Option elimination -
(A) that a star that was as bright as the full moon exploding into view 340,000 years ago, emitting - exploding modifies moon- wrong.
(B) that a star as bright as the full moon exploded into view 340,000 years ago, emitting - the star (sub) ...exploded (verb) - ok. Comma + ING modifies the verb. As a a result of explosion it emitted -ok.
(C) of a star that was as bright as the full moon exploding into view 340,000 years ago and that it emitted - exploding modifies moon- wrong.
(D) of a star as bright as the full moon, exploding into view 340,000 years ago and emitting - comma +ING is adverbial. It goes to have uncovered saying nonsensically that astronomers exploded and emitted. Wrong.
(E) of a star as bright as the full moon that exploded into view 340,000 years ago and that emitted - that modies moon and seems moon exploded. - wrong.