  We investigate the electromagnetic interaction of a relativistic stellar wind
with a planet or a smaller body in orbit around the star. This may be relevant
to objects orbiting a pulsar, such as PSR B1257+12 and PSR B1620-26 that are
expected to hold a planetary system, or to pulsars with suspected asteroids or
comets. We extend the theory of Alfv\'en wings to relativistic winds. When the
wind is relativistic albeit slower than the total Alfv\'en speed, a system of
electric currents carried by a stationary Alfv\'enic structure is driven by the
planet or by its surroundings. For an Earth-like planet around a "standard" one
second pulsar, the associated current can reach the same magnitude as the
Goldreich-Julian current that powers the pulsar's magnetosphere.
