  The process of gravitational scattering of planetesimals by a massive
protoplanetary embryo is explored theoretically. We propose a method to
describe the evolution of the disk surface density, eccentricity, and
inclination caused by the embryo-planetesimal interaction. It relies on the
analytical treatment of the scattering in two extreme regimes of the
planetesimal epicyclic velocities: shear-dominated (dynamically ``cold'') and
dispersion-dominated (dynamically ``hot''). In the former, planetesimal
scattering can be treated as a deterministic process. In the latter, scattering
is mostly weak because of the large relative velocities of interacting bodies.
This allows one to use the Fokker-Planck approximation and the two-body
approximation to explore the disk evolution. We compare the results obtained by
this method with the outcomes of the direct numerical integrations of
planetesimal orbits and they agree quite well. In the intermediate velocity
regime an approximate treatment of the disk evolution is proposed based on
interpolation between the two extreme regimes. We also calculate the rate of
embryo's mass growth in an inhomogeneous planetesimal disk and demonstrate that
it is in agreement with both the simulations and earlier calculations. Finally
we discuss the question of the direction of the embryo-planetesimal interaction
in the dispersion-dominated regime and demonstrate that it is repulsive. This
means that the embryo always forms a gap in the disk around it, which is in
contrast with the results of other authors. The machinery developed here will
be applied to realistic protoplanetary systems in future papers.
