Kozai effect

In celestial mechanics, the Kozai mechanism, or the Lidov–Kozai mechanism, is a perturbation of the orbit of a satellite by the gravity of another body orbiting farther out, causing libration (oscillation about a constant value) of the orbit's argument of pericenter. As the orbit librates, there is a periodic exchange between its inclination and its eccentricity.

The effect was described in 1961 by the Soviet specialist in space dynamics Michael Lidov (Russian: ) while analyzing the orbits of artificial and natural satellites of planets, This result was reported by Lidov at the Conference on General and Practical Topics of Theoretical Astronomy, held in Moscow on 20 - 25 November 1961. Among the participants of that conference was a Japanese astronomer Yoshihide Kozai (Japanese: ) who soon published this same result, in application to the orbits of the asteroids. Since then, this effect has been found to be an important factor shaping the orbits of irregular satellites of the planets, trans-Neptunian objects, and a few extrasolar planets and multiple star systems.

In the hierarchical, restricted three-body problem, it is assumed that the satellite has negligible mass compared with the other two bodies (the "primary" and the "perturber"), and that the distance between the primary and perturber is much greater than the distance from the primary to the satellite. These assumptions would be valid, for instance, in the case of an artificial satellite in a low-Earth orbit that is perturbed by the moon, or a short-period comet that is perturbed by Jupiter.

Under these approximations, the orbit-averaged equations of motion for the satellite have a conserved quantity: the component of the satellite's orbital angular momentum parallel to the angular momentum of the primary/perturber angular momentum. This conserved quantity can be expressed in terms of the satellite's eccentricity e and inclination i relative to the plane of the outer binary:

...
Wikipedia