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The longitudes of perihelia and orbital poles of the solar system's dozen orso most remote detected objects are clustered in a manner inconsistent withthat of a random sample of uniformly distributed orbits. While small numberstatistics and observational biases may explain these features, the statisticalsignificance of the clustering has led to the recent development of the "PlanetNine hypothesis." In the proposed scenario, orbits in the distant solar systemare shepherded via secular perturbations from an undetected massive planet onan eccentric orbit. However, the precession of perihelia and nodes in the outerKuiper Belt and inner Oort Cloud are also affected by the the giant planets,passing stars, and the galactic tide. We perform a large suite of numericalsimulations designed to study the orbital alignment of Extreme Trans-NeptunianObjects (ETNOs) and Inner Oort Cloud Objects (IOCOs). In our variousintegrations that include Planet Nine, we consistently find that >60% of ETNOsand IOCOs that are detectable after 4 Gyr are also anti-aligned in periheliawith the distant massive perturber. However, when we randomly select 17 objectsfrom this sample of remaining orbits, there is significant scatter in thedegree of longitude of perihelion and orbital pole clustering that might beobserved. Furthermore, we argue that, in the absence of Planet Nine, 17randomly drawn orbits should still exhibit some clustering even if theunderlying distribution is uniform. Thus, we find that still more ETNO and IOCOdetections are required to confidently infer the presence of Planet Nine.

Orbital precession in the distant solar system; further constraining the Planet Nine hypothesis with numerical simulations