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# What is the Kozai Effect or Kozai Mechanism?

The Kozai mechanism, or Lidov-Kozai mechanism refers to the fact that a body in orbit under gravitational forces can exchange the eccentricity with the inclination angle of the plane of the orbit (with respect to some reference direction). (The eccentricity is a measure of how “squashed” the orbit is with respect to a circle.) The result can a periodic oscillation in the inclincation angle that is accompanied by periodic variation in the eccentricity of the orbit.

The Kozai effect is thought to be relevant for some exoplanet systems, especially those in which the eccentricity is unusually high and/or difficult to explain otherwise. However, these studies are in their infancy and there are many missing pieces of information.

Advanced Readers: The technical term usually used for the result of the Kozai mechanism is “libration of the pericenter” of the orbit about a constant value. The mechanism is ultimately driven by angular momentum conservation and mathematically, the quantity $\sqrt{(1-e^{2})}\cos{i}$ is constant, where $e$ is the eccentricity of the orbit, and $i$ is the inclincation angle. The original paper by Lidov is in Russian and was not available on the internet last I checked (the reference is Lidov, M. L., 1961, in: Iskusst. sputniky Zemly 8, Acad. of Sci., USSR). The original paper by Y. Kozai is AJ, 67, 591. There also an interesting short note written by him in 2012 in which he points out how the original purpose of his paper was only meant for understanding asteroids. He explains that the effect was not directly observable in asteroids because the timescale is thousands of years but then he describes how people realized that the mechanism might be relevant for other systems such as galaxies, stars, and then finally exoplanets.

File under: Definition of the Lidov-Kozai effect or mechanism. Secular exchange of orbital inclination and eccentricity in dynamical systems. Eccentricities of exoplanet orbits.