Building a gas-giant colony ship is not as difficult as it looks.
- Build a fusion candle. It's called a "candle" because you're going to burn it at both ends. The center section houses a set of intakes that slurp up gas giant atmosphere and funnel it to the fusion reactors at each end.
- Shove one end deep down inside the gas giant, and light it up. It keeps the candle aloft, hovering on a pillar of flame.
- Light up the other end, which now spits thrusting fire to the sky. Steer with small lateral thrusters that move the candle from one place to another on the gas giant. Steer very carefully, and signal your turns well in advance. This is a big vehicle.
- Balance your thrusting ends with exactness. You don't want to crash your candle into the core of the giant, or send it careening off into a burningly elliptical orbit.
- When the giant leaves your system, it will take its moons with it. This is gravity working for you. Put your colonists on the moons.
- For safety's sake, the moons should orbit perpendicular to the direction of travel. Otherwise your candle burns them up.
- They should also rotate in the same plane, with one pole always illuminated by your candle (think "portable sunlight")
- The other pole absorbing the impact of whatever interstellar debris you should hit (think "don't build houses on this side")
But the logistics are mind-boggling. It seems things would get tricky piloting Jupiter to catch earth (but not impossible) - the maneuvers for getting into orbit seem basic, but the candle needs to be rotated pretty fast to not burn the earth (going out of the ecliptic, I'd imagine).
So my question revolves on the possibility of getting Earth to Jupiter instead. Rockets, explosions, throwing the moon like a baseball towards the sun - whatever it takes to get over there. Given the rocket equation's thirst for mass, how much of an Earth is left over by the time we get into orbit around Jupiter? Is it habitable? Main Question: Is this idea plausible or will we be forced to pilot Jupiter to pickup Earth like a hobo jumping on a moving train?
I'll assume a Hohmann transfer orbit, with methane-oxygen combustion to start, but who am I kidding? This is saving the Earth. If you want to Rich Purnell a couple of Venus Flybys to save the planet, go for it. If you want to light up a fusion candle on earth that slurps up the ocean, go for it. If you want to light all the nuclear bombs in the world on one side of a really big metal plate, go for it. Throw the moon into the sun and be propelled backwards? Go for it. The Earth will be grateful you did - I'm just looking for plausible solutions. Of course, the other logistics of having Earth orbit Jupiter (Tidal forces, radiation) - is bad, but that's another question.