Limits of Rigid Precession of Planetary Systems
Harry Braviner, University of Cambridge
Advisors: Doug Lin, Man Hoi Lee
Abstract:
We consider the parameter space for a planetary system with a distant, inclined companion under which the planets precess rigidly, rather than independently. Such behaviour is suspected to be occurring in the systems 55 Cancri and Kepler-56, both coplanar multiple-planet systems that are misaligned with their host stars. We test a prescription suggested by Takeda et al. (2008) and find (provided we are allowed to choose a single arbitrary constant appropriately) excellent predictive power for the boundary of rigid precession in a two-planet system.
We attempt to extend our results to three planets, but are frustrated by the presence of multiple Laplace-Lagrange timescales. We find that a crude result (the Lidov-Kozai timescale being the longest in the system implying rigid precession) appears to carry over from the two-planet case, but that more complicated behaviour ensues when this is not the case.
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