Orbital resonances and planetary formation sites

Orbital resonances may have played an important role in determining the locations where the planetesimal swarm eventually accreted into full-size planets. Several pairs of planets do indeed have commensurable orbital periods at present, but the case for control of planet formation by resonances is weakened by the fact that many pairs are not commensurable and that those which are do not necessarily exist at the strongest resonances. However, the mass loss and redistribution that occurred in the early solar system evolution can substantially alter the positions of planets and planetary embryos within the swarm. A cascaded resonance structure is hypothesized where planetesimal growth was accelerated at 2:1 interior and 1:2 exterior resonances with an early-formed Jupiter producing runaway growth of planetary embryos. These embryos produce their own resonances which, in turn, lead to additional embryos in a process that successively propagates inward and outward to generate a resonant configuration of embryos. In this manner, the early presence of Jupiter imposed a harmonic structure on the accumulating planetesimal swarm. For an accretion disk with surface density obeying a power law of index -1.2 the positions of the planetary embryos can be moved into a reasonably good agreement with most of the present planetary positions that is as good as that given by the Titius-Bode law.