  Gamma-ray binaries are systems that emit non-thermal radiation peaking at
energies above 1 MeV. One proposed scenario to explain their emission consists
of a pulsar orbiting a massive star, with particle acceleration taking place in
shocks produced by the interaction of the stellar and pulsar winds. We develop
a semi-analytical model of the non-thermal emission of the colliding-wind
structure including the dynamical effects of orbital motion. We apply the model
to a general case and to LS 5039. The model consists of a one-dimensional
emitter the geometry of which is affected by Coriolis forces owing to orbital
motion. Two particle accelerators are considered: one at the two-wind standoff
location, and the other one at the turnover produced by the Coriolis force.
Synchrotron and inverse Compton emission is studied, accounting for Doppler
boosting and absorption processes associated to the massive star. If both
accelerators are provided with the same energy budget, most of the radiation
comes from the region of the Coriolis turnover and beyond, up to a few orbital
separations from the binary system. The model allows us to reproduce some of
the LS 5039 emission features, but not all of them. In particular, the MeV
radiation is probably too high to be explained by our model alone, the GeV flux
is recovered but not its modulation, and the radio emission beyond the Coriolis
turnover is too low. The predicted system inclination is consistent with the
presence of a pulsar in the binary. The model is quite successful in
reproducing the overall non-thermal behavior of LS 5039. Some improvements are
suggested to better explain the phenomenology observed in this source, like
accounting for particle reacceleration beyond the Coriolis turnover, unshocked
pulsar wind emission, and the three-dimensional extension of the emitter.
