  Long-term changes in the tilt of the Earths 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 generally been calculated by numerical integration of Newtons equations of
motion, and there is some controversy over the results because they are
sensitive to numerical drift over the very long computer simulations involved.
In this paper the cycles are calculated from first principles, without any
reliance 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 of
41,000 years 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
years, and a third component of period 54,000 years 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 other different results in the literature
are incorrect.
