  We describe the possibility of using LISA's gravitational-wave observations
to study, with high precision, the response of a massive central body to the
tidal gravitational pull of an orbiting, compact, small-mass object. Motivated
by this application, we use first-order perturbation theory to study tidal
coupling for an idealized case: a massive Schwarzschild black hole, tidally
perturbed by a much less massive moon in a distant, circular orbit. We
investigate the details of how the tidal deformation of the hole gives rise to
an induced quadrupole moment in the hole's external gravitational field at
large radii. In the limit that the moon is static, we find, in Schwarzschild
coordinates and Regge-Wheeler gauge, the surprising result that there is no
induced quadrupole moment. We show that this conclusion is gauge dependent and
that the static, induced quadrupole moment for a black hole is inherently
ambiguous. For the orbiting moon and the central Schwarzschild hole, we find
(in agreement with a recent result of Poisson) a time-varying induced
quadrupole moment that is proportional to the time derivative of the moon's
tidal field. As a partial analog of a result derived long ago by Hartle for a
spinning hole and a stationary distant companion, we show that the orbiting
moon's tidal field induces a tidal bulge on the hole's horizon, and that the
rate of change of the horizon shape leads the perturbing tidal field at the
horizon by a small angle.
