# Theoretical: Habitable planet in a binary star system

I hope this is the right Stack exchange for this question. I'm designing a planet as a setting for a tabletop RPG campaign, and basically I'm looking for some help to make sure my idea is at least theoretically sound enough that players won't be completely derailed by my messing things up.

The concept, a very large blue main sequence star, I'm thinking around 100 solar mass, and orbiting that is a red dwarf, somewhere in the .25 to .5 solar mass range, and then the "Planet" is orbiting the red dwarf. My ideal concept is that the blue sun is distinctly brighter, but distance and positioning is such that, to a person on the surface, both suns appear equal in size.

So, the core question here is, is this at least theoretically sound, and which sun would provide more warmth to the planet?

Additional sub-question, what's the correct term for the habitable body orbiting the red dwarf? Is it a Planet, as it orbits a star even though that star orbits another star, or is it technically a Moon?

• I'm not sure if the (percived) size of both Suns can be maintained. If the Planet travels around the dwarf it will get closer to the blue one and so would get bigger and smaller depending on the (sub-) year. This assumes that orbits are roughly in the same plane. If the Orbit of the planet is 90° to the orbit of the dwarf it could work. But I don't know how likely this is, or if I described it correctly. Jul 4, 2016 at 17:01

## 1 Answer

If The blue giant and the red dwarf have the same apparent diameter from the planet, the blue giant will provide essentially all of the warmth and the light for the planet.

This is simple to prove as the spherical angle of the 2 suns in the same, the difference in perceived luminosity will be proportional the 4th power of the surface temperature. The blue giant will most likely be 12-40 thousand Kelvin, and the red dwarf will be around 4000 K. The blue giant will be most likely be about 80-1000 times as bright (and hot) as the red dwarf.

The planet is correctly speaking a planet, not a moon.

To make the brightness and warmth contribution identical, the dwarf would have to have an apparent area 80-1000 times that of the blue giant, having a diameter of square root of 80 to square root of 1000 times that of the blue giant.

• Okay, so if I wanted the Brightness and heat to be very similar, the Red Dwarf would appear much larger than the Blue sun, right? Jul 4, 2016 at 1:50
• @TiwazTyrsfist - added to answer Jul 4, 2016 at 1:55
• You are right: if you want different colored Suns in the sky that give your planet the same amount of energy, the bluer (hotter) one will have to be much smaller. This blog post might help with some ideas: planetplanet.net/2016/03/22/an-earth-with-five-suns-in-the-sky . Jul 4, 2016 at 9:53