TITIUS-BODE`S Relation and 55 Cancri

Abstract

Two kinds of important issues on Titius-Bode`s relation have been discussed up to now: one is if there is a simple mathematical relation between distances of natural bodies orbiting a central body, and the other is if there is any physical basis for such a relation. These may be tackled by answering a question whether Titius-Bode`s relation is valid universally in exo-planetary systems. We have examined whether Titius Bode`s relation is also applicable to exo-planetary systems by statistically studying the distribution of the ratio of rotational periods of two planets in an exo-planetary system, 55 Cnc, by comparing it with that derived from Titius-Bode`s relation. We find that the distribution of the ratio of rotational periods of randomly chosen two planets in the 55 Cnc system is apparently inconsistent with that derived from Titius-Bode`s relation. The probability that two data sets are drawn from the same distribution function is 50%. We also find that the Fourier power spectra show that the distribution of the semi-major axis of planets in the 55 Cnc system seems to be stretched. We conclude by pointing out that large numbers of planets should be examined to more convincingly explain the distribution of the distance of planetary formation regions.

Keywords

• celestial mechanics
• solar system
• general