The radii of the planetary and satellite orbits are in approximate agreement with geometric progressions. The question of whether the observed patterns have some physical basis or are due to chance may be addressed using a Monte Carlo approach. We find that the estimated probability of chance occurrence depends sensitively on the restrictions imposed on the population of orbits. We argue that it is not possible to conclude unequivocally that laws of Titius-Bode type are, or are not, significant. Therefore, the possibility of a physical explanation for the observed distributions remains open.