Dust pervades the Solar System, and is concentrated in the ring systems surrounding the giant planets and along the plane of the planetary orbits (the Zodiacal cloud). Individual dust gains are thought to be generated when impacts loft material from larger bodies(20,21,23-27), such as satellites. Uncertainties in theoretical models of this ejection process are large, and there have hitherto been no direct measurements with which to constrain these models. Here we report in situ measurements of submicrometre dust within a fe ev radii of Jupiter＇s satellite Ganymede. The directions, speeds and distribution of masses of the grains indicate that they come from Ganymede, and are consistent with an ejection process resulting from hypervelocity impacts of interplanetary dust onto Ganymede＇s surface. Dust appears also to be concentrated near Callisto and Europa, suggesting that these satellites too are significant sources of dusty debris.