This simply assumes that the Transhuman Space setting's version of Earth is forced to leave the solar system in the year 2150. Choose your reason for leaving the point of this setting is humanity in a set of vast spaceships much like the Norman Spinrad novella
Riding the Torch.
The PCs would be in the middle of a long flight. Neither they nor their grandparents would have seen the Earth. Their destination, or probable destination, is a few generations away. Humanity is basically contained within one vast city. All of humanity's conflicts and struggles are in this one city-fleet.