We discuss the relevance, for the search of gravitational-wave bursts, of upper limits on the total mass loss of the Galaxy which come from various astronomical observations. For sub-millisecond bursts we obtain limits on the event rate, as a function of the GW amplitude, which are stronger than the corresponding upper limits set by LIGO in the S2 run. A detection of a burst rate saturating these limits, with the sensitivities of present and near-future runs, would imply that, with some improvement on the accuracy of astronomical observations of the Galaxy, as foreseen with the GAIA mission, it might be possible to detect gravitational waves indirectly from their effect on galactic dynamics.