OSCILLATIONS IN ORBITAL AND AXIAL CHARACTERISTICS
As a result of gravitational perturbations by the other planets, most notably Jupiter and Saturn, the obliquity of the Earth’s axis of rotation, i, and the eccentricity, e, of its orbit undergo quasi-periodic variations. Also, the orientation of its axis steadily precesses around the normal to its orbital plane because of solar and lunar torques. The characteristic period over which i varies is 41,000 yr, with i varying between about 22.0 and 24.5° (its current value is 23.4°). The dominant period for e is 413,000 yr, with there also being a number of secondary periods clustered around 100,000 yr. e varies between 0 and 0.06, with its current value being 0.017. The precession period is 25,000 yr (Imbrie and Imbrie, 1980).
The above astronomical variations result in seasonal and latitudinal redistributions of solar energy, although only a minor change in the annually and globally averaged solar energy results (Pollack, 1979; Imbrie and Imbrie, 1980). In particular, the obliquity variations lead to a 10 percent peak-to-peak change in the annually averaged solar insolation near the poles, and eccentricity variations result in a 25 percent peak-to-peak modulation in the summertime insolation in a given hemisphere, with the two hemispheres being out of phase. These modulations may be particularly important at times when the continents in one hemisphere are marginally able to have ice sheets as a result of their location and the mean surface temperature.
The last several million years have been characterized by a succession of alternating glacial and interglacial epochs. Indeed, the last major ice age, the Wisconsin, ended only about 12,000 yr ago. Strong evidence that the above astronomical variations are in part responsible for these ice ages is given by comparisons of the characteristic frequencies and phases found in well-dated sea cores with those expected from the astronomical theory (Hays et al., 1976). In particular, periods of 41,000, 23,000, and 19,000 yr characterize certain climate indicators in the cores, which correspond quite closely to those expected from the obliquity variations and the combined eccentricity-precession variations. However, there is still a good deal of uncertainty as to whether the dominant period of the cores, a 100,000-yr period, should be associated with the corresponding eccentricity period. According to linear theories of the relationship between the astronomical variations and climate, only the combined eccentricity-precession variable is relevant. Conceivably, the nonlinear response characteristics of ice sheet growth and decay permit the eccentricity alone to affect climate, although details of the relationship need to be worked out (Imbrie and Imbrie, 1980).
Regardless of the outcome of the above problem, the astronomical variations are at most a necessary, but not a sufficient, cause of ice ages. Prior to several million years ago for a time span of several hundred million years, no large continental glaciations in subpolar and mid-latitude regions occurred, despite the occurrence of astronomical variations with about the same amplitudes as those for the last several million years. In all probability, the drift of the continents toward the poles set the stage for the Pleistocene ice ages and presumably for earlier ones as well (Pollack, 1979).
The amplitude of the astronomical variations in eccentricity are set by the initial orbits of the planets in the early history of the solar system and is not expected to change in any significant way subsequently (W.R.Ward, Jet Propulsion Laboratory, personal communication). However, the amplitudes of the obliquity variations depend on the relationship between the precession frequency, ωp, and the characteristic frequencies of the planetary perturbations. perturbations, ωi. When ωp≫ωi for all i, the amplitudes of the obliquity variations are relatively small and can be significantly augmented only if ωp decreases to a value comparable with ωi. At present, the torque exerted by the Moon on the Earth’s equatorial bulge accounts for about two thirds of its precession rate, with the rest due to the Sun’s torque. During past epochs when the Moon was closer to the Earth, ωp was presumably larger and hence the obliquity variations were somewhat smaller.
A dramatic event may occur in the future when the moon moves somewhat further from the Earth. ωp will increase to a 50,000-yr period, becoming comparable with one of the ωi.
When that occurs (~few× 108 yr from now), the amplitude of the obliquity oscillations will increase by more than an order of magnitude and enormous climatic changes will occur (W.R.Ward, Jet Propulsion Laboratory, personal communication).It is highly unlikely that the mean obliquity has varied significantly over the age of the Earth. In principle, such a change could occur because of core-mantle coupling: the mantle has a bigger bulge and is more strongly affected by the lunar and solar torques. Only very gradually through viscous interactions does the mantle drag the core along. Such a coupling would gradually decrease the mean obliquity with time. However, the time constant for the coupling may well exceed the age of the Earth.
Because its ωp is comparable with some of the ωi, the obliquity variations for Mars have a peak-to-peak amplitude of about 20°, i.e., almost an order of magnitude larger than that for the Earth (Ward, 1974). Furthermore, its eccentricity variations are about a factor of 2.5 larger than those for the Earth. These much larger astronomical variations for Mars may have played an important role in generating a quasi-periodic sequence of sedimentary layers in its polar regions (Cutts, 1973; Pollack, 1979). These layers are believed to consist of a mixture of water ice and suspendable dust particles, with the astronomical variations modulating both the deposition rate and the ratio of the two constituents. For example, at times of low obliquity, the atmospheric pressure may drop because of absorption of CO2 on surface dust grains (CO2 is the dominant constituent of the Martian atmosphere). As a result, the frequency of dust storms may decline sharply (Pollack, 1979).
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