At NASA's Goddard Space Flight Centre in Greenbelt, Maryland this week, the engineering team used a robot arm to lift and lower the hexagonal-shaped segment that measures just over 1.3 meters across and weighs approximately 40 kilogrammes.
After being pieced together, the 18 primary mirror segments will work together as one large 6.5-metre mirror. The full installation is expected to be complete early next year.
"The James Webb Space Telescope will be the premier astronomical observatory of the next decade," said John Grunsfeld, astronaut and associate administrator of the Science Mission Directorate at NASA.
Several innovative technologies have been developed for the Webb Telescope, which is targeted for launch in 2018, and is the successor to NASA's Hubble Space Telescope.
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Webb will study every phase in the history of our universe, including the cosmos' first luminous glows, the formation of solar systems capable of supporting life on planets like Earth, and the evolution of our own solar system.
The telescope's biggest feature is a tennis court sized five-layer sunshield that attenuates heat from the Sun more than a million times.
"After a tremendous amount of work by an incredibly dedicated team across the country, it is very exciting to start the primary mirror segment installation process," said Lee Feinberg, James Webb Space Telescope optical telescope element manager at Goddard.