Terraforming Jupiter

One of my favorite TV shows was the short lived Firefly series.  The premise of the show was that the Earth had been "used up" and that a bunch of humans had headed into space, finding another star system with dozens of planets that were near enough in size and temperature that they could be terraformed and turned into habitable enough planets they could be colonized.  The recent discovery that there are 7 roughly earth sized planets in the "habitable zone" around the red dwarf star TRAPPIST-1 suggests one way this could happen.  TRAPPIST-1 is about 40 light years from earth, which would take thousands of years to reach with a plausible rocket, which predicates effective hibernation or perhaps even full stasis for such a colony to get there.

But there's another alternative.  What if we blow up Jupiter and move the fragments into orbits close to that of earth?   Jupiter is a gas giant, which means it's mostly hydrogen, but there's a metal and rock core--it's been catching asteroids, meteors and comets for 5 billion years.  Estimates are that the core is between 12 and 45 times the mass of Earth.  The show predicates cheap, safe energy of sufficient efficiency that it can power a Firefly-sized spaceship between planets with no visible fuel tanks.  This can only be nuclear or perhaps something even better.   Since we don't really have such a technology yet, it's not exactly clear how to make a bomb that would get deep enough into Jupiter to blow up the core into suitably sized chucks, but if we have such an abundance of nuclear or better energy, we can probably figure that out.  Once the Jupiter fragments are out there, we can use solar sails or our nuclear rockets to move them into orbits at a distance from the sun to keep them comfortable, and at a sufficient density to accommodate billions of people fleeting Earth.  This will take a lot of energy, but the spin and kinetic energy of Jupiter is substantial and if we can figure out a way of redirecting it, there's more than enough for the purpose.

Once we have a bunch of rocks that are big enough to have gravity appropriate for human habitation--between .3 and 2G--they will quickly turn themselves into spheres on their own, and the terraforming process can begin.  Left to their own devices this would take a billion years and if we're fleeing Earth we won't be able to wait that long, but presumably the terraforming technology will be able cool them down quickly enough.

Since we're engineering these new planets, it seems to me the way to do it is to have them in groups.  The Earth and Moon orbit each other around their common center of gravity--there's no reason they shouldn't be about the same size.  A third planet could orbit their common CG at a greater distance.   A bunch of such groups could be placed in such groups around the Sun, all in the same circular orbit...We'd probably use the same orbit that Earth-that-was is in.  If the mass of each is about the same, it'll be billions of years before they collide with each other.