# What distances would be involved in this planetary system?

So, I have five habitable planets in my planetary system. These five planets are all in the Goldilocks zone, orbiting their star. However, only two are relevant to this question. The star is exactly the size of our Sun, and is identical in every way. Also, both planets have surface gravities 0.8 times that of Earth. Centered on Earth's orbit, I would like a pair of planets to have an orbit similar to Janus and Epimetheus

So, how close to each other's orbit do these two planets need to be to have this orbit? What is the closest their orbits could be and still have this work in the long term?

• By "80% the gravity of Earth" do you mean mass? – SE - stop firing the good guys Feb 11 '16 at 18:50
• I meant .8 Gs. I don't know what that is in mass. – Xandar The Zenon Feb 11 '16 at 18:59
• I'm not going to run the numbers on this, but I am pretty much 100% certain that there is no way a system like this can be stable. Five planets orbiting within the Goldilocks zone of a single G2V type star? It'd probably be difficult enough (but at least semi-plausible) with two planets within the Goldilocks zone. – user Feb 11 '16 at 19:23
• @bowlturner You might be right. Now add the perturbations from another two in between us and them. :) – user Feb 11 '16 at 19:37
• Also related: Maximum number of earth-like planets in a system – user Feb 11 '16 at 20:09

Saturn is surrounded by a crowded family of rings and moons, and two of those moons -- Epimetheus and Janus -- orbit Saturn so close together that it seems as though their different orbital speeds should make them crash into each other. But due to the complex interplay of their mutual gravitational attraction and their very slightly different distances from Saturn, they never get closer than about 15,000 kilometers (9,000 miles) from each other. Instead of crashing, they exchange orbital positions in a gravitational do-si-do once every four years, in a dance that takes 100 days to play out.

Here is how the dance works. Epimetheus and Janus are small, irregularly-shaped moons with diameters of about 120 and 180 kilometers (about 75 and 110 miles), respectively. Both are on slightly eccentric orbits around Saturn. Their orbits around Saturn differ in size by only 50 kilometers (30 miles). Because it was closer to Saturn, Epimetheus traveled at a faster angular rate than Janus, so inner Epimetheus slowly, inexorably caught up to outer Janus. As the two approached each other in their orbits, Epimetheus tugged on Janus from behind as Janus tugged on Epimetheus with equal and opposite force. The mutual tugging caused them to exchange angular momentum. Epimetheus gained momentum and rose in orbit as Janus lost an equivalent amount of momentum and fell.

So an object about 120 to 180 km diameter gets within 15000 km from it's twin before completely changing orbits a distance of about 50km between them.

Earth's diameter is approx. 12,742 km in diameter. So that is ~85 times the size of the moons (used an average of 150).

Now taking the 50 km difference as a % of the orbital radius (151,472 KM) and applying that to the earths orbital radius (149597870 km) we get ~ 50,000 KM distance to be similar.

If we compared the 50 Km difference to the diameters of the moons then the planet orbits would only be about ~4300 KM apart.

Either way they would be pretty close for space.

Now the harder part is how close to do they get to each other before switching orbits. Janus and Epimetheus never get closer than 15,000 KM. because I'm not very good at using large masses (which should be more accurate) I'm going to use diameters as relative and with the diameters with a difference 85 times larger it suggests one planet will won't get any closer than ~1,274,200 KM before they switch orbits. which is only about 5-6 times farther than our moon is orbiting right now. So it would be a huge body in the sky, even at that distance.

I think someone calculated once before that it would happen about 1 every 5,000 years at our current orbital radius. You would of course see for much longer than that. Janus switches about 1 every 4 years over the course of 100 days, so it might take a couple decades, as it gets closer and closer than fades away. (it would also be a time of great tectonic upheaval as well as they pull on each other.

All things being equal, a star which is otherwise identical to ours will not have a Goldilocks zone several times larger than that of our own Sun.

Two planets is reasonable. You may even be able to squeeze three into that life-sustaining sweet spot. But five is really pushing it.

However, have you considered that one or two of those habitable planets may have habitable moons?

Imagine the Moon having a slightly stronger gravity (maybe due to an alien artifact?) and being able to retain a thin, but still survivable atmosphere.

If you don't want any "magic" involved, then one of your planets can simply be bigger than the Earth, and have a significantly larger moon, with a gravitational field to match.

Of course you should also consider that it's extremely unlikely for so many Earth-like planets to exist in a single system.

I believe that having two Earth-like planets in a co-orbital arrangement would render both uninhabitable.

I'm no astrophysicist, so anyone with more knowledge should feel free to correct me, however it seems to me that the balance between Janus and Epimetheus is incredibly fragile, and results in the sort of interactions which would wreak havoc on planets which must support a relatively stable atmospheric, tidal, and tectonic balance.

The reason this particular interaction works is because neither body has an atmosphere to speak of, and because one moon is four times larger than the other. Numerous other factors also come into play.

However, an Earth-like planet requires a significantly more stable orbit.

• This doesn't answer the question. It's about 2 planets that change orbit like Janus and Epimetheus – bowlturner Feb 11 '16 at 19:38
• Would the dual-planet thing help in squeezing some extra bodies into the goldilock's zone? – Draco18s no longer trusts SE Feb 11 '16 at 19:40
• You're right. I failed to properly read the question. That being said, I'll edit my answer. – AndreiROM Feb 11 '16 at 19:42
• Why would an atmosphere prevent the co-orbit from working? Doesn't it work just fine with equal masses (or it moves to a fixed 60 degree position over long time period)? – JDługosz Feb 11 '16 at 20:07
• @JDługosz - I would imagine that as these two planets come together their gravitational fields will influence one another, and their atmospheres may even "scrape" against one another. This would wreak havoc on a planet such as Earth. Volcanoes would go off each time the planets got close to one another. The tides would become wildly unpredictable, etc. (or maybe just predictably destructive) – AndreiROM Feb 11 '16 at 20:10