Current observations indicate that the planet formation process often produces multiple planet systems with nearly circular orbits , regular spacing , a narrow range of inclination angles , and similar planetary masses of order m _ { p } \sim 10 M _ { \oplus } .
Motivated by the observational sample , this paper determines the tidal equilibrium states for this class of extrasolar planetary systems .
We start by considering two planet systems with fixed orbital spacing and variable mass ratios .
The basic conjecture explored in this paper is that the planet formation process will act to distribute planetary masses in order to achieve a minimum energy state .
The resulting minimum energy configuration — subject to the constraint of constant angular momentum — corresponds to circular orbits confined to a plane , with nearly equal planetary masses ( as observed ) .
We then generalize the treatment to include multiple planet systems , where each adjacent pair of planets attains its ( local ) tidal equilibrium state .
The properties of observed planetary systems are close to those expected from this pairwise equilibrium configuration .
In contrast , observed systems do not reside in a global minimum energy state .
Both the equilibrium states of this paper and observed multi-planet systems , with planets of nearly equal mass on regularly spaced orbits , have an effective surface density of the form \sigma \propto r ^ { -2 } , much steeper than most disk models .