Titius-Bode’s Relation and Distribution of Exoplanets

• Main Author: Heon-Young Chang
• Format: Article
• Language: English
• Published: Korean Space Science Society (KSSS) 2010-03-01
• Series: Journal of Astronomy and Space Sciences
• Subjects: celestial mechanics; solar system; general
• Online Access: http://ocean.kisti.re.kr/downfile/volume/kosss/OJOOBS/2010/v27n1/OJOOBS_2010_v27n1_1.pdf
• ISSN: 2093-5587; 2093-1409

The distance distribution in our planetary system has been a controversial matter. 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. We have examined, by applying it to exo-planetary systems, whether Titius-Bode’s relation is exclusively applicable to our solar system. We study, with the X^2 test, the distribution of period ratios of two planets in multiple planet systems by comparing it with that derived from not only Titius-Bode’s relation but also other forms of it. The X^2 value between the distribution of the orbital period derived from Titius-Bode’s relation and that observed in our Solar system is 12.28 (dof = 18) with high probability, i.e., 83.3 %. The value of X^2 and probability resulted from Titius-Bode’s relation and observed exo-planetary systems are 21.38 (dof = 26) and 72.2 %, respectively. Modified forms we adopted seem also to agree with the planetary system as favorably as Titius-Bode’s relation does. As a result, one cannot rule out the possibility that the distribution of the ratio of orbiting periods in multiple planet systems is consistent with that derived from Titius-Bode’s relation. Having speculated Titius-Bode’s relation could be valid in exo-planetary systems, we tentatively conclude it is unlikely that Titius-Bode’s relation explains the distance distribution in our planetary system due to chance. Finally, we point out implications of our finding.