Many asteroids have been observed around the triangular Lagrangian points (L4 and L5) of Jupiter, but none around Saturn's where they are difficult to observe. Hence, a study of their orbital stability would focus future searches, or place constraints on the last phases of Solar system formation. I numerically integrated orbits around the L4 and L5 points of Jupiter (Trojans) and Saturn ("Bruins"): 40 Trojans and 350 Bruins, all of inclination less than 12^circ. Four Bruins remained stable until the integration was stopped at 412 Myrs. Properties of these stable orbits were: (1) proper eccentricities less than 0.028; (2) librations in true longitude about L4 and L5 of more than 80^circ; (3) longitudes of perihelion that librated relative to a libration center 45^circ from Saturn's longitude of perihelion, such that the perihelia were never close when the forced eccentricity was near 0.08; (4) longitudes of perihelion that were never close to Jupiter's longitude of aphelion when their eccentricities were near maximum; and (5) maximum eccentricities that never occur at the same time as Jupiter's maximum eccentricity. These properties of a stable Bruin's orbit reduce the perturbations by Jupiter and Saturn. Orbits with librations in true longitude less than 80^circ were unstable, the time to instability being correlated with libration angle. While Bruins of small libration angle went unstable, no unstable region was found around Jupiter's triangular Lagrangian points, and stable Trojans may have longitudes of perihelion that either circulate or librate with respect to Jupiter's, with proper eccentricities as much as an order of magnitude larger than those for the Bruins. A major contributor to Bruins going unstable near L4 and L5 is the presence of three separatrices of motion caused, in part, by the Great Inequality (GI) between Jupiter and Saturn. The GI separatrices drive up the eccentricity of Bruins on small tadpole orbits, but have much less effect on large tadpole orbits (like the four long-lived Bruins).
- Pub Date:
- January 1993
- Physics: Astronomy and Astrophysics, Engineering: Aerospace, Physics: General