**Resonance and capture of Jupiter comets**

Koon, WS;
Lo, MW;
Marsden, JE;
Ross, SD;
**CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY**
**81**(1-2), 27-38, SEP 2001

**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 tubesf 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.

**Keywords:** comets, resonance, libration points, invariant manifolds, three-body problem

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