Resonance and Capture of Jupiter Comets
Koon, W. S., M. Lo, J. E. Marsden and S. Ross
Celestial Mech.and Dyn. Astron., 81, 27-38
Abstract:
A number of Jupiter family comets such as Oterma and Gehrels 3
make a rapid transition from heliocentric orbits outside the
orbit of Jupiter to heliocentric orbits inside the orbit of
Jupiter and vice versa. During this transition, the comet can be
captured temporarily by Jupiter for one to several orbits around
Jupiter. The interior heliocentric orbit is typically close to
the 3:2 resonance while the exterior heliocentric orbit is near
the 2:3 resonance. An important feature of the dynamics of these
comets is that during the transition, the orbit passes close to
the libration points L1 and L2, two of the equilibrium
points for the restricted three-body problem for the Sun-Jupiter
system. Studying the libration point invariant manifold
structures for L1 and L2 is a starting point for
understanding the capture and resonance transition of these
comets. For example, the recently discovered heteroclinic
connection between pairs of unstable periodic orbits (one around
the L1 and the other around L2) implies a complicated
dynamics for comets in a certain energy range. Furthermore, the
stable and unstable invariant manifold `tubes' associated to
libration point periodic orbits, of which the heteroclinic
connections are a part, are phase space conduits transporting
material to and from Jupiter and between the interior and
exterior of Jupiter's orbit.