Skip to main content
Log in

The chaotic obliquity of the planets

  • Article
  • Published:

From Nature

View current issue Submit your manuscript

Abstract

Numerical study of the global stability of the spin-axis orientation (obliquity) of the planets against secular orbital perturbations shows that all of the terrestrial planets could have experienced large, chaotic variations in obliquity at some time in the past. The obliquity of Mars is still in a large chaotic region, ranging from 0° to 60°. Mercury and Venus have been stabilized by tidal dissipation, and the Earth may have been stabilized by capture of the Moon. None of the obliquities of the terrestrial planets can therefore be considered as primordial.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Harris, A. W. & Ward, W. R. A. Rev. planet. Sci. 10, 61–108 (1982).

    Article  ADS  Google Scholar 

  2. Tremaine, S. Icarus 89, 85–92 (1991).

    Article  ADS  Google Scholar 

  3. Dones, L. & Tremaine, S. Science 259, 350–354 (1993).

    Article  ADS  CAS  Google Scholar 

  4. Safronov, V. S. Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets (Nauka, Moscow, 1969).

    Google Scholar 

  5. Laskar, J., Joutel, F. & Robutel, P. Nature 361, 615–617 (1993).

    Article  ADS  Google Scholar 

  6. Chirikov, B. V. Phys. Rep. 52, 263 (1979).

    Article  ADS  Google Scholar 

  7. Lambeck, K. The Earth's Variable Rotation: Geophysical Causes and Consequences (Cambridge Univ. Press, 1980).

    Book  Google Scholar 

  8. Laskar, J. Icarus 88, 266–291 (1990).

    Article  ADS  Google Scholar 

  9. MacDonald, G. J. F. Rev. Geophys. 2, 467–541 (1964).

    Article  ADS  Google Scholar 

  10. Goldreich, P. & Soter, S. Icarus 5, 375–389 (1966).

    Article  ADS  Google Scholar 

  11. Burns, J. A. Icarus 28, 453–458 (1976).

    Article  ADS  Google Scholar 

  12. Peale, S. J. Icarus 28, 459–467 (1976).

    Article  ADS  Google Scholar 

  13. Goldreich, P. & Peale, S. J. Astr. J. 75, 273–284 (1970).

    Article  ADS  Google Scholar 

  14. Dobrovolskis, A. R. Icarus 41, 18–35 (1980).

    Article  ADS  Google Scholar 

  15. Ward, W. R. J. geophys. Res. 79, 3375–3386 (1974).

    Article  ADS  Google Scholar 

  16. Hilton, J. L. Astr. J. 102, 1510–1527 (1991).

    Article  ADS  Google Scholar 

  17. Ward, W. R. & Rudy, D. J. Icarus 94, 160–164 (1991).

    Article  ADS  Google Scholar 

  18. Laskar, J. Nature 338, 237–238 (1989).

    Article  ADS  Google Scholar 

  19. Davies, M. E. et al. Celest. Mech. 53, 377–379 (1992).

    Article  ADS  Google Scholar 

  20. Laskar, J., Joutel, F. & Boudin, F. Astr. Astrophys. (in the press).

  21. Ward, W. R. Icarus 50, 444–448 (1982).

    Article  ADS  Google Scholar 

  22. Korycansky, D. G., Bodenheimer, P. & Pollack, J. B. Icarus 92, 234–251 (1991).

    Article  ADS  Google Scholar 

  23. Goldreich, P. Rev. Geophys. 4, 411–439 (1966).

    Article  ADS  Google Scholar 

  24. Murray, C. A. Vectorial Astrometry (Hilger, Bristol, 1983).

    Google Scholar 

  25. Laskar, J. in Chaos, Resonance and Collective Dynamical Phenomena in the Solar System (ed. Ferraz-Mello, S.) 1–16 (Kluwer, Dordrecht, 1992).

    Google Scholar 

  26. Laskar, J., Quinn, T. & Tremaine, S. Icarus 95, 148–152 (1992).

    Article  ADS  Google Scholar 

  27. Sussman, G. & Wisdom, J. Science 257, 56–62 (1992).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  28. Colombo, G. Astr. J. 71, 891–896 (1966).

    Article  ADS  Google Scholar 

  29. Henrard, J. & Murigande, C. Celest. Mech. 40, 345–366 (1987).

    Article  ADS  Google Scholar 

  30. Laskar, J., Froeschlé, C. & Celletti, A. Physica D 56, 253–269 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  31. Laskar, J. Physica D (in the press).

  32. Peale, S. J. Astr. J. 79, 722–744 (1974).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Laskar, J., Robutel, P. The chaotic obliquity of the planets. Nature 361, 608–612 (1993). https://doi.org/10.1038/361608a0

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/361608a0

  • Springer Nature Limited

This article is cited by

Navigation