  The first extrasolar planets have been detected by the measurement of the
wobble of the parent star. This wobble leads to the periodic modulation of
three observables: the radial velocity, the position on the sky and the time of
arrival of periodic signals. We show that the same wobble, and therefore the
same modulation of the three observables, can be due to the presence of a more
distant binary stellar companion. Thus, the observation of the wobble does not,
by itself, constitute a proof of a planet detection. In particular, astrometric
confirmation of a wobble does not necessarily provide a sufficient proof of the
existence of a planet candidate detected by radial velocity. Additional
conditions, which we discuss here, must be fulfilled. We investigate the
observed wobble for the planet candidates already detected and we find that,
for each case, a wobble due to a binary stellar companion can be excluded. But
for apparent Saturn-like planets in wide orbits, there may be an ambiguity in
future detections, especially in spaceborne astrometric missions. We conclude
that, in some cases, a definitive proof for the presence of a planet requires
further observations such as direct imaging.
