  The Jupiter-Saturn 2:5 near-commensurability is analyzed in a fully analytic
Hamiltonian planetary theory. Computations for the Sun-Jupiter-Saturn system,
extending to the third order of the masses and to the 8th degree in the
eccentricities and inclinations, reveal an unexpectedly sensitive dependence of
the solution on initial data and its likely nonconvergence. The source of the
sensitivity and apparent lack of convergence is this near-commensurability, the
so-called great inequality. This indicates that simple averaging, still common
in current semi-analytic planetary theories, may not be an adequate technique
to obtain information on the long-term dynamics of the Solar System.
  Preliminary results suggest that these difficulties can be overcome by using
resonant normal forms.
