Saturn's rings are more than 90–95% water ice, which implies that initially they were almost pure ice because they are continually polluted by rocky meteoroids. Saturn has only one large satellite, Titan, whereas Jupiter has four large satellites; additional large satellites probably existed originally but were lost as they spiralled into Saturn. Now, numerical simulations of the tidal removal of mass from a differentiated, Titan sized satellite as it migrates inward towards Saturn are reported. Planetary tidal forces preferentially strip material from the satellite's outer icy layers, while its rocky core remains intact and is lost to collision with the planet. The result is a pure ice ring.