KozaiLidov

The Kozai-Lidov mechanism is a secular perturbation effect in hierarchical three-body systems, where a distant perturber on an inclined orbit induces cyclic exchanges between the eccentricity and the inclination of the inner orbit. Under the quadrupole approximation, the outer potential is axisymmetric, and the component of the inner orbit's angular momentum along the total angular momentum is approximately conserved.

This leads to Kozai cycles when the mutual inclination exceeds a critical angle of about 39.2 degrees. During a cycle, the inner orbit's eccentricity and inclination oscillate: as eccentricity rises, periapsis distance decreases, while inclination changes inversely. The cycle timescale depends on the masses, semi-major axes, and the outer orbit.

Extensions to higher-order perturbations (octupole level) allow more complex behavior, including larger eccentricities, chaotic motion, and flips between prograde and retrograde orientations, especially when the outer orbit is eccentric. Additional forces such as general relativistic precession, tides, and planetary oblateness can suppress Kozai cycles.

Applications span various astrophysical contexts: asteroid and satellite dynamics in the solar system, hierarchical triple-star systems, and exoplanetary systems including hot Jupiters migrating via high-eccentricity pathways. The mechanism has also been invoked to explain dynamical interactions in multiple-body systems and irregular satellite configurations. The effect was independently discovered by Yoshihide Kozai (1962) and Mikhail Lidov (1962), hence the combined name Kozai-Lidov mechanism.