Kozai mechanism

The Kozai mech is the periodic exchange between inclination and eccentricity; see this.

It is a secular interaction between a wide-binary companion and a planet, in a triple system. When the relative inclination angle between the two orbital planes is greater than 39.2 degrees (the Kozai angle) a cyclic and long-term exchange of angular momentum occurs between the planet and more distant companion.

For an orbiting body with eccentricity e and inclination i,   is conserved. A perturbation may lead to a resonance between the two. Typcally, this results in the precession of the argument of pericenter, which then librates (oscillates) around either 90° or 270°. Increasing eccentricity while keeping the semimajor axis constant reduces the periapsis distance (the distance at closest approach), and the periapse occurs when the body is at highest inclination. The maximum eccentricity reached is independent of orbital parameters like mass and period: .

Oribital parameters, mass and semimajor axes only affect the period of the Kozai cycles. This is estimated as , where the indices are 0) central star, 1) planet, and 2) binary companion. If the Kozai period is large, it is highly unlikely the planet is highly eccentric at a given point in time. The binary companions are probably either a brown dwarf (larger orbital range, mass can approach Jupiter masses) and main-sequence dwarfs, about the mass of the sun. The Kozai period is inversely proportional to the mass of the binary companion, so oscillation periods of brown-dwarf companion systems are hundreds of times longer than that of a main-sequence dwarf star.