Orbital Evolution in Resonance Lock.I.The Restricted 3-Body Problem

Orbital evolution in resonance lock for the restricted 3-body problem is analyzed by two different approaches, both yielding the same expression that imposes constraints to the variation of the semimajor axis, eccentricity and inclination of a massless object's orbit. The analysis is carried on by the inclusion of extra terms coming from nonconservative forces acting on the massless body. Through the consideration of specific librating angles, separate equations for the variation of the eccentricity and inclination are deduced. The analytical results are applied to dust particle dynamics, where the orbital evolution of grains in resonance lock with planets is tested against theory. Particularly interesting results are obtained for dust particles in retrograde orbits. Evolution of planetesimals in resonance lock with migrating planets is another tested application of the theory. Pluto's hypothetical evolution in the 2:3 resonance lock with a migrating Neptune is reviewed, also including a possible variation of Pluto's orbital inclination. Another explored problem is the orbital evolution of primordial asteroids in resonance lock with migrating planets.