Kozai Mechanism - Kozai Resonance

Kozai Resonance

For an orbiting body in the restricted three-body problem with eccentricity and inclination relative to the fundamental plane, the following value is conserved:

Which is to say that orbital eccentricity can be traded for inclination, and perturbation may lead to an interchange between the two. Thus, near-circular, highly-inclined orbits can become very eccentric in exchange for lower inclination. Since increasing eccentricity while keeping the semimajor axis constant reduces the distance between the objects at periapsis, this mechanism can cause comets to become sungrazing.

Typically, for the objects in low-inclination orbits, the perturbations result in the precession of the argument of pericenter. Starting with some value of the angle, the precession is replaced by libration around 90° or 270°, and the pericenter (point of closest approach) is forced to oscillate around one of these values. The minimum required inclination angle, called the Kozai angle, is

For retrograde satellites the angle is 140.8°.

Physically, the effect is related to angular momentum transfer; the quantity conserved is actually the normal component of the angular momentum (see also Jacobi integral and Tisserand's relation).