The most common kinds of orbits in binary systems will be either going around one star, with the other one far away ("satellite type"), or going around both stars (which are close together), ("planet type"). There is also "libration type", where the planet is in a Lagrange point of the stars (60 degrees ahead or behind); these are likely uncommon since the orbit is unstable to perturbations over long time. Typical star orbits are many AU wide (from a few to hundreds), with eccentricities varying a lot. As a rule of thumb (good enough for RPGs at least), the planet needs to be three times closer to the one star it orbits than the closest distance of the stars, or more than three times their farthest distance when orbiting both. Otherwise the orbit will shift to some other orbit or be thrown out. (See also http://arxiv.org/abs/astro-ph/0701266v1 if you want some recent work) On satellite type planets most energy would be coming from the star it orbits, while the other star would mostly be highly visible in the sky rather than contribute much heat or light. If it was at its closest it would probably be just one ninth as bright as the primary sun - enough to matter a bit, and far brighter than the moon is on Terra. At its furthest it could be merely another star in the sky. This brightness would change slowly over its orbit, typically over a span of a few years to a century. Over a year it would move like an outer planet does in our sky, changing constellation. If it was in conjunction with the sun (both in same constellation) the day would be a bit brighter and nights normally dark. As it drifts away there will be a period of extended dawn or twilight where the secondary provides the light, culminating in opposition (half a year after conjunction) when it will be rising at twilight and setting at dawn, providing a bright night. If the colors are different this might produce fun effects: a blue-white outer star might create "white nights" and be visible even during the day, while a reddish outer star might make nights red and add purple to the day. Planet type, where the planet orbits both stars, requires the planet to be far away and the stars close. This typically happens if they are fairly bright (F spectral class and up) since the life zone needs to be big. This case looks fairly similar to Earth at first, except that objects cast two close shadows. Seasons and climate are likely fairly normal, with some changes if one of the stars has a notably different luminosity (say a bright F star with a dimmer red giant partner: then for part of the year there might be a reddish "eclipse" period) A special and likely rare (but fun) case is when the planet orbits a dim star that orbits within the life zone of a brighter star. This is essentially the same thing as being a moon of a gas giant in the habitable zone. Depending on how wide the orbit is the amount of heating will oscillate across the "short year". If the short year is like the Galilean moons of Jupiter it will last about a week, but it could conceivably be up to a month. Such planets are likely to be tidally locked, so one side is always pointed at the local dim sun and the other faces away. If the dim sun is somewhat bright this means the inner side will be pretty hot, bathed in eternal sunlight and for half of the short year the even stronger sunlight from the bright sun. Meanwhile the outer side will go half of the short year without any sunlight at all and then get half a short year of sunlight: such worlds will likely have big seasonal weather changes. Multiple star systems are fairly similar to binary star systems: orbits are stable if they are close to a star or far away from a group that their internal dynamics is negligible (technically, their multipole moments need to be small). Fun Janus-like orbits are of course possible, but I suspect they are not exceedingly stable: if a planet has been around long enough to get a biosphere, it probably has a very stable orbit.

NewtonPulsifer wrote:

Horseshoe orbits can be stable if the two planets are equal-mass.

Interesting papers. Note that both however deals with planets rather than binary stars: these are possible weird exoplanet pairs orbiting single primaries. It is amusing that something as simple as Newtonian gravity allows so many weird orbits. And that many show up for real in the solar system.

You can get some amazingly fun orbits in theory: http://www.scholarpedia.org/article/N-body_choreographies but in practice they won't be stable. Unless ETI intervenes.

Prophet710 wrote:

When you say unstable. How long would it take the orbits to eventually decay? Are we talking a handful of years or on a geological/cosmological timetable; millions of years?

Handful of years, if not even months. These are pretty extreme solutions, precariously balanced on mathematical symmetries (that is how they were found). The figure 8 case is actually "stable" in a very technical sense: there exist similar, but slightly perturbed orbits if the perturbations are in the plane and have zero angular momentum. Unfortunately this is practically useless. As the page describes: "Are there any figure eight orbits in the universe? Douglas Heggie, 2000 together with Piotr Hut performed numerical experiments by throwing binary pairs, all masses equal, at each other and seeing how often figure eight solutions formed. On the basis of these numerical experiments and other considerations, they estimate the number of figure eight orbits in the observable universe lies in the range of 1 to 100. One does not expect to see any of the other choreographies due to their dynamical instability. Thus choreographies are of extremely limited interest in astronomy." So if you find a figure 8 system, you are in a *really* special place. A suspiciously special place.

Arenamontanus wrote:

So if you find a figure 8 system, you are in a *really* special place. A suspiciously special place.

This makes me want to mess with my players. If they go gatecrashing, they would wind up in such a figure-8 system, with suspicious $foo.. but no ETI or other deliberate influence in any way. A true cosmological black swan. That might make a good name for the campaign - Black Swan.

What about planetary orbits which are out of the plane of the two stars orbiting each other? For example, a planet orbiting the axis formed by a line between the two stars? This would potentially replace the cold poles of a planet with a cold ring around the equator if the planet were rotating in plane with it's orbit, and could do some really interesting things to the day cycle and weather, and if the stars are different colors, it could make any moons look interesting... Has there been much work done on non-planar orbits? -Joe

I guess a ?la Grange Point? would then be at that + sign, so you'd be orbiting around it and the axis between the two stars? If the star orbits overlapped so one followed the other in more of a circle instead of the picture shown, could you form something stable with the above described orbit? -Joe

Thirteen new solutions to the the three body problem. Yay. http://news.sciencemag.org/sciencenow/2013/03/physicists-discover-a-whop...