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I have three planets. Let's call them Un, Deux and Trois.

Is it feasible for all three to be orbiting one another, close enough to be seen clearly by eye? All three are large enough to be earth equivalents.

What would the days be like? Let us say that each planet rotates once every 24 hours, performing an orbit with the other planets every three days? I'm thinking there would be hours/days of twilight as one planet blocked another.

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    $\begingroup$ While this question is not a duplicate per se, there are many, many questions on Worldbuilding involving similar situations. I would recommend reading some of them and they might have the answer you are looking for! Here and Here are a good place to start. $\endgroup$ – MozerShmozer Aug 12 '16 at 21:48
  • $\begingroup$ 4 planets definately wont work as the 4th falls out of orbit. Un deux trois, and quatre sank (cinq) if you will. (please recognize the bad joke) $\endgroup$ – Twelfth Aug 12 '16 at 22:05
  • $\begingroup$ @Twelfth I knew someone would go there! $\endgroup$ – Chris J Aug 13 '16 at 10:57
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Two planets in an orbit works fine: either a conventional binary system or a co-orbital system such as is found with Saturn's moons Janus and Epimetheus.

Three planets don't work. The conventional stable solutions to the n-body problem (the L4 and L5 points) are only stable if the objects in the Lagrange points are small relative to the primary objects. The unconventional solutions are all unstable.

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Not Really

This is a variation of the Three Body Problem. While one might imagine a situation wherein three bodies orbited each other, any variation in their mass, any cumulation of impacts, the passing of another body, etc. would all quickly throw off the balance and cause the orbits to destabilize. Such destabilization would likely cause two to collide and the third to spin off.

Most orbits are stable because one body is so much more massive than the other(s), and dominates the equation. However, even in these circumstances over time you might see real changes that suggest they are only in equilibrium on short time scales. Three roughly-equal bodies would not, in classical physics, find themselves in this situation.

But Assuming Magic...

If there was a non-classical situation (magic, crazy technology, etc.) that forced the situation of three Earth-like planets orbiting each other around a more distant star, all along the same stellar plane, this is what you'd probably see:

  • Two eclipses every time the planets completed a full orbit: each of the other planets passed between the one you're on and the sun. These eclipses may be large or small depending on how close the other planets were to each other. The moon, much smaller than the Earth, can eclipse the sun at it's current distance: therefore an Earth-like planet could do so and be much further out, or create a more complete eclipse if it were closer.
  • Wilder weather patterns (and by 'wilder' I mean 'harder to predict'), because the warming/cooling cycle is much more complex. In addition to the two cyclic eclipses, the distance to the three-body epicenter might be significant in relation to the sun: if they are very far, this could be significant.
  • Crazy tidal patterns, or no tidal patterns. I don't have an intuition where this would land, but it would be different.
  • Much brighter nights. At any given non-eclipse time you have two giant mirrors at least partially reflecting light at your planet.
  • A very interesting electromagnetic field. Presumably all three planets would have their own EM fields: these would combine into a much larger field, the shape of which would, again, depend on distance. If the magnetic poles are not all pointing the same way ("north"), this could lead to whackiness.
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Ah! My internet connection died while I was writing my answer, and it seems Mark beat me to the punch. So allow me to elaborate on the horseshoe orbit of Epimetheus and Janus, if I may.

As previously mentioned: three planets in such close proximity just isn't plausible. There are several realistic alternatives for 2 planets however, including a binary planets and the co-orbital horseshoe.

Binary planets are more in the vein of what you're looking for and relatively easy to explain. A binary/double planet is a system with two planet-sized objects, orbiting a common center of shared mass, orbiting a star. But we don't know a lot about systems like this.

(For more, see: https://en.wikipedia.org/wiki/Double_planet)

But I think the other option - the horsehoe orbit - is certainly notable and just as, if not more, romantic. We also have a very good example right in our very own solar system.

Epimetheus and Janus, both moons of Saturn, are co-orbital. Technically. It’s weird.

Their semi-major axes (think average distance from Saturn) are slightly different. Not a lot - less than either’s diameter - but still a bit.

Kepler’s laws of planetary motion dictate that the moon that is slightly closer to the sun will complete its orbit slightly faster than the other. In this case, the inner moon completes its orbit 30 seconds faster than its partner. That might not seem like a lot, but every day, the distance grows… and it adds up.

Eventually, they meet each other. And when they meet, it gets even weirder.

They switch orbits.

As they tug on each other, the inner moon loses speed, falling into a slightly more distant orbit, while the outer moon accelerates into a closer orbit. The cycle repeats.

It looks something like this:

Horshoe

Imagine seeing this from the surface of either moon: standing on Epimetheus, watching as Janus races toward you, getting closer and closer, larger and larger, then fall away into the darkness. Or maybe from the surface of Saturn? It would look weird.

There’s a lot to play with here. Who is to say they have to be moons? It could be possible for two planets to behave this way.

The idea of a binary planet + lone planet together in a horseshoe orbit springs to mind. I really doubt it's plausible, but it sounds neat. And who knows? maybe there's a way to make it work somehow. There's a lot of strange stuff out there.

You can find more information about horseshoe orbits here:

https://en.wikipedia.org/wiki/Co-orbital_configuration#Co-orbital_moons (this is the link Mark provided)

https://en.wikipedia.org/wiki/Epimetheus_(moon)

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I know for at least 2 planets, it is theoretically possible. Pluto and Charon are close in mass, though not classified as planets. The term for these kind of systems is a double planet or binary planet, I don't think they have found any actual planetary systems that meet this criteria, yet. I'm not an expert in orbits, but I believe that a triple planet system should be possible, as well.

As far as their frequency of rotation / eclipsing, etc, that could vary. Eclipsing may not even have to occur. Say 2 (or three) planets are in a binary group but their orbits with each other are always perpendicular to their orbit with their star, then they will not eclipse.

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There are several ways for 2 planets to share the same orbit. The simplest is for them to be in each other's mutual L4/L5 Lagrange points, essentially staying 60 degrees apart along their orbit.
enter image description here This configuration is generally stable. You can add a couple more planets in by making each of them a binary planet, with two Earths orbiting each other. (see here: https://planetplanet.net/2014/05/22/building-the-ultimate-solar-system-part-4-two-ninja-moves-moons-and-co-orbital-planets/ and here: https://planetplanet.net/2014/05/23/building-the-ultimate-solar-system-part-5-putting-the-pieces-together/).

With two planets orbiting in a co-orbital setup separated by 60 degrees, their rotation rates are not affected by the other planet. But, in the case of a binary planet, tides are likely to be strong enough to make the two planets tidally locked, so they always show each other the same face. In that case, both planets will have the same day, whose length is simply the time it takes the planets to orbit each other.

Two planets could also be in a horseshoe configuration, which can be stable but can only fit two planets, not three.

There are some other exotic classes of orbits that come close to satisfying your criteria (e.g., quasi-satellites and eccentric 1:1 resonant orbits).

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    $\begingroup$ OP doesn't want the planets to merely share an orbit, but rather orbit a common center of mass among them which in turn orbits the central star. $\endgroup$ – a CVn Aug 12 '16 at 22:03
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    $\begingroup$ L4 and L5 aren't stable if you've got bodies in them that are of similar mass to the primary object. $\endgroup$ – Mark Aug 12 '16 at 22:04
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    $\begingroup$ Oops looks like I misinterpreted the question. So I guess we are looking for three planets orbiting each other. This is the same setup as multiple star systems. Systems of 3+ stars are stable when they are in a hierarchical setup, where the size scale of orbits are very different. So, in this case, planets un and deux can orbit each other relatively closely, with planet trois much farther away. Then if all these planets want to orbit a star, then all these orbits must fit within about half the planets' Hill radius to maintain stability. $\endgroup$ – Sean Raymond Aug 12 '16 at 22:15
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    $\begingroup$ This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review $\endgroup$ – Frostfyre Aug 12 '16 at 23:16
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    $\begingroup$ @a4android This may be his field of expertise, but he didn't answer the that was asked, as he himself pointed out. $\endgroup$ – Frostfyre Aug 13 '16 at 16:57

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