Could planets switch orbits like Janus?

Question

I was reading up a little while ago about Janus and Epimetheus and how every few years they trade orbits. The mechanics is interesting but I'm not going into them here.

What I was wondering is first could planets going around a sun have a similar relationship and how might that affect any life on them? Would it change the seasons much? Janus and Epimtheus are pretty small and the orbits are about 50K apart which wouldn't do much for seasons, but planets I would expect to be a bit bigger because of scaling, wouldn't want the planets bumping into each other, which also makes me wonder if it's possible. How far apart would the orbits likely be to have a similar effect if both were Earth sized?

Answer 1

Before we get into seasons, life, etc., we have to address the question of whether or not such a configuration could exist. At first glance, I see no reason why two planets couldn't orbit a star in the same way Janus and Epimetheus orbit Saturn. It could be a bit tricky if the planets are gas giants, because they would have a strong gravitational influence on one another, but if they were terrestrial planets, they would be fine. Such a configuration could exist.

The more important question here is whether or not such a configuration could form in the first place. From the excellent site you mentioned,

Janus and Epimetheus may have formed from a disruption of a single parent to form co-orbital satellites. If this is the case, the disruption must have happened early in the history of the satellite system.

Wikipedia, interestingly enough, says the exact same thing:

Janus and Epimetheus may have formed from a disruption of a single parent to form co-orbital satellites, but if this is the case the disruption must have happened early in the history of the satellite system.

Let's consider how these planets could have formed:

1. Collision of two protoplanets. This is the idea behind the Giant Impact Hypothesis, which says that a protoplanet collided with Earth early in the history of the solar system; the Moon was formed from the resulting debris. The problem is, if this happened between two Earth-sized protoplanets, the result might not be two planets - it could be a planet and a large moon, and some debris.
2. The Roche limit and tidal forces. There are a number of questions here that investigate what would happen if certain things passed inside the Roche limit of another body. A body of more than two solar masses could definitely venture inside the Sun's Roche limit, and be torn apart. It's possible that the material would coalesce into two planets; not necessarily likely, but possible.

Both these scenarios could very well result in two co-orbital planets, though perhaps not in the desired arrangement. We'll know more about these kind of ideas if we ever learn about the true source of Janus and Epimetheus. For now, we can say that such a configuration con very well have formed, either from one of these two scenarios or something completely different.

So, to answer

first could planets going around a sun have a similar relationship

Yes.

---

Next up, we turn to life. It seems clear that the two bodies would be in some way related to one another, and would most likely be made up of the same materials. In fact, in lieu of another impact on one, the two might develop nearly identically, for a while. At least for a few hundred million years.

I see no reason why life couldn't exist on one or both of these worlds. Remember, they're only near each other for a short amount of time, so they don't have a huge influence on each other - most of the time. Going back to your site,

This exchange happens about once every four years.

Maybe this period is different for our planets, but still, you get the idea.

The really interesting thing here is that, because conditions might be really similar on both planets, we could see life develop similarly on both. Sure, there are a lot of factors that influence life's development, so we shouldn't expect the same creatures to develop on both, but life would likely form from the same compounds, and have the same evolutionary history, for a few hundred million years.

how might that affect any life on them?

Life could form, and it might be similar on both.

---

Finally, we go to seasons. Janus and Epimetheus are both in synchronous rotation with Saturn, so only one side faces Saturn at a time. This means that they are tidally locked with Saturn. I wrote a brief answer on seasons on tidally locked planets, but the setup was different, and it may not be relevant here because tidal locking is not necessarily the outcome.

If there isn't tidal locking, there should be normal seasons if the axis of each planet is inclined with respect to the star. If it isn't, there won't be any seasons, unless the orbit is somehow highly elliptical (See this question and this question). There also won't be a huge amount of interaction between the two planets, so any axial effects should be negligible.

Would it change the seasons much?

No.

Answer 2

Hope it's OK to bump an old question, but I saw another question on horseshoe orbits and I searched for related questions and came across this one.

Some small notes to add to the answer above.

1) Scaling up from Janus and Epimethius to planets around a star doesn't really work. The ratio of Earth's mass to the sun is 1 to about 330,000. The ratio of Janus, the heavier of the two horseshoe moons, to Saturn is about 1 in 300 million. 900 times more mass variation. That doesn't prove that two planets couldn't orbit in a horseshoe coorbital around a star, but it might not be stable. Here's an answered question on Astronomy with some research quoted. As the two bodies both acquire mass the stability and longevity of the horseshoe drops rapidly. If one of the two objects is small, then you can have a stable system for some time, so long as the larger one is less than 1/200th the mass of the central body. Earth to the Sun is actually 3,200 times the mass ratio as the smaller moon, Epimethius to Saturn. I don't know if 3,200 times greater mass ratio destabilizes the system. It might still be in the range of possible, but the math gets pretty difficult.

2) Horseshoe orbits happen very slowly. Janus and Epimethius swap every 4 years, but they are very close to Saturn and as a result, they orbit very quickly. Each orbits Saturn in less than a day. 4 years is 2,100 orbits for those two moons. Earth's horseshoe Moon, 3753 Cruithne is in a horseshoe pattern around earth with a 770 year period. The horseshoe period is determined by how far the two objects swap and the relative orbital periods at the different distances. Janus and Epimethius swap about 100 km between them. They maintain about a 50 km variation in their semi-major axis, which corresponds to about 2,100 orbits for the closer one to catch up to the farther one. The swapping takes about 200 orbits around Saturn.

Two theoretical Earths in a horseshoe orbit with each other would have a period of hundreds or thousands of years. The period is also inversely proportional to how far they move.

Earth and 3753 Cruithne swap about 1/2 million km when they swap. We can use that as a guideline because the gravitational acceleration remains mostly consistent as the 2nd body increases in mass. The difficulty with using that as an estimate is 3753's highly elliptical orbit, so the gravitational tugging is diluted. With more circular orbits, the exchange should happen faster, or it should be smaller.

The math behind the 3 body problem is very complicated and above my paygrade. I could do some ugly but better estimates, but it would be even longer. But a ballpark 1% variation in solar energy would be enough to trigger a small change on each planet, perhaps triggering little ice ages or medieval warm periods, but if you push the 1% a little higher, the period gets shorter, so I don't think there's any way to get a bigger effect than that. A few hundred years of frost, and a few hundred years of warmth.

A final point. The planets never actually get "close" to each other. The gravitational exchange happens at a distance. Janus and Epimethius never get closer than about 10,000 km in order to swap 100 km in orbital distance.

3753 Cruithne doesn't get closer than about 12.5 million km from Earth in order to swap about 0.5 million km in orbital distance. One way to think about how close they get is by angles of arc. 10,000 km is about 1/15th Janus semi major axis, which is roughly equivalent to 1/15th of a radian on the circular orbit or about 4 degrees. For Earth and 3753 Cruithne, 12.5 million km is about 1/12th Earth's distance from the sun, or about 5 degrees of arc in their respective orbits.

Two data points doesn't establish a pattern, but if the two planets get too close in order to exchange orbital energy, the system likely destabilizes. It's much more consistent if they amount the move is a small faction of how close they need to get. 1/200 for Janus/Epimethius or 1/25 for Earth/Cruithne (not Earth/Cruithne is diluted due to Cruithne's eliptical orbit, two circular orbits and that fraction gets smaller).

Similarly, if the angle of arc grows too large, say above 15 degrees or so, then system might have a greater gravitational attraction to enter into trojan orbits which are more stable and more common than horseshoe orbits. There's a sweet spot in there for degrees of arc that the two objects can get to each other before moving apart again. I'd guess somewhere between 1.5-2-3 degrees of arc on the low side, to maybe 6-8 degrees on the high side - if I was to make a bad guess and as the objects get more massive, that window shrinks.

Point of all of this, the two planets in a horseshoe orbit would never appear like moons to each other. They'd never get anywhere near that close because if they did, such a system would swap too much orbital energy and be irregular, not repeating. They would, as they approach, perhaps be a magnitude brighter than Venus, and by far the most impressive dot in the sky, but they'd remain dots to each other.

HDE is ofcourse right, that setting up a system of two large bodies with less than 1% variation in their semi major axis would be unusual. A system like this would certainly be rare and might even be impossible for long periods of time.

But to address the seasons question, the seasons wouldn't change much but they might change some. The climate might change, similar to a little ice age or Medieval warm period with each swap. That's around the biggest change you might expect with a system like this because the change in distance from the sun would be quite small. It wouldn't happen all at once, it would take many years to kick in, aided by natural feedback mechanisms on the planet.

Hope that wasn't too long or wordy.