We have numerically computed the orbital evolution of βΌ10 3 particles representing high-speed ejecta from Gilgamesh, the largest impact basin on Ganymede. The integration includes the four Galilean satellites, Jupiter (including J 2 and J 4 ), Saturn, and the Sun. The integrations last 100,000 years. The particles are ejected at a variety of speeds and directions, with the fastest particles ejected at 1.4 times the escape speed v esc β‘ β 2GM G /R G of Ganymede. Ejecta with speeds v < 0.96v esc follow suborbital trajectories. At v βΌ 0.96v esc there is a transition characterized by complex behavior suggestive of chaos. For v > 0.96v esc , most particles escape Ganymede and achieve orbits about Jupiter. Eventually most (βΌ71%) of the jovicentric particles hit Ganymede, with 92% of these hitting within 1000 years. The accretion rate scales as 1/t. Their impact sites are randomly distributed, as expected for planetocentric debris. We estimate that most of the resulting impact craters are a few kilometers across and smaller. The rest of the escaping ejecta are partitioned as follows: βΌ3% hit Io; βΌ10% hit Europa; βΌ13% hit Callisto; 2% reach heliocentric space; and less than βΌ1% hit Jupiter. Only two particles survived the entire 10 5 -year integration. Ejecta from large impact events do not appear to be a plausible source of large craters on the Galilean satellites; however, such ejecta may account for the majority of small craters.