According to the International Astronomical Union (IAU) in the Solar System, a planet is a celestial body which:
- is in orbit around the Sun;
- has sufficient mass to assume hydrostatic equilibrium (a nearly round shape);
- has “cleared the neighborhood” around its orbit.
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So, from this definition, it is clear that there cannot be two planets in one orbit; otherwise, they would no longer satisfy the definition provided by the IAU.
But, to answer the question, let us ignore the words above and consider the issue on the merits.
In the star system, Lagrange Points are positions where the gravitational forces of a two-body system like the Sun and the Earth produce a strong field of attraction and repulsion.
At these points, the attraction of the star and the planet and centrifugal forces balance each other. Points L1, L2 and L3 lie on the line connecting the two masses and therefore are unstable to small perturbations: objects at these points cannot have a stable orbit.
But the points L4 and L5 are stable in orbit. If you place an object at such a point with a negligible mass compared to a star and a planet, then the object could be at this point indefinitely. It would rotate around the star in the same orbit as the planet at a constant distance from it.
Lagrange Points in the orbit of the Earth have actively used for operating research vehicles. So, the recently launched domestic telescope “Spektr-RG” went to the Lagrange point L2, and next year; they plan to launch the James Webb telescope there, which would be the successor of Hubble.
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Objects at Lagrange Points can also arise naturally. So, Jupiter has two groups of asteroids orbiting the Sun in the same orbit. They are located in the vicinity of the Lagrange Points L4 and L5. They are called “Trojan” and “Hilda” asteroids. Other planets have similar asteroids: Mars, Neptune, Uranus. Even the Earth has one Trojan asteroid, in the region of the Lagrange point L4.
What about the planets?
As we found out, small bodies whose masses are very small compared to the mass of the planet and the stars can be in the same orbit as the planet.
What if a small asteroid is placed at the Lagrange Point, but a planet is of the same mass? In this case, the calculations show that the orbits of such planets will be unstable and sooner or later, they will either collide, or throw one of the planets out of orbit.
The orbits of the planets in one orbit can be quasi-stable, i.e. they can revolve around a star in one orbit for quite some time: millions, in some cases even billions of years, but in the long run only one planet will remain in orbit.
According to modern scientific ideas, at the dawn of the existence of the solar system in the Earth’s orbit, there was another body co-orbiting it: Theia (a planet the size of Mars). It was precise as a result of Theia’s collision with the proto-Earth when our Moon was formed.
Thus, two planets of comparable size can be in the same orbit, but this orbit will not be stable in the long term and it will end either in a collision or in dropping one of the planets from orbit. These situations are most likely in the early stages of planetary system formation. The older the planetary system is, the less likely it is to see something similar in it.