One of the great puzzles of modern astronomy is whether the Solar System hides a distant undiscovered planet. If this planet were relatively near — orbiting close to or within the orbit of Neptune — it ought to have been discovered by now. But if it were much more distant — orbiting in the Kuiper Belt far beyond the orbit of Neptune, for example — astronomers would find it extremely hard to track down.

There is indeed evidence to support the existence of such a planet. This comes from the study of the small, icy bodies and dwarf planets, like Pluto, Haumea and Quaoar, that orbit beyond Neptune. These so-called trans-Neptunian Objects are not distributed evenly but seem to follow certain patterns of distribution, as if they were being herded be an unseen gravitational force.

Gravitational Herding

That gravitational force must come from an undiscovered neighbor, say astronomers. The idea raises some interesting questions, not least of which is what this planet might be like and where we are likely to find it.

Now we get an answer thanks to the work of Patryk Lykawka at Kindai University in Japan and Takashi Ito at National Astronomical Observatory of Japan, who have used the pattern of trans-Neptunian objects to predict the likely mass and distance of the undiscovered planet.

Our mysterious neighbor, they conclude, probably orbits at a distance of 250-500 astronomical units (au=the distance from the Earth to the Sun) and has a mass between 1.5 and 3 times that of our home planet. If they are right, somewhere else in the Solar System there is a planet that is remarkably similar to Earth.

Trans-Neptunian objects turn out to have a remarkable set of properties that cannot have come about by accident. The specific details are clues to the way these objects must have been influenced in the past.

For example, smaller objects tend to occupy orbits that resonate with the orbit of larger ones. This is the result of constant gravitational nudging over billions of years as the larger planets sweep past. This makes only certain configurations stable.

So Lykawka and Ito focus on three fundamental properties of trans-Neptunian objects that cannot be explained by the ordinary gravitational nudging of known planets. The first is that a significant proportion of these objects orbit at a distance greater than 40 au, beyond the gravitational influence of Neptune.

That raises the question of how they came to be there. What kind of gravitational nudging could have shepherded them into this configuration?

Another property of trans-Neptunian objects is that a significant proportion have highly inclined orbits, that takes them out of the plane of the rest of the Solar System. Only a specific kind of nudging could have created such a sub-population.

And finally, a few trans-Neptunian objects have peculiar orbits that are difficult to produce with conventional models of gravitational nudging. The dwarf planet Sedna, for example, has an exceptionally elongated orbit that takes it from 60 au at its closest approach to almost 1000 au at its most distant.

Gravitational interactions with Neptune or the other known planets cannot explain this orbit. At least nine other trans-Neptunian objects have similarly peculiar orbits.

“A successful model for the distant Kuiper Belt should explain these constraints simultaneously,” say Lykawka and Ito.

Snowball Earth

Astronomers believe that the Solar System probably formed with several tens of sub-Earth and Earth-class planets that have mostly wandered off into interstellar space due to collisions and scattering. The hypothesis that Lykawka and Ito explore is whether one of these could still be in the Solar System and responsible for the various orbits of trans-Neptunian objects.

To find out, they created a gravitational model of the Solar System to simulate how an Earth-like planet might influence these distant bodies. “We used extensive simulations to demonstrate that a resident undiscovered Earth-like planet could explain the main constraints in the distant Kuiper Belt,” they say. “We found that a Kuiper Belt planet 1.5–3 times as massive as Earth can explain [these] properties,” they say.

This Earth-like planet must orbit at between 250 au and 500 au, in an orbit that is inclined at 30 degrees to the Solar System. What’s more, the model predicts the existence of more trans-Neptunian objects in peculiar orbits like Sedna’s. Any future discovery of these would lend credence to Lykawka and Ito’s claim.

That’s a fascinating result that suggests somewhere out there is another Earth-like planet waiting to be discovered, albeit one that must be significantly colder and darker than our own. There is no way of knowing whether Lykawka and Ito are correct but there will surely be more than a few astronomers dusting off their telescopes, reaching for their lens cloths and filling flasks with hot coffee in their efforts to discover it.

Ref: Is There an Earth-like Planet in the Distant Kuiper Belt? : arxiv.org/abs/2308.13765