Titius-Bode’s Relation in Exoplanetary Systems

The Titius-Bode’s relation has been historically successful in predicting the location of Ceres in the solar system, while its physical basis remains hidden. In this study, we attempt to answer the question of whether the Titius-Bode’s relation is universally valid for exoplanetary systems with plural exoplanets. For this purpose, we statistically study the distribution of the ratio of the orbiting periods of two planets in 32 exoplanetary systems hosted by a single star. We only consider the period ratios derived from exoplanets orbiting a single star since celestial objects under investigation are kept as simple as possible and free from uncertainties such as the mass of the host star. We find that the distribution of period ratios of two exoplanets appears inconsistent with that derived from the Titius-Bode’s relation using the χ² test. We also found that the distance distribution in exoplanetary systems unlikely follows the uniform distribution or the Poisson’s distribution. It is noted, however, that more rigorous statistical tests should be carried out to reach a more certain conclusion.