Prosperity

From Tardis Wiki, the free Doctor Who reference

Prosperity was the first of humanity's ark ships, sent out into space to colonise other worlds. Eventually, the transmissions from Prosperity stopped, and it was declared lost three hundred years after its launch. The ship continued on for thousands of years, piloted by Ana, who was kept alive artificially. The people aboard forgot their origin as colonists, the vegetation spread to cover the interior of the ship, and the culture regressed to a tribal state. One tribe called themselves "Umans" and were lead by their Elders, the left-tenant and the right-tenant. Over time, both the oak trees and the humans aboard became taller and spindlier in the lessened gravity.

The Fourth Doctor and Sarah Jane Smith landed on Prosperity three and a half thousand years into its journey. The Doctor offered to boost the engines so the ship would reach a habitable planet in a day or so, but the engines would be destroyed and Ana would die. She accepted. The Doctor and Sarah went forward a thousand years or so to check on the colonists progress on their new world. (PROSE: The Lost Generation)