What would it mean to leave this planet?Not just in orbit or for a period of months, but somewhere far away to not return for years or not at all?

Canadian astronaut Chris Hadfield said that the biggest challenge of a trip to Mars would be coping with the isolation. “Within a month or so you won’t be able to have a real-time conversation ever again with Earth, the delay will be so long…So that crew within weeks will become Martians psychologically. They will no longer be of Earth.”
“How do you keep your crew from going crazy?”
We define our sense of self through a context. What is the context of no longer being here?