The compact radio source Sagittarius A* (Sgr A*) at the centre of our Galaxy harbours a supermassive black hole, whose mass ( 3.7 * 106 M_o) has been measured from stellar orbital motions. Sgr A* is therefore the nearest laboratory where super-massive black hole astrophysics can be tested, and the environment of black holes can be investigated. Since it is not an active galactic nucleus, it also offers the possibility of observing the capture of small objects that may orbit the central black hole. We study the effects of the strong gravitational field of the black hole on small objects, such as a comet or an asteroid. We also explore the idea that the flares detected in Sgr A* might be produced by the final accretion of single, dense objects with mass of the order of 1020 g, and that their timing is not a characteristic of the sources, but rather of the space-time of the central galactic black hole in which they are moving. The problem of tidal disruption of small objects by a black hole is studied numerically, using ray-tracing techniques, in a Schwarzschild background. We find that tidal effects are strong enough to melt sufficiently massive, solid objects, and present calculations of the temporal evolution of the light curve of infalling objects as a function of various parameters. Our modelling of tidal disruption suggests that during tidal squeezing, the conditions for synchrotron radiation can be met. We show that the light curve of a flare can be deduced from dynamical properties of geodesic orbits around black holes and that it depends only weakly on the physical properties of the source.