Melpomenia was the one of the fifty Spacer worlds, colonized by the first wave of settlers from Earth. It was nineteenth in the order of settlement.
In their search for the planet of origin of the human species, the third set of co-ordinates given to Golan Trevize, Janov Pelorat and Bliss points to Melpomenia, an old, dead Spacer world with a very thin atmosphere and almost no signs of civilization except for some old ruins. One of these ruins was found to be the "Hall of the Worlds", within which was a wall inscribed with the names, co-ordinates and dates of settlement of all the fifty Spacer worlds in chronological order. This information is later used by Janov Pelorat to deduce the approximate position of Earth in the galaxy. The first try led Pelorat not to Earth but to the nearby planet Alpha (in the system of Alpha Centauri, approximately four light years away from Earth).
In addition, they also happen to find that even in this harsh, nearly air-less world, life does manage to survive in the form of a kind of moss that lives on the faintest traces of carbon dioxide. The moss starts to grow along the edges of the face-plates of their space suits, and Trevize realizes that if it were to somehow get within their ship, the Far Star, it would become impossible to control. It would follow the trail of carbon dioxide along their nostrils and into their lungs and kill them. Using his blaster on minimum power, he burns away the moss on their space suits and also along the Far Star's airlock so that they can get inside safely.