How to Flip a Planet or The Kozai Mechanism and Angular Momentum Conservation: Implication for Extrasolar Planets

Statistics – Applications

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Scientific paper

The theory of secular perturbations between two orbits in a hierarchical triple configuration has many astrophysical applications, from planetary dynamics to triple star systems. In the secular approximation the orbits may change their shape and orientation, but the semi-major axes remain constant. For sufficiently inclined systems, the Kozai mechanism can produce large-amplitude oscillations in the orbital eccentricities and relative inclination. We have re-derived the full set of secular evolution equations including both quadrupole and octupole orders using Hamiltonian perturbation theory. Our new derivation corrects an error in several previous treatments of the problem. We discuss various interesting implications of using the correct formalism for systems containing two coupled planets, including the possibility of forming retrograde planets.

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