[SPACE] Co-orbital Habitable Planets
 

Surfing the web today, I ran across an article about co-orbital configurations; in particular, the unique case of Saturn's moons Epimetheus and Janus caught my eye, and I'd like to see about putting together a situation involving a pair of planets co-orbiting in a star's habitable zone in the same manner. Unfortunately, I can't seem to find anything on the specifics of the underlying math, meaning that I'm unable to make appropriate determinations on such questions as the frequency of orbital swaps, how close the planets would be to each other at the point of closest approach, and what the effective eccentricity of the shared orbit would be (which factors in to the impact on each planet's climate). Can anyone help with this?

Re: [SPACE] Co-orbital Habitable Planets
 

Did you follow the link to the first reference?

Giuppone, C. A., Beaugé, C., Michtchenko, T. A., & Ferraz‐Mello, S. (2010). Dynamics of two planets in co‐orbital motion. Monthly Notices of the Royal Astronomical Society, 407(1), 390-398.

Also try these:

Salo, H. & Yoder, C. F. The dynamics of coorbital satellite systems. Astronomy and Astrophysics (ISSN 0004-6361), vol. 205, no. 1-2, Oct. 1988, p. 309-327.

Nicholson, P. D., Hamilton, D. P., Matthews, K., & Yoder, C. F. (1992). New observations of Saturn's coorbital satellites. Icarus, 100(2), 464-484.

These aren't the original or best treatments, but they are openly available.

For what it's worth, my recollection is that the classical osculating orbital elements won't tell you much: the devil is in the interactions, which only come out in more detailed analysis.

Re: [SPACE] Co-orbital Habitable Planets
 

Space mentions stable rosettes in which three objects may orbit at the same distance. Unless you are dead set on the dancing orbits which does sound interesting from the inhabitants' views.

Re: [SPACE] Co-orbital Habitable Planets
 

It's the only coherent explanation I've seen for the 'red planet' and Pern.

Re: [SPACE] Co-orbital Habitable Planets
 

Coherent... about a planet with giant flying teleporting telepathic dragons.... this is the point at which I smile, nod, and back away slowly.... jk I get your point. ;)

Re: [SPACE] Co-orbital Habitable Planets
 

I always figured that The red planet was one of:
A) pluto-like orbit that leaves a trail of spores behind while crossing the orbital path of Pern (where as Pern fills the Neptune role of that pair)
B) the 'Red Planet' is actually a large comet with spores on it that grow/disperse when it is close to the sun(possibly fed by passing through a methane/ethane rich section of the oort cloud)

I prefer B because I think the spores show up for ~ 1 year every ~50 years, so a comet that seeds the orbit of Pern with spores that fall as Thread until the orbital path is clear again. Perhaps a planet sized 'comet' but still in a comet-like orbit

Re: [SPACE] Co-orbital Habitable Planets
 

The problem is that no sensible path will result in seeding an area anywhere near the size of an entire year's orbit. The equivalent of your comet is something like the Perseid meteor shower, which lasts for less than a week.

Re: [SPACE] Co-orbital Habitable Planets
 

I would think the easiest co-orbital would be at the L4 and L5 of a Gas giant... IE, the "trojan" orbits. Sure, you're hurtling along in the same orbit as a number of asteroids, but thats a feature, not a bug.

Other configurations include orbiting each other: nothing says that two orbiting bodies can't be similarly sized.

Re: [SPACE] Co-orbital Habitable Planets
 

Pluto and Charon. Heck earth and our moon are almost a dual planet system.

Re: [SPACE] Co-orbital Habitable Planets
 

Yeah; I've already done things with dual planets, planet-sized moons of a brown dwarf, and L4/L5 planets (in fact, I once tried cramming as many habitable planets as possible into a system by combining all three of these methods: dual planets at the L4/L5 points of a brown dwarf, which itself has a trio of roughly Earth-sized moons in 1:2:4 resonant orbits). I've also done planets in 1:2 resonant orbits at the extreme edges of the biozone, and even experimented with a 2:3 resonance — though from what I understand, the latter requires a high eccentricity on the part of one of the participants to be at all stable, which is likely to defeat the purpose.

In this case though, I'm specifically interested in the "dancing orbits" dynamic, as Anthony put it.