Orbits Close to Asteroid 4769 Castalia

We use a radar-derived physical model of 4769 Castalia (1989 PB) to investigate close orbit dynamics around that kilometer- sized, uniformly rotating asteroid. Our methods of analysis provide a basis for systematic studies of particle dynamics close to any uniformly rotating asteroid. We establish that a Jacobi integral exists for particles orbiting this asteroid, examine the attendant zero-velocity surfaces, find families of periodic orbits, and determine their stability. All synchronous orbits and direct orbits within approx. 3 mean radii of Castalia are unstable and are subject to impact or escape from Castalia. Retrograde orbits are mostly stable and allow particles to orbit close to the asteroid surface. We derive a model which allows us to predict the escape conditions of a particle in orbit about Castalia and the (temporary) capture conditions for a hyperbolic interloper. Orbits within 1.5 km of Castalia are subject to immediate ejection from the system. Hyperbolic orbits with a V(sub infinity) less than 0.4 m/sec can potentially be captured by Castalia if their periapsis radius Is within approx. 2 km. For Castalia this capture region is small, but the results also apply to larger asteroids whose capture regions would also be larger. We determine bounds on ejecta speeds which either ensure ejecta escape or re-impact as functions of location on Castalia's surface. The speeds that ensure escape range from 0.28 to 0.84 m/sec and the speeds that ensure re-impact range from 0 to 0.18 m/sec. Speeds between these two bounds lead either to escape, re-impact, or potentially finite-time stable orbits. We develop a simple criterion which can establish whether a particle could have been ejected from the asteroid in the past and if it will impact the surface in the future.