Coorbital dynamics at large eccentricity and inclination

We show that coorbital dynamics at large eccentricity and inclination exhib it hitherto unknown types of stable motion in the gravitational three-body problem. In the solar system, the secular stability is observed in the evol ution of specific near-Earth asteroids. In particular, the slow diffusion o f such objects through the Earth's coorbital region which leads to temporar y capture suggests the existence of undiscovered retrograde moons of the Ea rth. In the Coulomb problem, the Kozai resonance is a primary candidate for stable low angular momentum states in two-electron atoms.