## On the long term evolution of the spin of the Earth
Laskar and Robutel (1993) have globally analyzed the stability of the planetary obliquities in a conservative framework. Here the same model is extended by adding dissipative effects in the Earth-Moon system: the body tides and the friction between the core and the mantle. Some constraints on the poorly known coefficients of dissipation are determined with the help of paleogeological observations. One consequence is that the scenario proposed by Williams (1993) for the past history of the Earth's obliquity seems unlikely. A synthesis of 500 numerical integrations of the Earth-Moon system with orbital perturbations for the next 5 Gyr is presented. It is shown that the time scale of the dissipative effects is long enough to induce an adiabatic-like evolution of the obliquity which is driven in the chaotic zone within 1.5 to 4.5 Gyr. A statistical study of possible evolutions conducted with a tidal dissipation coefficient of 600 seconds demonstrated that 68.4% of the trajectories attained an obliquity larger than 81 degrees, with a maximum of 89.5 degrees.
## Contents- 1. Introduction
- 2. Averaged equations for the precession of the Earth with planetary perturbations
- 3. Contributions of dissipative effects
- 3.1. The body tides
- 3.2. The core-mantle friction
- 3.3. The atmospheric tides
- 4. Some limits to the coefficients of dissipation
- 5. Williams' scenario for the history of the Earth's obliquity
- 6. The next five billion years evolution of the Earth-Moon system
- 7. Conclusion
- Acknowledgements
- References
© European Southern Observatory (ESO) 1997 Online publication: July 3, 1998 |