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Engineers lost contact with the probe in early November and later admitted it was lost and irrecoverable.
Nasa said that faulty changes made to the spacecraft's computer memory caused the battery to overheat.
The 10-year-old craft had sent thousands of images of Mars back to Earth, suggesting water once flowed.
"The loss of the spacecraft was the result of a series of events linked to a computer error made five months before the likely battery failure," said Dolly Perkins, of Nasa.
Mapping mineralogy
During its last communication with Global Surveyor on 2 November, engineers ordered the craft to adjust the position of its solar panels.
But during the craft's shift of one of its panels, it exposed one of two batteries to the heat of the sun. The spacecraft was lost within 12 hours, Nasa says.
Mars Global Surveyor was launched in November 1996, operating longer than any other Martian craft.
Carrying a powerful camera, it returned some 240,000 images, mapping the mineralogy of Mars and surveying potential landing sites for future surface missions.
The demise of MGS leaves three working orbiters at the Red Planet: Nasa's Mars Reconnaissance Orbiter and Mars Odyssey, and the European Space Agency's Mars Express.
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