  We used a sample of Kepler candidate planets with orbital periods less than
200 days and radii between 1.5 and 30 Earth radii to determine the typical
dynamical spacing of neighboring planets. To derive the intrinsic (i.e., free
of observational bias) dynamical spacing of neighboring planets, we generated
populations of planetary systems following various dynamical spacing
distributions, subjected them to synthetic observations by the Kepler
spacecraft, and compared the properties of observed planets in our simulations
with actual Kepler detections. We found that, on average, neighboring planets
are spaced 21.7 mutual Hill radii apart with a standard deviation of 9.5. This
dynamical spacing distribution is consistent with that of adjacent planets in
the Solar System. To test the packed planetary systems hypothesis, the idea
that all planetary systems are dynamically packed or filled to capacity, we
determined the fraction of systems that are dynamically packed by performing
long-term (10^8 years) numerical simulations. In each simulation, we integrated
a system with planets spaced according to our best-fit dynamical spacing
distribution but containing an additional planet on an intermediate orbit. The
fraction of simulations exhibiting signs of instability provides an approximate
lower bound on the fraction of systems that are dynamically packed; we found
that >31%, >35%, and >45% of 2-planet, 3-planet, and 4-planet systems are
dynamically packed, respectively. Such sizeable fractions suggest that many
planetary systems are indeed filled to capacity. This feature of planetary
systems is another profound constraint that formation and evolution models must
satisfy.
