# Silly orbits - can an orbit be both stable and interplanetary?

In our story's universe, a solar system is hand-crafted by a deity with seven smallish bodies working in a way that I can only describe as Lagrangian Points, where all planets have the same orbital path and rough mass and volume, but are separated by a seventh of a turn from each other. This is somewhat stable in the story and only needs to exist for a relatively small amount of time, astronomically speaking.

The trouble is, we also need a smaller body (a left-over chunk of a salvaged planet, not of much size) to pass by the planet regularly, say once every few years. I've devised a couple of silly paths that would allow the small body to pass each planet forming something like a 7-pointed star, but wondered if this were actually possible.

To be clear, the story won't go into any detail on the physics involved, and the orbit is acceptable even if it requires a high level of precision in set-up because it's going to be the result of a deity.

Edit:

To clarify, the orbit won't need to be stable for a period of time on the scale of billions of years, likely less than a few million years, though this will effect the context of the story significantly.

What you’re describing is a Klemperer Rosette, which is actually stable. Basically any regular polygon of equal mass planets with a star in the middle.

Given that, there’s probably an orbit for a small mass which visits them in turn, but I doubt there’s any way to prove this without serious computation.

• There is a lot of bad info on Klemplerer Rosettes out there. Here is the actual paper: adsbit.harvard.edu//full/1962AJ.....67..162K/0000162.000.html. It can't be any regular polygon; in particular it probably can't be 5 or 7 sided. Also, it can't have equal masses, there has to be two different masses for the 4, 6, and 8 orbit configurations described in the paper. Apr 13, 2018 at 0:10
• That's great, thanks. The extent of my knowledge of plausable orbital paths is gained from KSP and other games that simulate them, though I do understand a portion of the physics involved from A-levels, so both your putting a name on the formation and your direct answer were very useful. +1 and green tick :) Apr 13, 2018 at 0:13
• @kingledion, thanks for the further reading, I'm working through what I can of it now, though if you could expand on why 7 is an exception to the rule (or even form your own answer) I'd be especially pleased since my physics is rusty and I'm jumping into this paper 150 pages in. Edit: Thanks for the answer, editing this now Apr 13, 2018 at 0:18
• @kingledion: Thanks for that. I was wrong. Let me see how I can reshape that answer. Apr 13, 2018 at 11:54

# No

The Klemperer Rosette is theoretically stable for several configurations of planets. There is in fact a hexagonal, six-planet configuration discussed in the original paper that is stable.

Unfortunately, any sizable mass periodically interacting with the six planet ring will almost certainly destabilize the system. The $n$-body problem is famously chaotic. On planetary time scales (i.e. billions of years) any regular gravitational action on a Rosette will destabilize it.

• To be clear, on what timescale would a seven-body Klemperer Rosette be stable? This would be interesting and relevant to other elements of the story, but any amount of stability could be enough to allow the story to take place since the humans are brought to the solar system and did not evolve there. Your answer is definitely helpful and appreciated, thank you for your time and knowledge :) Apr 13, 2018 at 0:29
• @LiamGeorge It really depends on the size. I couldn't give you a number, but the time depends on the number of orbital interactions per unit time. If the orbits interact every 10,000 years, like a long period comet, then it will take 10,000 times longer for the planets orbits to be destabilized than an object that swings by every 1 year. Apr 13, 2018 at 0:37
• Out of curiosity, considering both the nature of solar system formation and the time required for any one planet to become habitable, is the Klemperer Rosette (or anything like it) actually stable enough to allow for the formation of life? It would seem that even a Haley's Comet over the course of formation and "terraforming" would destroy the stability. Indeed, it seems that any one planet having a sizable moon would destroy it before any planet is habitable, too.
– JBH
Apr 13, 2018 at 3:10
• @JBH I would doubt it. I am fairly certain that any moon would throw things off immediately. A Halley's comet might not be so bad, but the OP's 'left over chunk of a smaller planet' sounds a lot bigger than a comet, to me. Apr 13, 2018 at 3:26
• @LiamGeorge Gravitational influence is infinite in range. Merely having the Andromeda galaxy "nearby" (assuming that our planetary system is not bound to its own galaxy and where "nearby" means "in the visible universe") the rosette will eventually destabilize due to the very (very very) slight (and irregular!) gravitational slope towards Andromeda. How long does it take to collapse? Depends on the strength and irregularity of that influence. In all practical scenarios, on the order of a few hundred million years. Tops. (Note: I am not an astrophysicist, I just pretend on the internet) Apr 14, 2018 at 21:02

What you are describing is vaguely similar to what is described in these posts in PlanetPlanet:

They discuss much more complicated solar systems than yours, with multiple orbits with multiple co orbital planets in each orbit. These are not Trojan orbits or Lagrangian orbits or Kemplerer Rosettes, but vaguely similar.

As you can see by the "engineered" in the title the author believes that natural examples of such complex systems could never form, and thus assumes that they would be created by super advances societies.