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The relationship between the boundaries for Hill and Lagrange stability inorbital element space is modified in the case of resonantly interactingplanets. Hill stability requires the ordering of the planets to remain constantwhile Lagrange stability also requires all planets to remain bound to thecentral star. The Hill stability boundary is defined analytically, but noequations exist to define the Lagrange boundary, so we perform numericalexperiments to estimate the location of this boundary. To explore the effect ofresonances, we consider orbital element space near the conditions in the HD82943 and 55 Cnc systems. Previous studies have shown that, for non-resonantsystems, the two stability boundaries are nearly coincident. However the Hillstability formula are not applicable to resonant systems, and our investigationshows how the two boundaries diverge in the presence of a mean-motionresonance, while confirming that the Hill and Lagrange boundaries are similarotherwise. In resonance the region of stability is larger than the domaindefined by the analytic formula for Hill stability. We find that nearly allknown resonant interactions currently lie in this extra stable region, i.e.where the orbits would be unstable according to the non-resonant Hill stabilityformula. This result bears on the dynamical packing of planetary systems,showing how quantifying planetary systems' dynamical interactions (such asproximity to the Hill-stability boundary) provides new constraints on planetformation models.

Stability Limits in Resonant Planetary Systems