be more massive than the PB1, it just depends on how you like your sandwiches planetary systems. This means, in terms of mass, PB3=PB1>PB2 can happen. PB2>PB3>PB1 can also happen. According to your animation, though, you're looking at PB1=J.

You can fool with a planetary orbit simulator, like the one here, or here, or here, to find out how difficult it is to set up. (It's even harder to set up, say, a horseshoe orbit.)

Cem Kalyoncu messed around with the second simulator, and found some nice settings for your planetary system:

PB1: Mass: 200, Location: 150, 0, Speed: 0, 133

PB2: Mass: 100, Location: -100, 0, Speed: 0, -105

PB3: Mass: 100, Location: -50, 0, Speed: 0, 105

Thanks Cem Kalyoncu!

• Much better one: PB1: 200, 150, 0, 0, 130; PB2: 100, -100, 0, 0, -80, PB3: 100, -50, 0, 0, 80 Sep 1 '16 at 19:56
• Lol the PB+J system sounds pretty tasty. Sep 1 '16 at 21:26
• lol Be honest, did you use PB+J as a pun for a tasty snack? Sep 1 '16 at 22:17
• @DevNull Yes. It was my lunchtime. I even considered naming them "creamy, crunchy, and natural" but I thought that was too much. Sep 1 '16 at 22:24
• Yeah I logged in just to +1 the pun. That's my jam. Sep 2 '16 at 1:50

This is totally plausible, albeit with much larger separations than you show in the animation. You can easily have two bodies orbiting each other in space. Now, take one of those bodies and turn it into two bodies on a much smaller orbit. This works as long as the two smaller bodies are close enough that their mutual gravity is much stronger than the gravity of the other, distant body. (In technical terms, this means that the binary planet has to remain within the Hill sphere).

The punchline: there are plenty of little technical issues like tides, but this is totally plausible in principle.

It's basically analogous to multiple star systems, which tend to be set up in a hierarchical fashion, where any star is much closer to its closest companion than to any other star. If you're interested, I created a couple of fake systems in this mold. See here and here.

• " there are plenty of little technical issues" -- orbital simulators are particularly useful, because they help investigate whether any of those little technical issues turn out to accumulate over time, and occasionally fling one of your three bodies out of the system at enormous speed ;-) Sep 2 '16 at 1:03
• "Orbital simulations" are my day job ;) obs.u-bordeaux1.fr/e3arths/raymond Sep 2 '16 at 5:47
• I think this answer would be improved with some brief discussion of the stability of such a system, which also tends to be important to people trying to interact with/search for/live in them. Sep 2 '16 at 22:04

It's pretty easy to conceptually convince yourself that is possible. Just replace the biggest planet with the sun, the medium one with Earth, and the smallest one with the Moon and you have the same setup.

There is nothing special about stars, planets and moons as it applies to the way things orbit each other. It's just that the two smaller bodies wouldn't be planets by definition because they orbit another planet. They're both moons.

Your scenario is not super likely, because in order for the smaller bodies to stably orbit each other, they have to be sufficiently far away from the larger planet. But that makes them less strongly tied to it and more likely to be disturbed by something else like a nearby planet or just the central star.

• I don't think that is true, after making your suggested replacements the animation above would show the sun and the earth with its moon on the same revolution. Additionally it shows the earth with its moon on the same revolution. Neither of those things are the case in our solar system. The earth revolves around the sun and the moon revolves around the earth there are not on the same revolution path.
– John
Sep 2 '16 at 19:12
• @John "The earth revolves around the sun and the moon revolves around the earth there are not on the same revolution path." -- Sorry I really don't understand what you're trying to say. Surely, the earth and the moon revolve around the sun together. Sep 3 '16 at 16:08
• @John I'm not sure what you mean. In the original diagram, there are 3 bodies. The two smaller ones orbit the bigger one together, and the smallest one orbits the medium one as well. This is exactly the same setup as the Sun-Earth-Moon system, only the thing in the middle isn't rocky. What are you trying to say when you write "there are not on the same revolution path"? If you mean orbit, then there isn't actually such a thing as a single path Earth follows. It actually gets moved around by the moon constantly, so it isn't a smooth ellipse. Sep 6 '16 at 21:52
• I was just bringing up the point that the image above seems to show a smooth revolution where the moon and the earth revolve around a point as if their revolution path was close to a circle around that point. I agree that the moon will pull the earth some but in order to have a close circle revolution the two bodies in the smaller revolution would have to be very close in size.
– John
Sep 7 '16 at 13:25

Using the second simulator mentioned in the accepted answer, I came up with this:

This setup was like the OP wanted, and was stable for so long my computer ran out of battery, even when switched to the fastest mode.

• I think this answer would be improved with some brief discussion of the stability of such a system, which also tends to be important to people trying to interact with/search for/live in them. Sep 2 '16 at 22:07

Playing around with the sim suggested above, I got the configuration desired with the following:

Body 1 - Mass 200, position: x=0, y=0, velocity: x=0, y=-1
Body 2 - Mass 50, position: x=110, y=0, velocity: x=0, y=140
Body 3 - Mass 0.001, position x=125, y=0, velocity: x=0, y=305

This was stable for a very, very long time. Should be able to get this to orbit around a very, very massive star without too much headaches.

• I tested it, and it seems that body[3].velocity.y should be 31 instead of 305 to make it work.
– SOFe
Sep 2 '16 at 9:58
• Actually the "Double double" preset from that simulator already does the job.
– SOFe
Sep 2 '16 at 10:43
• I think this answer would be improved with some explanation of what you mean by "very, very long time." Millions of years might be great for an galactic empire's outpost or rest stop; not so great for independently-evolved life? Sep 2 '16 at 22:06

Well, yes.

For example, our Sun, Earth and Moon.

• That is only 3 objects, but the described situation has 4 (the implied star being the forth). Not quite the same. Sep 2 '16 at 12:45

I'm not sure if this is exactly what you're going for, but have a look at how Pluto and Charon interact with Pluto's moons:

https://en.wikipedia.org/wiki/Moons_of_Pluto