Exponential growth of eccentricity in secular theory

Understand

The Kozai mechanism for exponentially exciting eccentricity of a Keplerian orbit by a distant perturber is extended to a general perturbing potential.

• In particular, the case of an axisymmetric potential is solved analytically.
• The analysis is applied to orbits around an oblate central object with a distant perturber.
• If the equatorial plane of the central object is aligned with the orbit of the distant perturber (axisymmetric potential), a single instability zone, in which eccentricity grows exponentially, is found between two critical inclinations; if misaligned (non-axisymmetric potential), a rich set of critical inclinations separating stable and unstable zones is obtained (Vashkoviak 1974).