A new planet in the most remote corner of the solar system?

Modeling the hypothetical planets' effects on small bodies: Clement & Kaib (2020)

The possibility of a new planet residing in the far reaches of the outer solar system has captivated the public over the last several years (Batygin and Brown, 2016). Because the existence of the so- called Planet Nine is inferred via orbital clustering of extreme trans-Neptunian objects (ETNOs; see accompanying figure), we sought out to understand how many ETNO detections would be required to confidently infer the distant planets' existence in Clement and Kaib (2020). In other words, while Planet Nine remains undiscovered, how many distant objects like Sedna would we have to discover to know for sure something out there is tugging on their orbits. While our analysis confirmed that Planet Nine is the best explanation for the observed data, we found that it is impossible to distinguish between a Planet Nine-generated distribution of orbits, and a random sample of uniformly oriented orbits at greater than the 1σ level. We estimated that ∼100 detected ETNOs will be required to confidently infer Planet Nine’s existence. Unfortunately, we only know of a dozen or so ETNOs today, so proving Planet Nine's existence in this manner is still a long way off.

Distant Resonant Kuiper Belt Objects as a potential means of ruling out the existence of additional planets: Clement & Sheppard (2021)

Pluto-like objects in the distant Kuiper Belt are not typically considered in the Planet Nine discussion as their orbits periodically bring them close enough to the giant planets such that their dynamical evolution is largely governed and driven by interactions with Neptune. In particular, bodies in the outer regions of the Kuiper Belt (the so-called scattered disk) tend to periodically fall in and out of n:1 mean motion resonances with Neptune (e.g.: 6:1, 7:1, 8:1, and so on). Thus, an object in, for example, Neptune's 8:1 resonance orbits the Sun exactly once for every eight Neptune orbits. In Clement & Sheppard (2021), we studied each individual n:1 resonance out to the 14:1 to better understand if the most-distant resonances are stable in the presence of Planet Nine. It turns out that Planet Nine disturbs the resonances more distant than the 11:1 rather efficiently. Thus, we would expect the population of Kuiper Belt objects to drop off around these resonances. Currently, this does not seem to be the case (see accompanying figure). While we still do not know of enough objects to claim this speaks against the Planet Nine hypothesis in any meaningful way, these types of distant objects are easier to detect than those ETNOs described above (as their orbits typically bring them closer to Neptune, and thus closer to Earth). Thus, the detection of more objects beyond the 11:1 resonance might one day provide useful constraints on hypotheses invoking the existence of additional planets.

Observed objects near Neptune's distant n:1 resonances. Figure reproduced from Clement & Sheppard (2021)