  Recent investigations (e.g. Han et al. 2001) have shown that fitting the
Hipparcos observations with an orbital model when the astrometric wobble caused
by the companion is below the noise level can have rather unexpected
consequences. With new astrometric missions coming out within the next ten
years, it is worth investigating the orbit reconstruction capabilities of such
instruments at low signal-to-noise ratio. This is especially important because
some of them will have no input catalogue thus meaning that all the orbital
parameters will have to be derived from scratch. The puzzling case of almost
parabolic orbits is also investigated.
