I'm just curious if binary stars are low over the horizon and the conditions are just perfect for the formation of rainbow, would I see a single rainbow, double rainbow or two rainbows intersecting each other?
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8$\begingroup$ Here's a photo of 2 crossed rainbows from 2 stars – the sun and its mirror image due to the sea. $\endgroup$– A. P.Commented Jan 3 at 14:33
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8$\begingroup$ This XKCD post comes to the rescue what-if.xkcd.com/150 answering your exact question. $\endgroup$– VorbisCommented Jan 3 at 19:59
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A rainbow occurs when a viewer is looking towards refractive droplets (typically droplets of water) that are illuminated by a light source behind the viewer. One could imagine standing looking North towards a rain storm on a planet with one local star near the Southwest horizon and one near the Southeast horizon. In this case the Southwest star would form a rainbow towards the Northeast and the Southeast star would form a rainbow towards the Northwest.
Rainbows subtend 42 degrees of angle. Depending how close the stars are to each other in the sky it is possible the rainbows from each star could overlap.
I believe this is a shot of the two stars of the fictional Tatoo system as viewed from the planet Tatooine. These stars are very close in the sky. I imagine if there was a rainstorm behind the camera, and the camera was turned around, there would appear two overlapping rainbows.
Note: as pointed out in the comments by Vorbis, XKCD has a what if with this exact question. I'll just copy some of the figures from that page since it does a better explanation than I do here:
The geometry of rainbows (note in this picture it is important that there is a volume filled with refractive droplets at the right hand side where the rainbow appears):
Types of binaries and planets:
It is thought that Tatooine is a circumbinary. This would mean that you would usually see overlapping rainbows when you see any rainbow on Tatooine. In "the other kind" you would only see overlapping double rainbows for certain configurations of the three bodies.
What the rainbows might look like:
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2$\begingroup$ The most stable orbits for a planet around a binary have the close binary and a distant planet - the next most stable configuration has the planet and a distant red or brown dwarf orbiting the much larger star in the middle. I believe that Tatooine is supposed to be a planet orbiting a binary. As such, the angular distance between the stars would be fairly small $\endgroup$ Commented Jan 3 at 17:16