Sol is the star of the second Earth that the Fleet is lead to after a Jump by Kara Thrace.
The coordinates to the third planet orbiting Sol were coded in a piece of music known to (and later decoded) by Thrace. After discovering that Earth's humanoid life is genetically similar to the humans who evolved on Kobol, the Colonials settle this planet and decide to abandon all spacefaring technology; all ships incapable of landing on this new Earth are piloted into Sol by a Hybridized Samuel Anders (TRS: "Daybreak, Part II").