The reliability of the Titius–Bode relation and its implications for the search for exoplanets

Abstract

Abstract The major semiaxes of the planets in our solar system obey a simple geometric progression known as the Titius–Bode (TB) relation, whose physical origin remains disputed. It has been shown that the exoplanetary systems follow a similar (but not identical) progression of the form $a_n= a_0$ e$^{bn}$, where $a_0$ and b are constants to be determined for each system. Since its formulation, the TB relation has proved to be highly predictive in our solar system. Using data from 27 exoplanetary systems with five or more planets and applying a proposed method, we conclude that reliable TB-like fits can be obtained for systems with at least four planets and that the precision of the TB relation is $78\%$. By means of a statistical test we show that the periods of planets in real exoplanetary systems are not consistent with a random distribution. Rather, they show signs that their configuration is shaped by their mutual interactions.