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Astron. Astrophys. 318, 975-989 (1997)

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7. Conclusion

By adding the non-conservative effects to the previous model for the long time evolution of the obliquity of the Earth used by Laskar et al., (1993a, b), we possess now a complete model for the study of the long term variations of the spin of the Earth and of the orbit of the Moon over time scales comparable to the age of the Solar System. It has allowed us to find some significant constraints on the poorly known tidal time lag [FORMULA] and effective viscosity of the outer core [FORMULA] thanks to paleo-observations, in spite of the uncertainty in the interpretation of geological data. Any further improvement in the knowledge of one of these two quantities would directly induce an improvement for the second one and in the history of the Earth's spin by the way.

It appears in this study that the action of dissipative effects is weak enough not to cause very significative changes in the behavior of the obliquity compared to one could expect in a conservative framework, so to say that with a rough idea of the time scale of these effects, most of the essential dynamics could be described from Laskar et al. (1993b), Laskar and Robutel (1993). The combination of this model with Laskar's secular theory of the solar system provides us with a powerful tool for exploring plausible scenarii for the long term evolution of the obliquity of the terrestrial planets, and reinforces the importance of having a global view of the planetary dynamics.

It is still remarkable that in most cases, when using acceptable rates for the dissipation, the obliquity of the Earth explores a large part of the chaotic region discovered by Laskar et al. (1993b), reaching very high maximum values, close to 90 degrees.

The chaotic behavior of the obliquity of the Earth prevented us to describe precisely the evolution of its spin over its age, but here we have shown in a simple probabilistic manner that the most probable destiny of the Earth is to undergo very strong variations of its obliquity before the inflation of the Sun, if it does not occur.

These computations also confirms that in absence of the Moon, that is for precession constants of the order of 20 arcsec/year, the Earth would suffer very large variations of its obliquity, which could reach nearly 90 degrees with a high probability.

Finally, it should be noted that the chaotic regions for the obliquity of Venus (Laskar and Robutel, 1993) is very similar to the one of the Earth (Fig. 1), and thus similar behavior probably occurred for this planet in the past. We are presently undertaking similar computations for this planet, for which a supplementary difficulty consist in a precise understanding of the possible strong effect of the atmospheric tides.

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998