Brought on by weightlessness in protracted space flight, besides the obvious hazards of meteors, rocky debris, and radiation, astronauts also have to deal with muscle atrophy.
Here "Brought ... flight" seems to modify 'besides' which is wrong.
A. Brought on by weightlessness in protracted space flight, besides the obvious hazards of meteors, rocky debris, and radiation, astronauts also have to deal with muscle atrophy. - WRONG.
B. Besides the obvious hazards of meteors, rocky debris, and radiation in protracted space flight, astronauts also have to deal with muscle atrophy, which is brought on by weightlessness. - WRONG. Weightlessness in space flight causes muscle atrophy and using 'brought' does not signify the same meaning.
C. In protracted space flight, besides the obvious hazards of meteors, rocky debris, and radiation, astronauts also have to deal with muscle atrophy brought about through weightlessness. - WRONG. The sentence changes the meaning as if in long space flights all other mentioned hazards also occur when sentence means to say that long duration causes muscle atrophy. Also 'brought about through' suggests that something brought the muscle atrophy which is meant to be brought on by weightlessness.
D. Besides the obvious hazards of protracted space flight, which include meteors, rocky debris, and radiation, astronauts also have to deal with another problem, which is the muscle atrophy that occurs after an extended period of weightlessness. - WRONG. 'which' modifies flight which is incorrect. Besides the wordiness loses focus to communicate meaning.
E. Besides the obvious hazards of meteors, rocky debris, and radiation, astronauts in protracted space flight also have to deal with muscle atrophy brought on by weightlessness. - CORRECT. Hazards are listed correctly. Prepositional phrase 'protracted space flight' modifies astronauts correctly.
IMO Answer E.