Long-term changes in the tilt of the Earth's axis, relative to the plane of its orbit, are of great significance to long-term climate change, because they control the size of the arctic and Antarctic circles. These “Milankovitch cycles” have hitherto been calculated by classical perturbation methods or by direct numerical integration of Newton's equations of motion. This paper presents an approximate calculation from simple considerations of angular momentum using similar methods to those used to study the precession of a spinning top. It is an instructive exercise in classical mechanics and gives a simple explanation of the phenomenon in terms of angular momentum. It is shown that the main component of “Milankovitch cycles” has a period of 41,000 yr and is due to one of the modes of precession of the Earth-Venus system. The other mode of this system produces a component of period 29,500 yr, and a third component of period 54,000 yr results from the influence of the precession of the orbits of Jupiter and Saturn. These results agree closely with several of the numerical simulations in the literature and strongly suggest that some other results in the literature are incorrect.
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