The Le Verrier was a space station orbiting Neptune in the 38th century.
Professor Gagan Rassmussen invented the Morpheus pod on the space station in the 38th century. Sometime after this event, the sleep dust on the eyes of the people who used Morpheus turned into the Sandmen, which completely enveloped the crew and transformed them into creatures of their own kind. Rassmussen, at this point a Sandman, devised a plot to spread the Sandmen throughout the solar system, by using the same encoded signal inside Morpheus that created Sandmen out of the sleep dust. He did this by orchestrating a scenario filled with plot twists and a climax on board for dramatic effect "like a story", and send a video of this story with the signal.
Le Verrier was destroyed by letting it fall from its orbit after the Twelfth Doctor destroyed the gravity shields, leaving it fully exposed to Neptune's gravitational pull. (TV: Sleep No More)