Could two planets trapped between two stars orbit each other?

Question

Say there are two stars, each exerting and equal force on a point in the midde of them. For simplicity, we'll say the two stars have the same mass and are equidistant from the point. Now suppose that there are two, equally massive planets, moving at a great speed around that point. Would the two planets be able to create a sustainable orbit between the two stars? Could such a situation ever naturally occur?

Answer 1

What you are asking is essentially whether a double planet can have its barycenter at a Lagrange point of a binary star system. This is definitely true. As long as the pair can be well approximated as a point mass much smaller than the stellar distance and much lighter, it is a standard restricted 3-body problem. (There is a slight complication due to the minor perturbations from the star potentials maybe setting up some resonant wobble in the planets orbits, but this is a very weak and long-term issue.)

The more major issue is whether the planets are stable. The L1, L2 and L3 Lagrange points are unstable, so any deviation from them will make the planets eventually drift away and end up in some other orbit. L4 and L5 are neutral, and there is no strong tendency to drift away: here they could in principle stay forever. Even better, there are periodic halo orbits around the points that also allow the planets to remain.

Could this ever happen? The universe is very big, so many rare things surely occurs somewhere. Small objects do get temporarily or permanently trapped around Lagrange points (trojan asteroids, for example) and planets may end up in a similar situation in a binary system - it is just that planets tend to be much rarer than asteroids, so there will be far fewer "attempts" for this. Similarly binary planets do not seem to be uncommon (we kind of live on one), so maybe a binary planet does end up in a L4 Halo orbit around a heavy binary here and there. It will be a rare coincidence, though.

Answer 2

Would you count this? Imagine two copies of the James Webb telescope in orbit. As you can see, the Webb telescope travels in a small circle as it orbits the Sun. Two could orbit in opposite sides of the circle.

It isn't quite what you asked, but almost. They orbit outside the Earth's orbit.

It also isn't really right to say they orbit each other. They are held by the gravity of the Sun and Earth. Their mutual attraction is very weak and isn't what makes them travel around each other.

But it fits the idea of what you asked. So yes, this is possible.

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Edit

There is another possibility. It too isn't exactly what is asked for. But it requires equal size Suns, as Carl asks.

You start with two equal size Suns and equal size planets between them. But you make the planetary orbits so big that the Suns and planets form a square. This forms a Klemperer rosette. All 4 rotate at the same speed. It still isn't stable, but it is more stable than having planets in small orbits rotating with a different period from the Suns.

Answer 3

This wiki article says , yes

In astronomy, a double planet (also binary planet) is a binary system where both objects are planets, or planetary-mass objects, that share an orbital axis external to both planetary bodies.

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There is debate as to what criteria should be used to distinguish "double planet" from a "planet–moon system". The following are considerations.

At its 2006 General Assembly, the International Astronomical Union considered a proposal that Pluto and Charon be reclassified as a double planet,[2] but the proposal was abandoned in favor of the current IAU definition of planet.

Addition after comment

So there is no problem for two planets to revolve about each other and also their center of mass about a star.

So the doubt in your question is not about a binary system, but if there can be a stable orbit for a planet at the point of zero gravity, because the planet could be a binary planet as above. I guess there would be no orbit, but maybe a meta-stable point, where the planet ( or system) would hover. Meta-stable because it would be easy to be attracted to one or the other star from a small perturbation due to their extended masses.