Generalization of Szebehely's regions for asteroid stability

Using Hill's modified stability criterion in the three-dimensional restricted three-body problem with the Sun and Jupiter as the primaries, regions of stability for the semi-major axis (a) are determined. These regions are given for a range of eccentricity (e) and inc.l.ination (i), and include the effects of the remaining orbital elements. This generalizes Szebehely's previous results which only examined the effects of e and i on the regions of stability for the semima jor axis. It is shown that if the other orbital elements are also considered, the previous results are sharpened but are not contradicted.