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.

  • Letter
  • Published:

Mercury's capture into the 3/2 spin-orbit resonance as a result of its chaotic dynamics


Mercury is locked into a 3/2 spin-orbit resonance where it rotates three times on its axis for every two orbits around the sun1,2,3. The stability of this equilibrium state is well established4,5,6, but our understanding of how this state initially arose remains unsatisfactory. Unless one uses an unrealistic tidal model with constant torques (which cannot account for the observed damping of the libration of the planet) the computed probability of capture into 3/2 resonance is very low (about 7 per cent)5. This led to the proposal that core–mantle friction may have increased the capture probability, but such a process requires very specific values of the core viscosity7,8. Here we show that the chaotic evolution of Mercury's orbit can drive its eccentricity beyond 0.325 during the planet's history, which very efficiently leads to its capture into the 3/2 resonance. In our numerical integrations of 1,000 orbits of Mercury over 4 Gyr, capture into the 3/2 spin-orbit resonant state was the most probable final outcome of the planet's evolution, occurring 55.4 per cent of the time.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Probability density function of Mercury's eccentricity.
Figure 2: Typical cases of capture into the 3/2 resonance.

Similar content being viewed by others


  1. Pettengill, G. H. & Dyce, R. B. A radar determination of the rotation of the planet Mercury. Nature 206, 1240 (1965)

    Article  ADS  Google Scholar 

  2. McGovern, W. E., Gross, S. H. & Rasool, S. I. Rotation period of the planet Mercury. Nature 208, 375 (1965)

    Article  ADS  Google Scholar 

  3. Colombo, G. Rotation period of the planet Mercury. Nature 208, 575 (1965)

    Article  ADS  Google Scholar 

  4. Colombo, G. & Shapiro, I. I. The rotation of the planet Mercury. Astrophys. J. 145, 296–307 (1966)

    Article  ADS  Google Scholar 

  5. Goldreich, P. & Peale, S. J. Spin orbit coupling in the Solar System. Astron. J. 71, 425–438 (1966)

    Article  ADS  Google Scholar 

  6. Counselman, C. C. & Shapiro, I. I. Spin-orbit resonance of Mercury. Symp. Math. 3, 121–169 (1970)

    Google Scholar 

  7. Goldreich, P. & Peale, S. J. Spin-orbit coupling in the solar system 2. The resonant rotation of Venus. Astron. J. 72, 662–668 (1967)

    Article  ADS  Google Scholar 

  8. Peale, S. J. & Boss, A. P. A spin-orbit constraint on the viscosity of a Mercurian liquid core. J. Geophys. Res. 82, 743–749 (1977)

    Article  ADS  Google Scholar 

  9. Anderson, J. D., Colombo, G., Espsitio, P. B., Lau, E. L. & Trager, G. B. The mass, gravity field, and ephemeris of Mercury. Icarus 71, 337–349 (1987)

    Article  ADS  CAS  Google Scholar 

  10. Brouwer, D. & Van Woerkom, A. J. J. The secular variations of the orbital elements of the principal planets. Astron. Pap. Am. Ephem. XIII, part II, 81–107 (1950)

    Google Scholar 

  11. Bretagnon, P. Termes à longue périodes dans le système solaire. Astron. Astrophys. 30, 141–154 (1974)

    ADS  MATH  Google Scholar 

  12. Laskar, J. The chaotic motion of the solar system. Icarus 88, 266–291 (1990)

    Article  ADS  Google Scholar 

  13. Laskar, J. Large-scale chaos in the Solar System. Astron. Astrophys. 287, L9–L12 (1994)

    ADS  Google Scholar 

  14. Laskar, J. et al. Long term evolution and chaotic diffusion of the insolation quantities of Mars. Icarus (in the press)

  15. Spohn, T., Sohl, F., Wieczerkowski, K. & Conzelmann, V. The interior structure of Mercury: what we know, what we expect from BepiColombo. Planet. Space Sci. 49, 1561–1570 (2001)

    Article  ADS  CAS  Google Scholar 

  16. Hansen, P. A. Entwickelung der products einer potenz des radius vectors mit dem sinus oder cosinus eines vielfachen der wahren anomalie in reihen. Abhandl. K. S. Ges. Wissensch. IV, 182–281 (1855)

    Google Scholar 

  17. Murray, C. D. & Dermott, S. F. Solar System Dynamics (Cambridge Univ. Press, Cambridge, 1999)

    MATH  Google Scholar 

  18. Correia, A. C. M. & Laskar, J. Néron de Surgy, O. Long term evolution of the spin of Venus. I. Theory. Icarus 163, 1–23 (2003)

    Article  ADS  Google Scholar 

  19. Munk, W. H. & MacDonald, G. J. F. The Rotation of the Earth; A Geophysical Discussion (Cambridge Univ. Press, Cambridge, 1960)

    MATH  Google Scholar 

  20. Kaula, W. Tidal dissipation by solid friction and the resulting orbital evolution. J. Geophys. Res. 2, 661–685 (1964)

    Google Scholar 

  21. Yoder, C. F. Astrometric and geodetic properties of Earth and the Solar System. Glob. Earth Physics: A Handbook of Physical Constants 1–31 (American Geophysical Union, Washington DC, 1995)

    Google Scholar 

Download references


This work was supported by PNP-CNRS, Paris Observatory CS, and Fundação para a Ciência e a Technologia, POCTI/FNU, Portugal. The numerical computations were made at IDRIS-CNRS, and Paris Observatory. Authors are listed in alphabetic order.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Jacques Laskar.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Correia, A., Laskar, J. Mercury's capture into the 3/2 spin-orbit resonance as a result of its chaotic dynamics. Nature 429, 848–850 (2004).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


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