Yes, with no more servicing missions it will eventually stop working - another gyro will fail, the filter wheel will get stuck, a micrometeorite will break something, or one of a hundred other problems.
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Yes, eventually the Hubble will fail. The good news, however, is that NASA is already developing the next generation space telescope, the James Webb Space Telescope, named for NASA's first administrator.
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It is going to be artificially brought down to burn in the atmosphere sometime in 2014 or before. It will then be replaced by the new generation telescope named, The James Webb Space Telescope.
Edit: That's alright man. Peace.
Edit: That's alright man. Peace.
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kinda sad. i thought they would keep it going, if not for it being useful to confirm other telescopes findings then for satelite imagery of Earth...