Bode's Law

Abstract

M. W. OVENDEN1 has outlined a theory intended to provide a dynamical explanation for Bode's Law. I suggest instead that the approximately constant spacing ratio expressed in Bode's mnemonic can be generated by a sequence of random numbers subject to the constraint that adjacent planets cannot be “too close to each other”. The physical basis for the constraint is that if in the process of accretion two planets were “too close to each other”, they would coalesce or cease to grow because they were competing for the same material. Such a constraint was embodied in a series of computer-generated planetary systems published by S. H. Dole2. Dole generated planets by injecting nuclei into a Laplace-type nebula and allowing them to accrete dust and also gas (if their mass was sufficiently large and their temperature sufficiently low). He kept track of the dust and gas accreted (so that it could not be used twice) and coalesced planets if their orbits crossed. The initial semimajor axes of the proto-planets were chosen at random.