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Long-term changes in the tilt of the Earths axis, relative to the plane ofits orbit, are of great significance to long-term climate change, because theycontrol the size of the arctic and antarctic circles. These Milankovitch cycleshave generally been calculated by numerical integration of Newtons equations ofmotion, and there is some controversy over the results because they aresensitive to numerical drift over the very long computer simulations involved.In this paper the cycles are calculated from first principles, without anyreliance on computer simulation. The problem is one of planetary precession,and is solvable by the methods used to study the precession of a spinning top.It is shown that the main component of Milankovitch cycles has a period of41,000 years and is due to one of the modes of precession of the Earth-Venussystem. The other mode of this system produces a component of period 29,500years, and a third component of period 54,000 years results from the influenceof the precession of the orbits of Jupiter and Saturn.  These results agree closely with several of the numerical simulations in theliterature, and strongly suggest that other different results in the literatureare incorrect.

The Earths long-term climate changes and ice ages: a derivation of Milankovitch cycles from first principles