We investigate whether any multi-planet systems among Kepler candidates ( 2011 February release ) can harbor additional terrestrial-mass planets or smaller bodies .
We apply the “ packed planetary systems ” hypothesis that suggests all planetary systems are filled to capacity , and use a Hill stability criterion to identify eight 2-planet systems with significant gaps between the innermost and outermost planets .
For each of these systems , we perform long-term numerical integrations of 10 ^ { 7 } years to investigate the stability of 4000 - 8000 test particles injected into the gaps .
We map out stability regions in orbital parameter space , and therefore quantify the ranges of semi-major axes and eccentricities of stable particles .
Strong mean-motion resonances can add additional regions of stability in otherwise unstable parameter space .
We derive simple expressions for the extent of the stability regions , which is related to quantities such as the dynamical spacing \Delta , the separation between two planets in units of their mutual Hill radii .
Our results suggest that planets with separation \Delta < 10 are unlikely to host extensive stability regions , and that about 95 out of a total of 115 two-planet systems in the Kepler sample may have sizeable stability regions .
We predict that Kepler candidate systems including KOI 433 , KOI 72/Kepler-10 , KOI 555 , KOI 1596 , KOI 904 , KOI 223 , KOI 1590 , and KOI 139 can harbor additional planets or low-mass bodies between the inner and outer detected planets .
These predicted planets may be detected by future observations .