The discovery was made using the Cassini spacecraft, which flew by Dione nearly two years ago. Instruments on board the unmanned probe detected a thin layer of oxygen around the moon, so thin that scientists prefer to call it an "exosphere" rather than an atmosphere.
But the discovery is important because it suggests there is a process at work around the solar system's gas giants, Saturn and Jupiter, in which oxygen is released from their icy satellites.
It seems that highly charged particles from the planets' powerful radiation belts split the water in the ice into hydrogen and oxygen.
Dione's sister moon, Enceladus is thought to harbour a liquid ocean below its icy surface. The same is thought to be true of Europa, Callisto and Ganymede which orbit Jupiter.
Prof Coates is among a group of scientists lobbying the European Space Agency to send an orbiter to explore Jupiter's icy moons - known as the Juice mission.
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