Eccentric rings of co-orbital planets
More than one planet can occupy the same orbit around a star.
As long as there are at least 7 planets evenly spaced along the ring, and the planets’ masses are appropriate, a ring of co-orbital planets is perfectly stable for billions of years (details here).
For Earth-mass planets orbiting a Sun-like star, the maximum number of planets that can share a ring is 42. It looks like this (planet and star sizes not to scale):
Within a co-orbital ring, the planets generally remain evenly-spaced, maintaining a constant separation relative to their neighbors. Except when they don’t.
If a co-orbital ring system gets kicked (maybe by a small stray planet), it can cause the planets to start interacting with each other. This may push the system into a co-orbital horseshoe constellation, like this one (full details here):
I recently wondered, could a co-orbital ring system remain stable if the planets’ orbit wasn’t circular?
As a theoretical astrophysicist, I have the tools to answer that kind of question. So, I ran some N-body simulations of a stretched-out (eccentric) ring of planets, accounting for gravity of the star and planets.
The answer is that eccentric rings of planets are surprisingly stable. Here is one of my first tries, with 12 planets — each the mass of Earth — orbiting a Sun-like star. The orbital eccentricity (or degree of stretched-out-ness) is 0.4 (or 40%). The orbit’s average distance to the star (semimajor axis) is 1 astronomical unit, or au (the same as Earth’s), but the closest approach to the star is at 0.6 au — interior to the orbit of Venus — and the farthest distance from the star is 1.4 au, close to the orbital distance of Mars.
Instead of being evenly spaced in distance, as for the circular co-orbital ring, here the planets are evenly spaced in time. As it travels along an eccentric orbit, a planet moves faster when it’s closer to the Sun, and slower farther out (following Kepler’s third law). So in an eccentric co-orbital ring, the planets are more closely-packed during their long cold winter, and more spread out during the hot summer. (Note, for an orbit this stretched-out, the seasons would likely be determined by the orbital shape rather than the tilt of the planet’s spin axis).
Next, I tried an extreme case in which the orbit’s eccentricity is 0.9 (technical note: the eccentricity cannot go above 1 because at that point the planet is no longer bound to the star). Again, it was perfectly stable.
In this case, the closest approach to the star is at 0.1 au, far closer than Mercury’s orbit to the Sun, in the realm of hot Jupiters. The planets’ farthest approach from the star is way out past Mars’ orbit (1.9 au).
I went ahead and tried packing 42 planets into an eccentric ring. I had a mathematically-backed suspicion that this would not be a stable configuration. Drumroll…. I was wrong. The 42-planet case is perfectly stable.
I burned almost two months of computing time running this simulation out past 100 million years to ensure that it remained stable. I saw no chinks in its armor, no hint that the system was sliding toward instability.
I’ve been testing other setups with different numbers of planets and different orbital characteristics (and sometimes multiple co-orbital rings in the same system). I’ll report on those in a later post.
A couple of final thoughts.
First, planets on eccentric orbits can be habitable (as I’ve discussed before). So, feel free to imagine what it would be like to live on a planet in an eccentric co-orbital ring. I can envision all sorts of things…
Second, it’s worth pondering how such a ring could ever form. Just because something like this would be stable does not guarantee that nature will ever produce it (remember the million-Earth Solar System?). The closest I can imagine in nature, is that an eccentric co-orbital ring could maybe be produced from a single massive planet that passed too close to a dense star and was tidally torn to shreds. Otherwise, an orbital structure like this might have to be engineered by an advanced civilization.
Questions? Comments? Words of wisdom?
Additional Resources
- Details on co-orbital ring stability (The Ultimate Engineered Solar System)
- All about horseshoe constellations (Constellations of co-orbital planets)
- Co-orbital rings around a supermassive black hole (the million Earth Solar System)
- Habitability of planets on eccentric orbits
This is really cool! I didn’t think it would be stable at all.
You may look into the Helliconia trilogy by Brian Aldiss for a description of how life can adapt to the conditions of an eccentric orbit around a star in a binary system. The twist is that an entire system is on an eccentic orbit around a bigger star, so the habitable zone around the original star always exists.
Very good story with long timescales, but it gets a little weird in the end.
Do tides cause any issue for stability in the 0.9 case? With this kind of n-body simulation, it’s too complex to also check tides, isn’t it? But it might be that since you can estimate the tidal force at closest approach, you can know how rapidly the world’s should be dragged in or pushed away (depending on reasonable assumptions about the spin of the star).
If the star is sun-like and rotates like the sun, is 0.9 extreme enough that the planets will be pulled into even closer orbits due to tidal decceleration, destroying the stability? Or is that even at 0.9 eccentricity, the size of this effect in the cases you tested would be minimal enough to be discounted?
Good question. I imagine that tides would indeed pose a problem for stability in the very high-eccentricity case, by slowly dissipating orbital energy and changing the shapes of the planets’ orbits. Maybe, if all of the planets had an identical tidal response, the ring could be maintained but change shape. But maybe not… It’s not impossible to test this idea with N-body simulations that also include a simple recipe for tidal dissipation (like this code) but it would be computionally intensive. So, for now I’m leaving tides aside and considering that either they are too weak to matter or that maybe there is a limit in close approach distance to the star for this type of ring.