  The relationship between the boundaries for Hill and Lagrange stability in
orbital element space is modified in the case of resonantly interacting
planets. Hill stability requires the ordering of the planets to remain constant
while Lagrange stability also requires all planets to remain bound to the
central star. The Hill stability boundary is defined analytically, but no
equations exist to define the Lagrange boundary, so we perform numerical
experiments to estimate the location of this boundary. To explore the effect of
resonances, we consider orbital element space near the conditions in the HD
82943 and 55 Cnc systems. Previous studies have shown that, for non-resonant
systems, the two stability boundaries are nearly coincident. However the Hill
stability formula are not applicable to resonant systems, and our investigation
shows how the two boundaries diverge in the presence of a mean-motion
resonance, while confirming that the Hill and Lagrange boundaries are similar
otherwise. In resonance the region of stability is larger than the domain
defined by the analytic formula for Hill stability. We find that nearly all
known resonant interactions currently lie in this extra stable region, i.e.
where the orbits would be unstable according to the non-resonant Hill stability
formula. This result bears on the dynamical packing of planetary systems,
showing how quantifying planetary systems' dynamical interactions (such as
proximity to the Hill-stability boundary) provides new constraints on planet
formation models.
