Planetary embryos embedded in a gas disc suffer a decay in semimajor axis – type I migration – due to the asymmetric torques produced by the interior and exterior wakes raised by the body (Goldreich & Tremaine 1980; Ward 1986). This presents a challenge for standard oligarchic approaches to forming the terrestrial planets (Kokubo & Ida 1998) as the timescale to grow the progenitor objects near ...

The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with two-body interaction, where the interesting cases of singular, hard-core and discontinuous interaction are included. We start with the special case of pure hard core repulsion in order to sho...