  About $20\%$ of exoplanets discovered by radial velocity surveys reside in
stellar binaries. To clarify their origin one has to understand the dynamics of
planetesimals in protoplanetary disks within binaries. The standard
description, accounting for only gas drag and gravity of the companion star has
been challenged recently, as the gravity of the protoplanetary disk was shown
to play a crucial role in planetesimal dynamics. An added complication is the
tendency of protoplanetary disks in binaries to become eccentric, giving rise
to additional excitation of planetesimal eccentricity. Here, for the first
time, we analytically explore secular dynamics of planetesimals in binaries
such as $\alpha$ Cen and $\gamma$ Cep under the combined action of (1) gravity
of the eccentric protoplanetary disk, (2) perturbations due to the (coplanar)
eccentric companion, and (3) gas drag. We derive explicit solutions for the
behavior of planetesimal eccentricity ${\bf e}_p$ in non-precessing disks (and
in precessing disks in certain limits). We obtain the analytical form of the
distribution of relative velocities of planetesimals, which is a key input for
understanding their collisional evolution. Disk gravity strongly influences
relative velocities and tends to push sizes of planetesimals colliding with
comparable objects at the highest speed to small values, $\sim 1$ km. We also
find that planetesimals in eccentric protoplanetary disks apsidally aligned
with the binary orbit collide at lower relative velocities than in mis-aligned
disks. Our results highlight a decisive role that disk gravity plays in
planetesimal dynamics in binaries.
