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Resonance, Chaos and Stability: The Three-Body Problem in Astrophysics

  • Rosemary A. Mardling
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 760)

In his Oppenheimer lecture entitled “Gravity is cool, or, why our universe is as hospitable as it is”, Freeman Dyson discusses how time has two faces: the quick violent face and the slow gentle face, the face of the destroyer and the face of the preserver (Dyson 2000). He entirely attributes these two faces to gravity and the ease with which gravitational energy can change irreversibly into other forms of energy. The simplest system exhibiting these two faces is that of three gravitating bodies; for most configurations, the slow gentle face is the norm, while for a very important subset, violence is the order of the day.

Keywords

Stability Boundary Orbital Element Resonance Angle Exact Resonance Disturbing Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Aarseth S. J., 1971, Ap&SS, 13, 324CrossRefADSGoogle Scholar
  2. Aarseth S. J., 2007, MNRAS, 378, 285CrossRefADSGoogle Scholar
  3. Arnol’d V. I., 1963, Russian Mathematical Surveys, 18, 9zbMATHCrossRefADSGoogle Scholar
  4. Arnol’d V. I., 1978, Mathematical Methods of Classical Mechanics. Springer-Verlag, New YorkGoogle Scholar
  5. Barrow-Green J., 1997, Poincare and the Three Body Problem (History of Mathematics, V. 11). American Mathematical SocietyGoogle Scholar
  6. Brouwer D., Clements G. M., 1961, Methods of Celestial Mechanics. Academic Press, New York and LondonGoogle Scholar
  7. Chirikov B. V., 1979, Phys. Rep., 52, 263CrossRefADSMathSciNetGoogle Scholar
  8. Dyson F. J., 2000, Oppenheimer Lecture, University of California, Berkeley. http://www.hartford-hwp.com/archives/20/035.htmlGoogle Scholar
  9. Eggleton P., Kiseleva L., 1995, ApJ, 455, 640CrossRefADSGoogle Scholar
  10. Eggleton P. P., Kiseleva-Eggleton L., 2001, ApJ, 562, 1012CrossRefADSGoogle Scholar
  11. Fabrycky D., Tremaine, S., 2007, ApJ, 669, 1298CrossRefADSGoogle Scholar
  12. Goldstein H., 1980, Classical Mechanics. Addison-Wesley, PhilippinesGoogle Scholar
  13. Heggie D. C., 1975, MNRAS, 173, 729ADSGoogle Scholar
  14. Hills J. G., 1976, MNRAS, 175, 1PADSGoogle Scholar
  15. Hills J. G., 1988, Nature, 331, 687CrossRefADSGoogle Scholar
  16. Jackson J. D., 1975, Classical Electrodynamics, Wiley, New York, 2nd edzbMATHGoogle Scholar
  17. Kaula W. M., 1961, Geophys. J. Roy. Astr. Soc., 5, 104zbMATHGoogle Scholar
  18. Kolmogorov A. N., 1954, Dokl. Akad. Nauk, 98, 527zbMATHMathSciNetGoogle Scholar
  19. Kozai Y., 1962, AJ, 67, 591CrossRefADSMathSciNetGoogle Scholar
  20. Mardling R. A., 1995a, ApJ, 450, 722CrossRefADSGoogle Scholar
  21. Mardling R. A., 1995b, ApJ, 450, 732CrossRefADSGoogle Scholar
  22. Mardling R. A., 2007, MNRAS, 382, 1768ADSGoogle Scholar
  23. Mardling R. A., 2008a, submitted to MNRASGoogle Scholar
  24. Mardling R. A., 2008b, submitted to MNRASGoogle Scholar
  25. Moser J., 1962, Nachr. Akad. Wiss. Gottingen II, Math. Phys. KD, 1, 1Google Scholar
  26. Murray C. D., Dermott S. F., 2000, Solar System Dynamics. Cambridge Univ. Press, CambridgeGoogle Scholar
  27. Poincaré H., 1993, New Methods of Celestial Mechanics (Vol. 1). Goro D. L., ed., AIP, New York, I23, 22Google Scholar
  28. Reichl L. E., 1992, The Transition to Chaos in Conservative Classical Systems: Quantum Manifestations, Springer-Verlag, New YorkzbMATHGoogle Scholar
  29. Reipurth, B., & Clarke, C. 2001, AJ, 122, 432CrossRefADSGoogle Scholar
  30. Rivera E. J., et al., 2005, ApJ, 634, 625CrossRefADSGoogle Scholar
  31. Spurzem R., Giersz M., Heggie D. C., Lin D. N. C., 2006, astro-ph/0612757Google Scholar
  32. Tokovinin, A., Thomas, S., Sterzik, M., & Udry, S. 2006, A&A, 450, 681CrossRefADSGoogle Scholar
  33. Walker G. H., Ford J., 1969, Physical Review, 188, 416CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Rosemary A. Mardling
    • 1
  1. 1.School of Mathematical SciencesMonash UniversityAustralia

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