Journal of Astronomy and Space Sciences

The Korean Space Science Society (한국우주과학회)
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Titius-Bode's Relation in Exoplanetary Systems

  • Heon-Young Chang (Department of Astronomy and Atmospheric Sciences, Kyungpook National University)
  • Received : 2023.05.03
  • Accepted : 2023.05.31
  • Published : 2023.06.15
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Abstract

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.

Keywords

Acknowledgement

The author thanks the anonymous referees for critical comments and helpful suggestions which greatly improve the original version of the manuscript. This study was supported by a National Research Foundation of Korea Grant funded by the Korean government (NRF-2018R1D1A3B070421880) and Basic Science Research Program through the National Research Foundation (NRF) of Korea funded by the Ministry of Science, ICT and Future Planning (No. 2018R1A6A1A06024970).

References

  1. Basano L, Hughes DW, A modified Titius-Bode law for planetary orbits, Il Nuovo Cimento C 2, 505-510 (1979). https://doi.org/10.1007/BF02557750
  2. Blagg MA, On a suggested substitute for Bode's law. (Plate 12.), Mon. Not. R. Astron. Soc. 73, 414-422 (1913). https://doi.org/10.1093/mnras/73.6.414
  3. Brodetsky S, Some problems of astronomy (XVII Bode's law), Observatory 37, 338-341 (1914).
  4. Chang HY, Titius-Bode's relation and 55 Cancri, J. Astron. Space Sci. 25, 239-244 (2008). https://doi.org/10.5140/JASS.2008.25.3.239
  5. Chang HY, Titius-Bode's relation and distribution of exoplanets, J. Astron. Space Sci. 27, 1-10 (2010). https://doi.org/10.5140/JASS.2010.27.1.001
  6. Chapman DMF, Reflections: the Titius-Bode rule, part 1: discovering the asteroids, J. R. Astron. Soc. Can. 95, 135-137 (2001).
  7. Cuntz M, Application of the Titius-Bode rule to the 55 Cancri system: tentative prediction of a possibly habitable planet, Publ. Astron. Soc. Jpn. 64, 73 (2012). https://doi.org/10.1093/pasj/64.4.73
  8. Dermott SF, On the origin of commensurabilities in the solar system-II. the orbital period relation, Mon. Not. R. Astron. Soc. 141, 363-376 (1968). https://doi.org/10.1093/mnras/141.3.363
  9. Dermott SF, The Origin of the Solar System (John Wiley & Sons, New York, 1997).
  10. Filippov AE, Collapse of a dusty medium and Titius-Bode law in natural units, JETP Lett. 54, 351 (1991).
  11. Goldreich P, Sciama DW, An explanation of the frequent occurrence of commensurable mean motions in the solar system, Mon. Not. R. Astron. Soc. 130, 159-181 (1965). https://doi.org/10.1093/mnras/130.3.159
  12. Hayes W, Tremaine S, Fitting selected random planetary systems to Titius-Bode laws, Icarus 135, 549-557 (1998). https://doi.org/10.1006/icar.1998.5999
  13. Jaki SL, The original formulation of the Titius-Bode law, J. Hist. Astron. 3, 136-138 (1972). https://doi.org/10.1177/002182867200300205
  14. Lara P, Cordero-Tercero G, Allen C, The reliability of the Titius-Bode relation and its implications for the search for exoplanets, Publ. Astron. Soc. Jpn. 72, 24 (2020). https://doi.org/10.1093/pasj/psz146
  15. Laskar J, Petit AC, AMD-stability and the classification of planetary systems, Astron. Astrophys. 605, A72 (2017). https://doi.org/10.1051/0004-6361/201630022
  16. Lecar M, Bode's law, Nature 242, 318-319 (1973). https://doi.org/10.1038/242318a0
  17. Li XQ, Zhang H, Li QB, Self-similar collapse in nebular disk and the Titius-Bode law, Astron. Astrophys. 304, 617-621 (1995).
  18. Louise R, A postulate leading to the Titius-Bode law, Moon Planets 26, 93-96 (1982). https://doi.org/10.1007/BF00941371
  19. Lynch P, On the significance of the Titius-Bode law for the distribution of the planets, Mon. Not. R. Astron. Soc. 341, 1174-1178 (2003). https://doi.org/10.1046/j.1365-8711.2003.06492.x
  20. McFadden LA, Weissman PR, Johnson TV, Encyclopedia of the Solar System (Academic Press, New York, 1999).
  21. Miller J, Bode's law and the systems of the planets and satellites, Nature 142, 670-671 (1938). https://doi.org/10.1038/142670b0
  22. Mousavi-Sadr M, Gozaliasl G, Jassur DM, Exoplanets prediction in multiplanetary systems, Publ. Astron. Soc. Aust. 38, e015 (2021). https://doi.org/10.1017/pasa.2021.9
  23. Neuhauser R, Feitzinger JV, A generalized distance formula for planetary and satellite systems, Astron. Astrophys. 170, 174-178 (1986).
  24. Nieto MM, Conclusions about the Titius Bode law of planetary distances, Astron. Astrophys 8, 105 (1970).
  25. Nieto MM, The Titius-Bode Law of Planetary Distances: Its History and Theory (Pergamon Press, Oxford, 1972).
  26. Ortiz JL, Moreno F, Molina A, Santos Sanz P, Gutierrez PJ, Possible patterns in the distribution of planetary formation regions, Mon. Not. R. Astron. Soc. 379, 1222-1226 (2007). https://doi.org/10.1111/j.1365-2966.2007.12017.x
  27. Ovenden MW, Physical sciences: Bode's law and the missing planet, Nature 239, 508-509 (1972). https://doi.org/10.1038/239508a0
  28. Patterson CW, Resonance capture and the evolution of the planets, Icarus 70, 319-333 (1987). https://doi.org/10.1016/0019-1035(87)90138-2
  29. Patton JM, On the dynamical derivation of the Titius-Bode law, Celest. Mech. 44, 365-391 (1988). https://doi.org/10.1007/BF01234273
  30. Pletser V, Lois exponentielles de distance pour les systemes de satellites, Earth Moon Planets 36, 193-210 (1986). https://doi.org/10.1007/BF00055159
  31. Pletser V, Exponential distance relations in planetary-like systems generated at random, Earth Moon Planets 42, 1-18 (1988). https://doi.org/10.1007/BF00118035
  32. Poveda A, Lara P, The exo-planetary system of 55 Cancri and the Titius-Bode law, Rev. Mex. Astron. Astrofis. 44, 243-246 (2008). https://doi.org/10.48550/arXiv.0803.2240
  33. Ragnarsson SI, Planetary distances: a new simplified model, Astron. Astrophys. 301, 609 (1995).
  34. Rawal JJ, Modified Titius-Bode relation, Bull. Astron. Soc. India 6, 92 (1978).
  35. Rawal JJ, Contraction of the solar nebula, Earth Moon Planets 31, 175-182 (1984). https://doi.org/10.1007/BF00055528
  36. Rawal JJ, Further considerations on contracting solar nebula, Earth Moon Planets 34, 93-100 (1986). https://doi.org/10.1007/BF00054038
  37. Rawal JJ, Contractions of subsolar nebulae, Earth Moon Planets 44, 265-274 (1989). https://doi.org/10.1007/BF00054242
  38. Rica S, Pattern formation through gravitational instability, C. R. Acad. Sci. 320, 489-496 (1995).
  39. Richardson DE, Distances of planets from the sun and of satellites from their primaries, Popular Astron. 53, 14 (1945).
  40. Ruediger G, Tschaepe R, The Titius-Bode law in the light of density wave theory, Gerlands Beitr. Geophys. 97, 97-102 (1988).
  41. Scardigli F, A quantum-like description of the planetary systems, J. Phys. Conf. Ser. 67, 012038 (2007). https://doi.org/10.1088/1742-6596/67/1/012038
  42. Smirnov VA, The physical meaning of the Titius-Bode formula, Odessa Astron. Publ. 28, 62-64 (2015). https://doi.org/10.18524/1810-4215.2015.28.70335
  43. Stone EC, Miner ED, The Voyager 2 encounter with the Uranian system, Science 233, 39-43 (1986). https://doi.org/10.1126/science.233.4759.39
  44. Todd GW, Kepler, Newton and Bode, Nature 141, 412 (1938). https://doi.org/10.1038/141412a0
  45. Wilson DJ, Froning CS, Duvvuri GM, France K, Youngblood A, et al., The Mega-MUSCLES spectral energy distribution of TRAPPIST-1, Astronphys. J. 911, 18 (2021). https://doi.org/10.3847/1538-4357/abe771
  46. Wylie CC, Bode's and similar empirical laws, Pop. Astron. 39, 75 (1931).