A Hill problem with oblate primaries and effect of oblateness on Hill stability of orbits

We introduce a new version of Hill's problem to include the effect of oblat eness of the primaries, and briefly discuss its equilibrium points and zero velocity curves. As a first application we use this to study Hill stabilit y of direct orbits around the small primary. This can be employed to study the stability of a planet's moon perturbed by an oblate Sun, or of a star's planet perturbed by a distant disk-shaped galaxy. Oblateness of the `Sun' is found to decrese the maximum distance of Hill stable direct `moon' orbit s.