  Two types of stability boundaries exist for any planetary system consisting
of one star and two planets. Lagrange stability requires that the planets
remain bound to the star, conserves the ordering of the distance from the star,
and limits the variations of orbital elements like semi-major axis and
eccentricity. Hill stability only requires that the ordering of the planets
remain constant; the outer planet may escape to infinity. A simple formula
defines a region in orbital element space that is guaranteed to be Hill stable,
although Hill stable orbits may lie outside the region as well. No analytic
criteria describe Lagrange stability. We compare the results of 1000 numerical
simulations of planetary systems similar to 47 UMa and HD 12661 with these two
types of boundaries. All cases are consistent with the analytic criterion for
Hill stability. Moreover, the numerically determined Lagrange boundary lies
close to the analytic boundary for Hill stability. This result suggests an
analytic formulation that may describe the criterion for Lagrange stability.
