A quantum-like model of gravitational system is introduced to explore the formation of the solar system structure. In this model, the chaos behavior of a large number of original nebular particles in a gravitational field can be described in terms of the wave function satisfying formal Schrödinger equation, in which the Planck constant is replaced by a constant on cosmic scale. Numerical calculation shows that the radial distribution density of the particles has the character of wave curves with decreasing amplitudes and elongating wavelengths. By means of this model, many questions of the solar system, such as the planetary distance, mass, energy, angular momentum, the distribution of satellites, the structure of the planetary rings, and the asteroid belt and the Kuiper belt etc., can be explained in reason. In addition, the abnormal rotations of Venus and Mercury can be naturally explained by means of the quantum-like model.
KeywordsSchrödinger EquationPlanetary Distances and MassesSatellites DistributionRings structureKuiper BeltAsteroid Belt
M. M. Nieto, “Conclusions about the Titius Bode Law of Planetary Distances,” Astronomy and Astrophysics, Vol. 8, 1970, pp. 105-111.
L. Basano and D. W. Hughes, “A Modified Titius-Bode Law for Planetary Orbits,” Nuovo Cimento C, Vol. 2C, No. 5, 1979, pp. 505-510. doi:10.1007/BF02557750
E. Badolati, “A Supposed New Law for Planetary Distances,” Moon and the Planets, Vol. 26, May 1982, pp. 339-341. doi:10.1007/BF00928016
V. Pletser, “Exponential Distance Laws for Satellite Systems,” Earth, Moon, and Planets, Vol. 36, 1986, pp. 193- 210. doi:10.1007/BF00055159
R. Neuhaeuser and J. V. Feitzinger, “A Generalized Distance Formula for Planetary and Satellite Systems,” Astronomy and Astrophysics, Vol. 170, No. 1, 1986, pp. 174-178.
P. Lynch, “On the Significance of the Titius-Bode Law for the Distribution of the Planets,” Monthly Notice of the Royal Astronomical Society, Vol. 341, No. 4, 2003, pp. 1174-1178. doi:10.1046/j.1365-8711.2003.06492.x
L. Neslu?an, “The Significance of the Titius-Bode Law and the Peculiar Location of the Earth’s Orbit,” Monthly Notice of the Royal Astronomical Society, Vol. 351, No. 1, 2004, pp. 133-136.
G. Gladyshev, “The Physicochemical Mechanisms of the Formation of Planetary Systems,” Moon and the Planets, Vol. 18, April 1978, pp. 217-222. doi:10.1007/BF00896744
J. J. Rawal, “Contraction of the Solar Nebula,” Earth, Moon, and Planets, Vol. 31, October 1984, pp. 175-182. doi:10.1007/BF00055528
X. Q. Li, Q. B. Li and H. Zhang, “Self-similar Collapse in Nebular Disk and the Titius-Bode Law,” Astronomy and Astrophysics, Vol. 304, 1995, pp. 617-621.
F. Graner and B. Dubrulle, “Titius-Bode Laws in the Solar System 1: Scale Invariance Explains Everything,” Astronomy and Astrophysics, Vol. 282, No. 1, 1994, pp. 262-268.
R. Louise, “A Postulate Leading to the Titius-Bode Law,” Moon and the Planets, Vol. 26, February 1982, pp. 93-96. doi:10.1007/BF00941371
R. Wayte, “Quantisation in Stable Gravitational Systems,” Moon and the Planets, Vol. 26, February 1982, pp. 11-32. doi:10.1007/BF00941366
R. Louise, “The Titius-Bode Law and the Wave Formalism,” Moon and the Planets, Vol. 26, June 1982, pp. 389- 398. doi:10.1007/BF00941641
R. Louise, “Quantum Formalism in Gravitation Quantitative Application to the Titius-Bode Law,” Moon and the Planets, Vol. 27, August 1982, pp. 59-63. doi:10.1007/BF00941557
Daniel and M. Greenberger, Quantization in the Large,” Foundations of Physics, Vol. 13, No. 9, 1983, pp. 903- 951.
Q. X. Nie, “Simulated Quantum Theory for Seeking the Mystery of Regularity of Planetary Distances,” Acta Astronomica Sinica, Vol. 34, No. 3, 1993, pp. 333-340.
K. U. Lu, “Mathematical Investigation of Bode’s Law and Quantilization of Gravity,” Astrophysics and Space Science, Vol. 225, No. 2, 1995, pp. 227-235. doi:10.1007/BF00613237
B. E. Yang, “Introduction to Quantum Theory on Planets and Satellites (in Chinese),” Dalian University of Technology Press, Dalian, 1996, pp. 27-32.
A. G. Agnese and R. Festa, “Clues to Discretization on the Cosmic Scale,” Physics Letters A, Vol. 227, No. 3-4, 1997, pp. 165-171. doi:10.1016/S0375-9601(97)00007-8
L. Nottale, G. Schumacher and J. Gay, “Scale Relativity and Quantization of the Solar System,” Astronomy and Astrophysics, Vol. 322, 1997, pp. 1018-1025.
Q. X. Nie, “The Characteristics of Orbital Distribution of Kuiper Belt Objects,” Chinese Astronomy and Astrophysics, Vol. 27, No. 1, 2003, pp. 94-98.
Q. X. Nie, Cuan Li and F.-S. Liu, “Effect of Interplanetary Matter on the Spin Evolutions of Venus and Mercury,” International Journal of Astronomy and Astrophysics, Vol. 1, No. 1, 2011, pp. 1-5. doi:10.4236/ijaa.2011.11001
G. G. Comisar, “Brownian-Motion Model of Nonrelativistic Quantum Mechanics,” Physical Review, Vol. 138, No. 5B, 1965, pp. 1332-1337. doi:10.1103/PhysRev.138.B1332
E. Nelson, “Derivation of the Schr?dinger Equation from Newtonian Mechanics,” Physical Review, Vol. 150, No. 4, 1966, pp. 1079-1085. doi:10.1103/PhysRev.150.1079
A. P. Boss, “Astrometric Signatures of Giant-planet Formation,” Nature, Vol. 393, No. 6681, 1998, pp. 141-143. doi:10.1038/30177
A. P. Boss, “Rapid Formation of Outer Giant Planets by Disk Instability,” The Astrophysical Journal, Vol. 599, No. 1, 2003, pp. 577-581. doi:10.1086/379163
N. Murray and M. Holman, “The Origin of Chaos in the Outer Solar System,” Science, Vol. 283, No. 5409, 1999, pp. 1877.doi:10.1126/science.283.5409.1877
D. Jewitt, “Kuiper Belt,” 2011. http://www2.ess.ucla. edu/~jewitt/kb.html
J. X. Luu and D. C. Jewitt, “Kuiper Belt Objects: Relics from the Accretion Disk of the Sun,” The Annual Review of Astronomy and Astrophysics, Vol. 40, 2002, pp. 63- 101. doi:10.1146/annurev.astro.40.060401.093818
R. Malhotra, “The Origin of Pluto’s Orbit: Implications for the Solar System beyond Neptune,” Astronomical Journal, Vol. 110, 1995, pp. 420-429. doi:10.1086/117532
Q. L. Zuo, Qing-xiang Nie, et al., “Simulations for Original Distribution of KBOs,” Acta Astronomica Sinica., Vol. 49, No. 4, 2008, pp. 413-418
C. D. Murray and S. F. Dermott “Solar System Dynamics,” Cambridge University Press, Cambridge, 1999, pp. 532-533.
J. A. van Allen, et al., “Saturn’s Magnetosphere, Rings, and Inner Satellites,” Science, Vol. 207, January 25 1980, pp. 415-421. doi:10.1126/science.207.4429.415
W. S. Dai, “An Interpretation of the Titius-Bode Law,” Acta Astronomica Sinica, Vol. 16, No. 2, 1975, pp. 123- 130.
R. M. Canup and W. R. Ward, “Formation of the Galilean Satellites: Conditions of Accretion,” The Astronomical Journal, Vol. 124, No. 6, 2002, pp. 3404-3423. doi:10.1086/344684