From time to time, I wonder why we don't see two exoplanets sharing the same path.
Co-orbital objects can exist for two reasons.
There are five regions of gravitational stability when you solve the equations for the forces that exist around a small object and a large object. If you put something there they will stay there. The L1 - L5 points are called the lagrange points.
Three of them are meta-stable, in that an object there can easily wander off under a small amount of force, but L4 and L5 are more stable. If you poke an object there, it will settle back into place like a ball in a bowl.
The two points are 60 ahead of a planet and 60 behind it in its journey. Earth has at least one asteroid, and Jupiter has many of them. There are two reasons we know co-orbital objects can exist. Some moons of gas giants have asteroids in their vicinity.
No two of the 5,000 exoplanets have been found to be in the same area. It is possible for a gas giant planet with more mass than Jupiter to have enough gravity to support an Earth-sized planet. This is the only one that has been found.
It is possible that we missed some, since smaller planets are harder to observe, but still, having found exactly zero feels like the Universe is telling us that these are not stable.
The physicists looked at the physics of this to see if it was possible. I took a class on this during my time in graduate school and it was difficult, but the equations showing the existence of the Lagrange points is easy to understand. In particular, the tides are left out.
The force of gravity depends on how far away the star is. There is a higher force of gravity on the side facing away from the star than on the side closest to it. The change in gravity is called the tidal force.
This can have a big effect. The moon feels tides from our planet that have moved it away from Earth and locked its rotation rate. The Moon's tides squeeze and stretch the planet, creating more or less twice daily ocean tides, and are slowing the Earth's rotation.
The equations for the gravity of a star in a three-body system of planets were looked at by the astronomer. Both of them agreed that tides can destabilize a co-orbital object by using a computer.
The small planet may be a little more tilted or elliptical than the bigger planet, but it doesn't need to be the same as the bigger one. The smaller planet can still be stable if it ignores the tides and stays in the same spot as the larger planet. The scientists found that the tides make the smaller planet more circular. That is actually okay. Tides tend to keep the object in a more stable position.
There is a case where the smaller planet is moving slightly ahead and behind the stable Lagrange point. Ignored tides are generally stable. When they include tides, they found that this type of oscillation, called a tadpole obit due to its shape, grows over time. The smaller planet eventually moves so far that it leaves the region of stability, and then it collides with the larger planet or the star.
We don't see co-orbital objects because of that. Slamming into a planet or a star can be hard to continue.
The results are consistent with earlier work that was done in a different way. When the third object is small like an asteroid, it can work, but once it gets large enough to have strong gravity, the system becomes unstable.
It appears that co-orbital planets aren't possible. We haven't seen one yet but that doesn't mean they aren't out there The fact that no co-orbital planets have been seen is telling us that the situation is rare.
It is too bad. It is a staple of sci-fi and would make space travel to other worlds a lot simpler. TRAPPIST-1 is a system where the planets are close together, so it is still pretty nifty. There is a chance that we will only see two planets in fiction.
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