  By numerically integrating the orbits of the giant planets and of test
particles over a period of four billion years, we follow the evolution of the
location of the midplane of the Kuiper belt. The Classical Kuiper belt conforms
to a warped sheet that precesses with a 1.9 Myr period. The present-day
location of the Kuiper belt plane can be computed using linear secular
perturbation theory: the local normal to the plane is given by the theory's
forced inclination vector, which is specific to every semimajor axis. The
Kuiper belt plane does not coincide with the invariable plane, but deviates
from it by up to a few degrees in stable zones. For example, at a semimajor
axis of 38 AU, the local Kuiper belt plane has an inclination of 1.9 deg and a
longitude of ascending node of 149.9 deg when referred to the mean ecliptic and
equinox of J2000. At a semimajor axis of 43 AU, the local plane has an
inclination of 1.9 deg and a nodal longitude of 78.3 deg. Only at infinite
semimajor axis does the Kuiper belt plane merge with the invariable plane,
whose inclination is 1.6 deg and nodal longitude is 107.7 deg. A Kuiper belt
object keeps its inclination relative to the Kuiper belt plane nearly constant,
even while the latter plane departs from the trajectory predicted by linear
theory. The constancy of relative inclination reflects the undamped amplitude
of free oscillation. Current observations of Classical Kuiper belt objects are
consistent with the plane being warped by the giant planets alone, but the
sample size will need to increase by a few times before confirmation exceeds
3-sigma in confidence. In principle, differences between the theoretically
expected plane and the observed plane could be used to infer as yet unseen
masses orbiting the Sun, but carrying out such a program would be challenging.
