Hunting for Planet Nine by its perturbations on the Main Asteroid Belt

Abstract: In recent years, scientists have found unconfirmed evidence for a ninth planet in the solar system at a very wide orbit. The parameters for this planet are poorly constrained. Current estimates mostly come from the effect the planet has on trans-neptunian objects. Here we investigate an alternative scenario, that is whether this proposed planet can exert observable perturbation on Main Belt asteroids through a particular resonance, active when the precession period of the asteroid is close to the orbital period of Planet Nine. As the apsidal precession period of the Main Belt asteroid is mainly driven by Jupiter, we first derive the precession period under the disturbance of Jupiter. We find that for asteroids at ~3 AU, the resonant condition is fulfilled when Planet Nine has a semi-major axis of ~600 AU. With the asteroids' behaviour known we add a Planet Nine to the simulations at the semi-major axis of optimal resonance conditions with asteroids positioned around 3 AU and analyse the output orbital data. However, in simulations where we assign Planet Nine a mass of 1000 Earth masses, no resonances are observed. To increase the chance of capture into resonance we let Planet Nine migrate inward or outward, causing the resonance to sweep through the asteroids. The mass of the planet is also increased to the somewhat unreasonable values of a solar mass and a tenth of a solar mass. With these implausible parameters, we find that the resonance is possible and when in libration, the periapsis of the asteroid is locked to the position of Planet Nine. Further studies are needed to determine the possibility of resonance for a more reasonable planetary mass and how effectively the planet can capture asteroids into resonance. We note that the effect investigated here may be the only known mechanism able to constrain the instantaneous location of Planet Nine.