It is possible, and we’ve actually found a number of planets orbiting double stars, like Luke’s homeworld in Star Wars does. However, outside of the Star Wars Universe, there are a lot of ways for this setup to go very wrong. So far, we haven’t found an enormous number of planets orbiting double stars, which seems to speak to how rare it is for a planet to survive in an environment like Tatooine’s.
At the beginning of Star Wars, Luke Skywalker lives on a planet with a double sunrise, on a planet which orbits two stars. We can presume that the two stars are orbiting each other, and that this planet then orbits around both stars. The technical term for two stars which orbit each other is a binary system, and the easiest way for the stars to find themselves in this situation is if they both form out of the same cloud of gas, at the same time. The remainders of that cloud of gas would hang around long enough to make planets to surround the pair of stars.
If a planet were orbiting far enough away from the two stars, it wouldn’t really notice a difference between orbiting the double star set, and orbiting one star of their combined mass. However, by the time you get really far away from the stars, there’s not a tremendous amount of sunlight reaching the surface of your planet. If you want your world to be habitable (and a desert world still counts), you’ll have to be on a planet that’s a little closer to the stars, and this is where things start to get tricky.
If you are a planet, it’s nicest if the two stars orbit each other closely and circularly. This kind of setup for the stars means that you’re more or less always the same distance from the stars, which guarantees you a pretty consistent amount of light from the stars. If you’re trying to be a habitable world, this is important, because it keeps your surface temperature roughly consistent as well. You’d still have some variability, because the stars will still eclipse or partially eclipse each other periodically, which would lower the amount of light you’d get on the surface.
However, if you are a star, close orbits are more complicated than wide ones. Wide orbits are easier to maintain, because the two stars have a weaker gravitational influence on each other. In a smaller orbit, the two stars will exert a reasonably strong tidal force on each other, and will change each other’s orbits over time. When the orbits of the stars begin to change around, the planets’ orbits also change, and you are in prime conditions for what’s called a three-body interaction.
The three body interaction happens when you have three objects orbiting each other in relatively close range. This could be three stars or two stars and a planet, and in either case, the lowest mass object can wind up getting flung suddenly out of the solar system entirely. The other outcome is for the planet to wind up crashing into one of the two stars - not a habitable outcome there, either. The three-body interaction is of particular concern for two stars and a planet, as this means that if your planet is close enough to the star to get caught up in one of these interactions, it won’t stay as a planet in the solar system for a particularly long time. This might partially explain the relatively low number of circumbinary planets we’ve seen so far with Kepler - these planets are prone to either being ejected or consumed by their parent stars.
So it’s not impossible for a Tatooine-like planet to orbit a binary system, but given how rare they are in our solar system, everything has to be exactly so, or Tatooine will wind up on a one-way trip out of its solar system on a journey through its home galaxy.
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