In Asimov's fictional universe, the innermost planet orbiting Tau Ceti was mankind's very first extrasolar planetary settlement, established in 2065. Originally named "New Earth", in later millennia the planet would be renamed "Aurora", which means "dawn", to signify the dawning of a new age for the Spacer culture. It was also considered the strongest of the Spacer worlds, and was their de facto leader.
Aurora at its height had a population of 200 million humans and 10 billion robots. The head of its planetary government was called the Chairman. The largest city on the planet was Eos (which also means "dawn"), the administrative and robotic center of Aurora, where Han Fastolfe and Gladia Solaria lived. The University of Eos and the Auroran Robotics Institute were both located within Eos. We see the planet at its height in The Robots of Dawn.
In Prelude to Foundation, we learn that at least some of its inhabitants emigrated to Trantor, settling in the Mycogen Sector. The descendants of the Aurorans, or Mycogenians, never forgot Aurora, but they apparently evolved to the point where they were indistinguishable from Settlers. The scripture of the Mycogenians mentions Aurora, robots, and other topics; Hari Seldon peruses this document during the events of Prelude to Foundation and finds a presumably long-inactivated robot in Mycogen also. Ironically, the culture of Mycogen appears to be in many ways a complete opposite of Aurora's. Where the society of Aurora had complete gender equality and social mobility, Mycogen has a restrictive caste system with women apparently taking the place of Auroran robots, having no rights. It is also very restrictive sexually, whereas Aurora was basically a free love society. The changes are implied to be a deliberate effort to differentiate Mycogenians from outsiders.
In Foundation and Earth, the searchers for Earth visit Aurora, along with other ancient settlements. The planet is by then not inhabited by human beings, and its desertified ecology is dominated by feral dogs.