Long-term cycling of Kozai-Lidov Cycles: Extreme eccentricities and inclinations excited by a distant eccentric perturber

Kozai-Lidov oscillations of Jupiter-mass planets, excited by comparable planetary or brown dwarf mass perturbers were recently shown in numerical experiments to be slowly modulated and to exhibit striking features, including extremely high eccentricities and the generation of retrograde orbits with respect to the perturber. Here we solve this problem analytically for the case of a test particle orbiting a host star and perturbed by a distant companion whose orbit is eccentric and highly inclined. We give analytic expressions for the conditions that produce retrograde orbits and high eccentricities. This mechanism likely operates in various systems thought to involve Kozai-Lidov oscillations such as tight binaries, mergers of compact objects, irregular moons of planets and many others. In particular, it could be responsible for exciting eccentricities and inclinations of exo-planetary orbits and be important for understanding the spin-orbit (mis)alignment of hot Jupiters.