when not obliterating planets, which was most of the time, the Death Star emitter dish was used as a radio telescope by astronomers on board the space station. may they rest in peace.
inspired by the Arecibo radio dish which could both transmit and receive.
the whole Death Star needs to turn to face its dish toward an observation (or obliteration) target, and it needs to stably keep facing exactly that direction for the duration of the observation. presumably gyroscopes. however, any movement of mass inside the space station, e.g., a person walking, will induce via conservation of angular momentum a rotation of the station. (future work: calculate how much rotation.) this seems difficult to deal with. maybe the dish is mechanically isolated from the station: it floats a short distance from the superstructure.
or, the Force keeps the station in line with its target. the Emperor and Darth Vader are keen astronomers. this was original purpose for the space station: politics forced them to add a military capability in order to get it built, much like how the Hubble Space Telescope succeeded becoming approved and built because research and development for its design was reused a dozen times over for U.S. spy satellites.
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