The secular planetary three body problem revisited

High inclination orbits in the secular quadrupolar three-body problem

The Lidov-Kozai mechanism (Kozai 1962; Lidov 1962) allows a body to periodically exchange its eccentricity with inclination. It was first discussed in the framework of the quadrupolar secular restricted three-body problem, where the massless particle is the inner body, and later extended to the quadrupolar secular nonrestricted three body problem (Harrington 1969; Lidov & Ziglin 1976; Ferrer & ...

Three - Body Problem

Secular Evolution of Planetary Systems in Binaries

The orbital eccentricity of a single planet in a stellar binary system with a sufficiently large mutual inclination angle is known to oscillate on a secular timescale through the Kozai mechanism. We have investigated the effects of the Kozai mechanism on double-planet systems in binaries. The evolutionary sequence of a pair of planets under the influence of a binary companion is fairly complex....

Secular Evolution of Hierarchical Planetary Systems

We investigate the dynamical evolution of coplanar hierarchical two-planet systems where the ratio of the orbital semimajor axes α = a1/a2 is small. Hierarchical twoplanet systems are likely to be ubiquitous among extrasolar planetary systems. We show that the orbital parameters obtained from a multiple Kepler fit to the radial velocity variations of a host star are best interpreted as Jacobi c...

A Trilinear Three-Body Problem

In this paper we present a simplified model of a three-body problem. Place three parallel lines in the plane. Place one mass on each of the lines and let their positions evolve according to Newton’s inverse square law of gravitation. We prove the KAM theory applies to our model and simulations are presented. We argue that this model provides an ideal, accessible entry point into the beautiful m...