Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

The chaotic obliquity of the planets


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.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  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).

    ADS  Article  Google Scholar 

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

    ADS  Article  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).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  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).

    ADS  Article  Google Scholar 

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

    ADS  MathSciNet  CAS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  MathSciNet  Article  Google Scholar 

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

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

    ADS  Article  Google Scholar 

Download references

Author information

Authors and Affiliations


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).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing