http://www.nasa.gov/images/content/55954main_rxj1242_comp_250.jpg
This is why, assuming the earth survives even as a boiling cauldron due
to tidal disrupion and rotation momentum transfer, it would be stuck
in orbit around this black hole, receiving X-ray Gamma Rays enough
to disrupt your innards. Esp even the earth cools and frezes the
atmosphere would freeze, even less protection to any suvivors.
If mars were to be cast out (I doubt it) and cast out alone you could
certainly try to settle there, but since you have no way to
steer a planet let alone Slow it when a suitable suns is closeby,
I don't see a future there, esp at 1/3 G.
Unforutunately Jupiters Moons are not quite large enough
to have suitable gravity. And it's a ways off and expensive Delta
Vee wise to maneuver and land on the moons. On top of which
there have no aero braking to be had.
So?
None of this adresses the simple fact that both Gravity and Radiation are emminently solvable problems and that having a ready supply of power and raw materials is vastly superior to not having a ready supply.
The "Blasted Earth" you describe is just as habitable if not more so than any other celestial body we currently know of other than "Non-blasted Earth".
Unless you've already got a pre-made habitable planet already picked out and can reach it within a generation. Burrowing underground or building O'Niel Colonies in the mid to outer Solar System is going to be vastly safer and more practical than attempting an interstellar journey.
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