# Central planet in binary star system?

https://en.wikipedia.org/wiki/Habitability_of_binary_star_systems

The wikipedia article describes P-type and S-type orbits for planets in binary star systems. There are possibly some other quasistable funky orbits.

But what about a central planet? I have added one to the diagram with its "W-type" nonorbit. The Ptolemy planet is parked between its two suns of equal mass. It does not orbit but sits there in the middle, centered between the stars. Physics wise it seems like it should be stable. How the planet would get there is a different matter - probably it would need to be a construct or perhaps a survivor of a more complex multiplanet arrangement in which other players are now gone and Ptolemy is sitting still.

Of course the stars would need to be suitably far away from each other such that their combined light did not bake a planet that we want to be redolent with sweet alien life. Ptolemy would be outside the habitability zone of either star considered alone, and probably there is no P or S type orbit around these wide spaced binaries that would not bake or deep freeze the planet.

The joint efforts of the 2 stars produce this small habitability zone centered between.

Plausible?

• As it is pointed out in the answers, Location W is unstable. It is actually a L1 Lagrange point in the two stars system. Sep 15, 2021 at 17:22
• It would be as impossible as suspending a magnet between two magnets without touching either. The slightest movement towards one would instantly snap it to the nearer one. Same mathematics, different time scale. Sep 16, 2021 at 7:04
• “Walk on road. Walk right side, safe. Walk left side, safe. Walk middle, sooner or later, get squish, just like grape.” Sep 16, 2021 at 11:14
• The other possibility (equally as unlikely as your W-type) would be some sort of figure-8 orbit, where the planet is periodically traded off between each of the two stars. This is even less likely to be stable, and certainly less likely to be habitable, but it's possible in theory, and would be really cool in a hyper-futuristic fictional universe. (You'd almost have to deliberately set up such a system, and possibly maintain it over time - possibly with in reach of a Type II Civilization - but we're not even Type I yet...) Sep 16, 2021 at 17:02

Physics wise it seems like it should be stable

Does it?

Seems like it is balanced on a bit of a knife-edge... a little nudge towards either star will cause it to accelerate out of position because the gravitational pull from the nearer star will be stronger than the farther star. You'll end up with a plummet to firey doom (or at least, a cometary trajectory that will spread the firey doom out over a few orbits).

The presence of any other body in the system seems like it could upset the delicate balance. Even if it were just these three, I wouldn't want to bet on it remaining stable long enough to develop life.

• No need for a fourth body. Any small deviations from a perfect spherically symmetrical form for any of the three bodies would be enough. Sep 15, 2021 at 17:39
• This can be termed as a state of 'unstable equilibrium' in physics. Sep 17, 2021 at 1:17

## L1Lagrange points are unstable

You are correct that between two large masses there are gravitational equilibrium points. These are known as Lagrange Points.

There are five such points, labeled L1 to L5, all in the orbital plane of the two large bodies, for each given combination of two orbital bodies. L1, L2, and L3 are on the line through the centers of the two large bodies, while L4 and L5 each act as the third vertex of an equilateral triangle formed with the centers of the two large bodies. L4 and L5 are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies.

The unstable Lagrange points are exactly that: points. Any real object with real mass will extend into the area where there are gravity differentials (which are not uniform unless the two major objects are exactly the same mass, density and perfect spheres - so, not stars) and will drift away.

Natural Trojans can exist at L4 and L5. Such systems are only meta-stable in any system with more than 3 bodies (i.e all real systems) because sufficient perturbation from other bodies will knock them out of the stable zone. The rule of thumb for long-term stability is m1 > 100m2 > 10,000m3 for the primary, secondary and trojan respectively. There are certainly binary systems that could meet this criterion.

There are and are planned missions that place satellites at both stable and unstable Earth (and other planets) Lagrange points. While the unstable ones do require station keeping, the fuel requirement is small. This means, for example, that a solar observatory at L1 can be kept on station with minimal fuel, is closer to the Sun than Earth and is always in communication. However, without thrust, an object at an unstable Lagrangian will rapidly drift away.

In the Solar System, the Jovian trojans are about as numerous as the asteroids in the asteroid belt and trojans have been identified for Venus, Earth, Mars, Uranus, Neptune, Ceres and Vesta - some are transient and some are stable.

• Well not as sexily symmetric as L1 right between but I guess a planet at L4 or L5 would be ok. L4 _and_L5. They could glare at each other. Sep 16, 2021 at 2:20
• @Willk thees are in fact the locations of the Greek and Trojan asteroids in Jupiter-Sol system. It's certainly plausible that you could have a single planetary body at these Lagrange points rather than a set of asteroids. Because of how Trojans and Greeks form, you would expect roughly the same mass at both the L4 and L5 lagrange points, although depending on historical accident (e.g. a passage from a large external body), it's possible one might have a single planet and the other still have asteroids Sep 16, 2021 at 9:19

I don't think that position is stable: any small deviation from the exact center where the gravitational forces balance each other would cause the planet to drift further away.

Reasons for the deviation can be, just to name a few: mass unbalance in the planet, mass unbalance in any of the two stars, different gravitational forces on any of the 3 bodies.

Also don't forget that the center or mass of the system would be orbiting some other attractor (c.o.m. of the Galaxy), and such an orbit would inevitably result in one of the bodies moving away from the sweet spot, with catastrophic (for the planet) consequences.

Location W is what we would call "unstable equilibrium".

While there is an atom-precise location between two binary stars where gravitational attraction to each star is equal, any perturbation away from that point will lead to a greater attraction to one star that will inevitably pull planet "W" out of that central location.

Furthermore, the same logic applies to making a planet out of the accretion disc at location W: dust will be pulled away by any perturbation.

Planet W is not plausible and cannot exist. The best option for something at location W would be an artifact from an advanced civilisation (with propulsion to hold it in place, or an inevitable orbital decay).

• I was hoping this would turn out to be like one of those stable Lagrange points where forces tend to pull the planet back to the center. Forces, you know. Maybe if I added some epicycles... Sep 15, 2021 at 16:22
• It IS one of those Lagrange points. One of the unstable ones. Sep 15, 2021 at 23:47