Planets orbiting binary stars

[TeleMad]

I was watching a show last night called Extraterrestrials (a National Geographic show ... not good in my opinion, but that's a different matter) that said it used to be believed that binary stars couldn't provide stable orbits for planets, but that such is not longer accepted because a planet could revolve around both stars OR AROUND JUST ONE OF THEM.

My imagination must be insufficient, because I am having trouble figuring out how a planet could stably orbit one star of a binary system.

If the planet orbits in the plane of the two stars' own orbit, passing between them, then it would be approaching more closely to one star at some times and moving farther away from it at other times. How would that be stable?

If the planet orbits perpendicularly to the orbital plane of the two stars, it would still approach and retreat from the star it's not orbiting, just not as dramatically.

It seems to me that either way, the planet would have to orbit about its sun at an exactly appropriate rate or an exactly appropriate angle to keep it on the opposite side of its star as the other star is.

[TeleMad]

I figured it out.

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I was thinking about 2 stars of equal mass that are relatively close to one another. That situation seems problematic to have a stable orbit for a planet orbiting one of them.

But use the Sun-Earth-Moon system as an analogy. The Sun and Earth would be like two stars orbiting each other, and the Moon would be like a planet orbiting only one of them. Here, the two stars are of such different masses that their center of mass is very close to one (the star the Sun represent) and very far away from the other (the star the Earth represents). The planet (represented by the Moon) can orbit the one star because its mass is much less than its own star, and so close to it while so far away from the other star, that the planet responds basically only to its one star's gravity.

But then my question is, why was it once thought that planets could not stably orbit binary stars?

[UncleAl]

The three-body problem has no closed solutions. A large number of computer simulations have identified time-stable orbits around various binary star systems. Essentially none of them provide reasonably constant conditions on the planet. The stable orbits tend to be shallow minima. Dink the system and the planet gets ejected.

It required about three billion years for single-celled life to get going on Earth, and five billion years cumulative for it to invent pantihose and iPods. Earth appears to be a really sweet case for life to appear. Unless pond scum is your idea of a biological good time, binary star systems are not good candidates for SETI.

[maddog]

Originally Posted by UncleAl

The three-body problem has no closed solutions.

This is definitely true in the general case. However, there are very special cases
where a closed solution can be made. The one Telemad made by analogy of the
Sun-Earth-Moon system where the Sun & Earth were binary stars can be stable.
Requirements would be necessary for proximity of the Earth star to the Sun star
for the Moon planet to be stable. Another example is where two binary stars
were of the eclipsing variety. The ratio of said planet would go around both of
them and its radius about the common center was much more than the distance
between the stars. These are both special cases where solutions can exist.

maddog