While the story is reminiscent of the classic For the World Is Hollow and I Have Touched the Sky (1968), the concept of a biosphere, a damaged generational spacecraft about to be destroyed by a star, and a semi-agrarian society that religiously suppresses knowledge of the truth, was the premise of the Canadian-produced television series The Starlost (1973). Similarly, the Robert A. Heinlein stories "Universe" and "Common Sense" (published in 1941 in Astounding Science Fiction, and later combined in the novel "Orphans of the Sky") feature a ship whose residents are unaware they are on a ship, controlled by a religious totalitarian government who worshiped the builders of the ship as the creators of the "universe".
To feel better, Klyden watches The Sound of Music (1965). Seth MacFarlane has declared his love for the movie several times.
The Orville responds to a distress call from a ship called the Druyan - undoubtedly a reference to Ann Druyan, who co-wrote Cosmos (1980), with her husband Carl Sagan, and who collaborated with Seth MacFarlane to create Cosmos: A Spacetime Odyssey (2014)).
Claire quotes from Ralph Waldo Emerson's 'Nature' essay (1836), "If the stars should appear one night in a thousand years, how would men believe and adore and preserve for many generations the remembrance of the city of god...". The quote also appears at the front of one of the most famous science fiction short stories ever written - Isaac Asimov's Nightfall, which has a similar plot.
When the shuttlecraft docks with the derelict ship, and during their first exploration inside the ship, the musical cues and soundtrack are an obvious variation of the Star Trek: The Motion Picture (1979) soundtrack, specifically The Cloud and VGER Flyover.