Scientists say the 1,100-kilogram (2,425-pound) satellite already has fallen to an altitude of 170 kilometers (105 miles) and is spiraling steadily downward.
Once it reaches an altitude of 80 kilometers (50 miles) the earth observation satellite will break apart and four-fifths will burn in the atmosphere.
ESA said Friday that humans are 250,000 times more likely to win the lottery than to get hit by the debris weighing up to 90 kilograms (200 pounds) that may survive the breakup.
GOCE was launched in 2009 to map the Earth's gravitational field. It ran out of fuel last month, ending the mission.
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