  Detectable debris discs are thought to require dynamical excitation
(`stirring'), so that planetesimal collisions release large quantities of dust.
We investigate the effects of the secular perturbations of a planet, which may
lie at a significant distance from the planetesimal disc, to see if these
perturbations can stir the disc, and if so over what time-scale. The secular
perturbations cause orbits at different semi-major axes to precess at different
rates, and after some time t_cross initially non-intersecting orbits begin to
cross. We show that t_cross is proportional to a_disc^(9/2)/(m_pl e_pl a_pl^3),
where m_pl, e_pl and a_pl are the mass, eccentricity, and semi-major axis of
the planet, and a_disc is the semi-major axis of the disc. This time-scale can
be faster than that for the growth of planetesimals to Pluto's size within the
outer disc. We also calculate the magnitude of the relative velocities induced
amongst planetesimals and infer that a planet's perturbations can typically
cause destructive collisions out to 100's of AU. Recently formed planets can
thus have a significant impact on planet formation in the outer disc which may
be curtailed by the formation of giant planets much closer to the star. The
presence of an observed debris disc does not require the presence of
Pluto-sized objects within it, since it can also have been stirred by a planet
not in the disc. For the star epsilon Eridani, we find that the known RV planet
can excite the planetesimal belt at 60 AU sufficiently to cause destructive
collisions of bodies up to 100 km in size, on a time-scale of 40 Myr.

Earth and Planetary Astrophysics