  Apart from being chaotic, the inner planets in the Solar System constitute an
open system, as they are forced by the regular long-term motion of the outer
ones. No integrals of motion can bound a priori the stochastic wanderings in
their high-dimensional phase space. Still, the probability of a dynamical
instability is remarkably low over the next 5 billion years, a timescale
thousand times longer than the Lyapunov time. The dynamical half-life of
Mercury has indeed been estimated recently at 40 billion years. By means of the
computer algebra system TRIP, we consider a set of dynamical models resulting
from truncation of the forced secular dynamics recently proposed for the inner
planets at different degrees in eccentricities and inclinations. Through
ensembles of $10^3$ to $10^5$ numerical integrations spanning 5 to 100 Gyr, we
find that the Hamiltonian truncated at degree 4 practically does not allow any
instability over 5 Gyr. The destabilisation is mainly due to terms of degree 6.
This surprising result suggests an analogy to the Fermi-Pasta-Ulam-Tsingou
problem, in which tangency to Toda Hamiltonian explains the very long timescale
of thermalisation, which Fermi unsuccessfully looked for.
