  The observational census of trans-Neptunian objects with semi-major axes
greater than ~250 AU exhibits unexpected orbital structure that is most readily
attributed to gravitational perturbations induced by a yet-undetected, massive
planet. Although the capacity of this planet to (i) reproduce the observed
clustering of distant orbits in physical space, (ii) facilitate dynamical
detachment of their perihelia from Neptune, and (iii) excite a population of
long-period centaurs to extreme inclinations is well established through
numerical experiments, a coherent theoretical description of the dynamical
mechanisms responsible for these effects remains elusive. In this work, we
characterize the dynamical processes at play, from semi-analytic grounds. We
begin by considering a purely secular model of orbital evolution induced by
Planet Nine, and show that it is at odds with the ensuing stability of distant
objects. Instead, the long-term survival of the clustered population of
long-period KBOs is enabled by a web of mean-motion resonances driven by Planet
Nine. Then, by taking a compact-form approach to perturbation theory, we show
that it is the secular dynamics embedded within these resonances that regulates
the orbital confinement and perihelion detachment of distant Kuiper belt
objects. Finally, we demonstrate that the onset of large-amplitude oscillations
of orbital inclinations is accomplished through capture of low-inclination
objects into a high-order secular resonance and identify the specific harmonic
that drives the evolution. In light of the developed qualitative understanding
of the governing dynamics, we offer an updated interpretation of the current
observational dataset within the broader theoretical framework of the Planet
Nine hypothesis.
