  The dynamical interactions of planetary systems may be a clue to their
formation histories. Therefore, the distribution of these interactions provides
important constraints on models of planet formation. We focus on each system's
apsidal motion and proximity to dynamical instability. Although only ~25
multiple planet systems have been discovered to date, our analyses in these
terms have revealed several important features of planetary interactions. 1)
Many systems interact such that they are near the boundary between stability
and instability. 2) Planets tend to form such that at least one planet's
eccentricity periodically drops to near zero. 3) Mean-motion resonant pairs
would be unstable if not for the resonance. 4) Scattering of approximately
equal mass planets is unlikely to produce the observed distribution of apsidal
behavior. 5) Resonant interactions may be identified through calculating a
system's proximity to instability, regardless of knowledge of angles such as
mean longitude and longitude of periastron (e.g. GJ 317 b and c are probably in
a 4:1 resonance). These properties of planetary systems have been identified
through calculation of two parameters that describe the interaction. The
apsidal interaction can be quantified by determining how close a planet is to
an apsidal separatrix (a boundary between qualitatively different types of
apsidal oscillations, e.g. libration or circulation of the major axes). The
proximity to instability can be measured by comparing the observed orbital
elements to an analytic boundary that describes a type of stability known as
Hill stability. We have set up a website dedicated to presenting the most
up-to-date information on dynamical interactions:
http://www.lpl.arizona.edu/~rory/research/xsp/dynamics
