  Star clusters and dwarf galaxies gradually dissolve as they move in the
potential of their host galaxy. Once their density falls below a certain
critical density (which is comparable with the background density of the
galaxy) it is often assumed that their evolution is completed. In fact the
remnant of such a system forms a distribution of stars which are unbound to
each other and which move on similar orbits in their host potential. With this
motivation we study the evolution of an idealised unbound system and follow its
expansion and dissolution in the tidal field of a model galaxy. Initially the
stars are uniformly distributed (with a density below the critical density)
within an ellipsoidal volume. The system itself travels on a circular orbit
within a galaxy modelled as an isothermal sphere. The initial velocities of the
stars are chosen by assuming that they move on (three-dimensional) epicycles
with guiding centre at the centre of the ellipsoid, though the usual epicyclic
theory is altered to account for the self-gravity of the system. This is
believed to be the first exact equilibrium model of a stellar system in a tidal
field. Our main task is to study the stability of such configurations and the
time-scale of their dissolution, as a function of the initial density and size
of the ellipsoid. If the time of dissolution is measured by an increase of the
half-mass radius of 50 %, we find that systems of low density (about 1 % of the
background density) and small radius (50 pc on an orbit of radius 10 kpc) can
survive for about 20 galactic orbits. For small systems we show that the
lifetime is approximately proportional to the inverse square root of the
density.
