# Question about the possibility of a Ternary planet system

Ok, I know it sounds very far-fetched, but I'm curious. We know that Binary stars truly exist, and that binary planets are all but confirmed.

Here's my insane question: can there be a TERNARY planet orbit?

Is it even remotely possible that three sister planets can orbit each other?

This would be awesome to add to my story, but I'd rather not include something that's absolute fiction.

• Assuming that your story will take part on these trinary planets (or binary in case the three-body-problem is thwarting your plans) - hoe is that not absolute fiction? – dot_Sp0T Aug 13 '17 at 6:12
• @dot_Sp0T The Three Body Problem [3BP] is only a computational problem, it is difficult to solve 3 simultaneous differential equations. Seehttps://en.wikipedia.org/wiki/Three-body_problem --- The Earth-Moon-Sun was the first 3BP and studied by Newton himself. The 3BP is only about us puny humans calculating whether such a system is stable or not: Obviously the Moon orbits the Earth and the pair orbit Sol and this has been going on for billions of years; so they can be stable. If anything, the OPs Q is about a 4-body problem: a stable 3B solution orbiting a star. – Amadeus-Reinstate-Monica Aug 13 '17 at 9:45
• Hi, welcome to Worldbuilding! When you say 'sister planets', do you mean planets that are similar sizes? Or do you mean similar masses? Or is there something else about them that has to be similar? Answers so far are pretty clear that you can have 3 body orbits with planets of considerably different masses, but personally I wouldn't consider these to be 'sister planets'... – Mithrandir24601 Aug 13 '17 at 11:41
• @Mithrandir24601 Yes, these three planets are all relatively the same size and mass of each other. Also, thanks for the warm welcome! – Rangoon Aug 13 '17 at 13:57

Klemperer Rosettes are (kind of) gravitationally stable sets of celestial bodies that come in many configurations and the definition includes a number of three world configurations. These sets are completely stable unless perturbed at which point they come apart immediately because they don't have any self correcting mechanism, like a gravitational centre.

• There are a couple of issues with this: The smallest configuration of Klemperer Rosettes consists of four bodies, not three, unless you're considering 3 larger bodies + 3 smaller ones, which isn't explicit in your answer. The other issue is that "completely stable unless perturbed at which point they come apart immediately" is actually the definition of unstable, not stable – Mithrandir24601 Aug 13 '17 at 11:34
• @Mithrandir24601 Klemperer specifically lists a three body system as a basic element from which to work. The systems are stable unless acted on by an external force just like any system under Newton One. – Ash Aug 14 '17 at 11:53
• Yes, he does. A Klemperer rosette consists of two of these 'basic elements'. 3 planets + 3 moons is fine - I was just clarifying that as it's not mentioned in your answer. For your second statement, that's not the definition of stable. If anything, you've just defined an unstable system – Mithrandir24601 Aug 14 '17 at 12:46

Any planet with more than 1 moon satisfy your question. Take Mars, or even better Jupiter or Saturn. That's the only way to have a stable sistem: a body largely more massive than the others, so that it can be the center of mass of the system. Other configuration are unstable on the long run.

### Yes. But it might not be satisfying...

In particular, you can have two co-planets orbit each other (by all rights the Earth Moon system should be considered co-planets; the Moon is larger than most moons in our solar system. But Saturn Titan is even a better candidate: Titan is 3200 miles in diameter and 80% more massive than the Moon).

Then they can orbit a much more massive object at some distance. Or alternatively, a much less massive object can orbit them.

As my comment above says; The Three Body Problem [3BP] is only a computational problem, it is difficult to solve 3 simultaneous differential equations.

That said, we already do know 3BP can be stable: I just gave two examples! The Earth-Moon-Sun was the first 3BP recognized and studied extensively by the guy that invented gravitational problems in the first place: Isaac Newton himself.

The Saturn-Titan-Sun system is another non-trivial example, and also stable. Titan is about half the diameter of Earth (the moon is a bit over one quarter the diameter of Earth). Titan is about 2.25% the mass of Earth (the moon is 1.2% the mass of Earth). Surface Gravity on Titan is about 85% of that on the Moon (this sounds counter-intuitive, but Titan is 44% less dense than the Moon).

The 3BP is only about us puny humans calculating whether such a system is stable or not: Obviously it is possible but in our examples (and what we know about other moons in our system), the stable ones have large factors of scale, at least as far as mass: factors of 20 or more.

In terms of mathematics, this allows orbits that cause small perturbations, so in laymen terms they basically cancel out or can be ignored, as long as we don't have any resonance patterns that cause an amplification of relative movement (so that some part reaches either escape velocity or gravitational collapse so they crash into each other).

but the mass factors should not concern you too much: Our Moon is 1.2% the mass of Earth but has a surface area that is 7.4% that of Earth; 14.7 million square miles; about 4 times the size of China (or USA). Plenty of space to support a population.

If the Moon were denser it would have a smaller radius and therefore a higher surface gravity. Platinum is a very dense element; about 3x that of iron and a noble metal (not very reactive). If nearly the entire mass of the Moon were Platinum (say except for a crust about a kilometer deep), the radius would be 934.9 km (instead of 1737.1), and the surface gravity would be 57% that of Earth. That might be enough to hold a breathable atmosphere.

Good luck!

• The three body problem is not difficult to solve, it is unsolvable. All gravitationally bound system consisting of more than two bodies are chaotic; if all but one or two of the bodies are very small the chaos may take some time to manifest itself, but it is still there; for example, the very own Solar System is chaotic on long enough time scales. As for your Sun-Earth-Moon example: (1) the Sun is much more massive than the other two, and (2) it is not a stable system; the orbit of the Moon cannot be calculated with precision over more than a few centuries... – AlexP Aug 13 '17 at 13:21
• @AlexP Unsolvable? Good to know mathematics has reached its finale, I guess. An inability to predict more than a few centuries? Stability is clearly only important over some reasonable time period, and a few billion years of the Moon orbiting the Earth and those two orbiting the Sun should clearly qualify as "stable"; it is stable enough to persist over evolutionary time scales (longer than there has been life on Earth, to our current state of knowledge). You are being argumentative for no reason I can discern: I answer in service to a layman's question about fiction, not theoretical math. – Amadeus-Reinstate-Monica Aug 13 '17 at 16:25

According to the Three Body Problem, a ternary planet would be unstable because this, actually, would involve at least four bodies: The triple planet plus the star they're orbiting (plus another possible planets on the star system).

I have two different suggestions for you:

However, there are triple star systems which are stable. A small, rocky, planet-sized habitable moon could, then, be orbiting a double gas planet from a relatively large distance and in a ressonant orbit, in a way that the double planet could be considered a single source of gravity.

But the most radical and cool idea is to put the planet somehow on one of the Lagrangian points of the double planet. Again, the more massive these two were the most stable the Lagrangian orbit would be. There's a well known gravitation result for two large and close bodies called the Roche geometry. These contours show imaginary surfaces with constant gravity, and the L1 to L5 points are the Lagrangian points, points in space with the gravity pull from both bodies cancel each other.

You don't need to go far away to see this. Jupiter and Saturn have dozens of asteroids trapped on their L4 and L5 points. For Jupiter, these are called the Trojan and the Greek asteroids. In fact, trojan is a generic designation for any kind of asteroid that sits on a Lagrangian point of a planet.