Phase-Space Areas of the Body Motion in the Solar System Deduced from the Bohr-Sommerfeld Atomic Theory and Approximate Invariance of Their Ratios for the Pairs of Planets and Satellites

ABSTRACT

Energy-time and momentum-position phase spaces defined by the electron orbits in the hydrogen-like atom exhibit special properties of equivalence. It is demonstrated that equivalence of the same kind can be obtained for the phase-space areas defined by the orbit pairs of planets, or satellites, which compose the solar system. In the choice of the examined areas it is useful to be guided by the Bohr-Sommerfeld atomic theory.

Energy-time and momentum-position phase spaces defined by the electron orbits in the hydrogen-like atom exhibit special properties of equivalence. It is demonstrated that equivalence of the same kind can be obtained for the phase-space areas defined by the orbit pairs of planets, or satellites, which compose the solar system. In the choice of the examined areas it is useful to be guided by the Bohr-Sommerfeld atomic theory.

Cite this paper

Olszewski, S. and Kwiatkowski, T. (2012) Phase-Space Areas of the Body Motion in the Solar System Deduced from the Bohr-Sommerfeld Atomic Theory and Approximate Invariance of Their Ratios for the Pairs of Planets and Satellites.*Journal of Modern Physics*, **3**, 1142-1151. doi: 10.4236/jmp.2012.329149.

Olszewski, S. and Kwiatkowski, T. (2012) Phase-Space Areas of the Body Motion in the Solar System Deduced from the Bohr-Sommerfeld Atomic Theory and Approximate Invariance of Their Ratios for the Pairs of Planets and Satellites.

References

[1] J. C. Slater, “Quantum Theory of Atomic Structure,” Vol. 1, McGraw-Hill, New York, 1960.

[2] L. D. Landau and E. M. Lifshitz, “Mechanics,” Pergamon Press, Oxford, 1960.

[3] A. Sommerfeld, “Mechanik (in German),” Akademische Verlagsgesellschaft, Leipzig, 1943.

[4] V. M. Blanco and S. W. McCuskey, “Basic Physics of the Solar System,” Addison-Wesley, Reading, 1961.

[5] K. L. Lang, “Astrophysical Data: Planets and Stars,” Springer, New York, 1991.

[6] S. Olszewski, “Equivalence of Energy-Time and Momentum-Position Phase Spaces of the Solar System,” Earth, Moon and Planets, Vol. 74, No. 2, 1996, pp. 151-173. doi:10.1007/BF00056411

[7] A. Sommerfeld, “Atombau und Spektrallinien,” Vol. 1, 5th Edition, Vieweg, Braunschweig, 1931.

[1] J. C. Slater, “Quantum Theory of Atomic Structure,” Vol. 1, McGraw-Hill, New York, 1960.

[2] L. D. Landau and E. M. Lifshitz, “Mechanics,” Pergamon Press, Oxford, 1960.

[3] A. Sommerfeld, “Mechanik (in German),” Akademische Verlagsgesellschaft, Leipzig, 1943.

[4] V. M. Blanco and S. W. McCuskey, “Basic Physics of the Solar System,” Addison-Wesley, Reading, 1961.

[5] K. L. Lang, “Astrophysical Data: Planets and Stars,” Springer, New York, 1991.

[6] S. Olszewski, “Equivalence of Energy-Time and Momentum-Position Phase Spaces of the Solar System,” Earth, Moon and Planets, Vol. 74, No. 2, 1996, pp. 151-173. doi:10.1007/BF00056411

[7] A. Sommerfeld, “Atombau und Spektrallinien,” Vol. 1, 5th Edition, Vieweg, Braunschweig, 1931.