Constraints on Planet Nine in a Mean-Motion Resonant Framework
Despite the substantial evidence for the existence a super-Earth sized planet in the distant solar system (Batygin & Brown 2016), the hypothetical Planet Nine’s orbit and sky location are still uncertain. In early 2017, I published a paper that aimed to derive constraints on Planet Nine’s orbit and sky position. Under the assumption that Planet Nine is in small integer ratio mean-motion resonances (MMRs) with some subset of the most distant Kuiper Belt Objects (KBOs), I found that the observed KBO semi-major axes present a set of commensurabilities with an unseen planet at ~654 AU that has a greater than 98% chance of stemming from a sequence of MMRs rather than from a random distribution. I performed a Monte-Carlo optimization scheme that used billion-year dynamical integrations of the outer solar system to pinpoint the orbital properties of a planet that is capable of maintaining the KBOs’ apsidal alignment.
Below is a 3D GIF of the KBO orbits and our proposed best-fit orbit of Planet Nine. To manipulate the diagram yourself, check out the following link: https://smillholland.github.io/P9_Orbit/.