 Solution

The body now returns on a bound, highly eccentric orbit whose periapsis crosses more deeply into the planet's neighborhood. Repeated planetary scattering produces a sequence of energy and angular-momentum kicks rather than smooth secular evolution. Possible endpoints include ejection onto an unbound orbit, collision with the planet or star, tidal disruption, or diffusion onto a detached orbit that no longer encounters the planet. Temporary protection by a mean-motion resonance is also possible. The approximate Tisserand parameter constrains weak separated encounters, but the close-encounter sequence is chaotic and does not select a unique final orbit.