The significance of the Titius-Bode law and the peculiar location of the Earth's orbit

Abstract

Using the Lynch method, we continue the discussion on the statistical significance of agreement between planetary distributions and a power law. The Lynch method determines the probability that a power law (e.g. the Titius—Bode law) will agree by chance, at the observed level, with a given sequence of planetary distances. We find interesting results by assuming not only that the mean asteroid-belt distance should be considered as a regular planetary distance, but also that the current distance of the Earth should be regarded as peculiar and omitted from the Titius— Bode law. We examine these assumptions under two cases: (a) where no physical limitations are imposed and (b) where relatively close planetary orbits are excluded. We find that the corresponding sequence of distances matches the power law by chance with a probability of only 0.3 per cent for case (a) and 3 per cent for (b). These values are in direct contrast to those corresponding to the traditional Titius—Bode law as well as those corresponding to some common alternative assumptions. These range from 29 to 100 per cent for (a) and 95 to 100 per cent for (b).