# Evaluating the Dynamical Stability of Outer Solar System Objects in the Presence of Planet Nine

## TL;DR

This study uses numerical simulations to assess how the hypothetical Planet Nine influences the stability and orbital behavior of distant solar system objects, providing evidence supporting its existence and characterizing its possible orbital parameters.

## Contribution

It introduces a comprehensive Monte Carlo simulation approach to evaluate the dynamical effects of Planet Nine on TNOs, offering new constraints on the planet's orbital elements and object interactions.

## Key findings

- Some orbital configurations of Planet Nine stabilize TNOs.
- TNOs can transition between resonances while remaining stable.
- Results support the existence of Planet Nine with specific orbital parameters.

## Abstract

We evaluate the dynamical stability of a selection of outer solar system objects in the presence of the proposed new Solar System member Planet Nine. We use a Monte Carlo suite of numerical N-body integrations to construct a variety of orbital elements of the new planet and evaluate the dynamical stability of eight Trans-Neptunian objects (TNOs) in the presence of Planet Nine. These simulations show that some combinations of orbital elements ($a,e$) result in Planet Nine acting as a stabilizing influence on the TNOs, which can otherwise be destabilized by interactions with Neptune. These simulations also suggest that some TNOs transition between several different mean-motion resonances during their lifetimes while still retaining approximate apsidal anti-alignment with Planet Nine. This behavior suggests that remaining in one particular orbit is not a requirement for orbital stability. As one product of our simulations, we present an {\it a posteriori} probability distribution for the semi-major axis and eccentricity of the proposed Planet Nine based on TNO stability. This result thus provides additional evidence that supports the existence of this proposed planet. We also predict that TNOs can be grouped into multiple populations of objects that interact with Planet Nine in different ways: one population may contain objects like Sedna and 2012 VP$_{113}$, which do not migrate significantly in semi-major axis in the presence of Planet Nine and tend to stay in the same resonance; another population may contain objects like 2007 TG$_{422}$ and 2013 RF$_{98}$, which may both migrate and transition between different resonances.