  Gamma-ray binaries, composed of a massive star and compact object, have been
established as a new class of sources of very high energy (VHE) photons. The
gamma-rays are produced by inverse Compton scattering of the stellar light by
VHE electrons accelerated in the vicinity of the compact object. The VHE
emission from LS 5039 displays an orbital modulation.
  The inverse Compton spectrum depends on the angle between the incoming and
outgoing photon in the electron rest frame. Since the angle at which an
observer sees the star and electrons changes with the orbit, a phase dependence
of the spectrum is expected. The phase-dependent spectrum of LS 5039 is
calculated, assuming a continuous injection of electrons. The shape of the
electron distribution depends on the injected power-law and on the magnetic
field intensity.
  Anisotropic scattering produces hard emission at inferior conjunction, when
attenuation due to pair production of the VHE gamma-rays on star light is
minimum. The computed lightcurve and spectra provide good fits to the HESS and
EGRET observations, except at phases of maximum attenuation where pair cascade
emission may be significant for HESS. Detailed predictions are made for a
modulation in the GLAST energy range. The magnetic field intensity at
periastron is 0.8+-0.2 G.
  Anisotropic inverse Compton scattering plays a major role in LS 5039. The
derived magnetic field intensity, injection energy and slope suggest a
rotation-powered pulsar wind nebula. Gamma-ray binaries are promising sources
to study the environment of pulsars on small scales.
