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

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5. Williams' scenario for the history of the Earth's obliquity

The dissipation mechanisms presented therein give us some constraints on scenarios of the Earth's evolution, and our aim here would be to provide a general framework in which all scenario for the evolutions of the Earth's obliquity should be described. As an example, we show here that the dynamical constraints obtained here allow to question the scenario proposed by Williams (1993). Interpreting observations of various deposits in the Earth's soil which depend on weathering conditions, Williams devised the following scenario for the past evolution of the Earth's obliquity:

a) a slow and regular decreasing from [FORMULA] to [FORMULA] between -4.5 Gyr and -630 Myr;

b) a quick falldown from [FORMULA] to [FORMULA] between -630 and -220 Myr;

c) a slow decreasing till the present value.

Concerning the first stage, the main objection to such a smooth evolution arises from the fact that a [FORMULA] obliquity would imply a crossing of the chaotic zone (see Fig. 1), hence strong fluctuations ranging from about 65 degrees to about 90 degrees (Laskar et al., 1993b).

Then, we have estimated the value of [FORMULA] which would correspond to the second and third ones. The slow decreasing of [FORMULA] during the last 430 Myr might be possible, the corresponding [FORMULA] being about 300 m2 s-1. Now, a falldown from [FORMULA] to [FORMULA] within 220 Myr gives, with [FORMULA] 200 seconds, a huge value of [FORMULA] m2 s-1 which exceeds the upper limit of Lumb and Aldridge (1991). Such a viscosity would strongly slow down the Earth and the corresponding LOD in the past would be very far from the observed one with [FORMULA].

More simply and independently of the problem of the possible evolution of the value of [FORMULA], it is straightforward to verify that the variations proposed by Williams do not respect relation (R). Indeed, as


we should have [FORMULA] which does not correspond to any plausible despinning factor even during the whole last Gyr.

Williams found a support to his assessment in the very large rate of [FORMULA] (Kakuta and Aoki, 1972) due to core-mantle coupling. One one hand, as Rochester (1976) noticed it, this value was based on a model which is irrelevant since it does not take into account the inertial coupling; Aoki's model (Aoki, 1969) is adapted only to a slow-rotating planet like Venus at present time for which [FORMULA] is proportional to [FORMULA] (if [FORMULA] is not too small). On the other hand, Aoki's model also verifies relation [FORMULA] - which does not depend on Rochester's approximations -, and such a rate for [FORMULA] does not correspond to the low rate of braking [FORMULA] proposed by Aoki and Kakuta (1971); Williams thought this last rate was coherent with the loss of rotational kinetic energy due to CMF estimated by Rochester, but he did not take the right term of this loss to compare with.

Williams mentions that some "special conditions" should have occurred at the CMB in order to explain the drastic falldown. He also suggests that a resonance between the free core nutation and the retrograde annual nutation caused by the solar torque may have played an important role. Climate friction (Bills, 1995) might also be a candidate for additional variations of the obliquity. Such effects remain uncertain. Characteristics of the Earth's interior may have been somewhat different in a remote past, but unless system [FORMULA] has been very incomplete for some time in the last Gyr, his scenario should be rejected.

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998