The idea of turning Jupiter into a second sun is an old one, going far back to the 20th Century. The idea became popular in the science fiction novel 2010: Odyssey Two when an alien race purposely turned Jupiter into a second sun. As mankind's technology developed and they reached the stars, the idea was somewhat abandoned for many thousands of years, but the idea was brought back when a team orbiting a J-Class planet Occam managed to successfully 'ignite' the planet and turn it into a dim brown dwarf, which in turn made a few of Occam's moons inhabitable.
With the success of Occam's Star, many others began refining the technology and successfully ignited other suitable J-Class worlds, even a few rogue planets were ignited. On July 5, 9999, a motion was put on the ballot during the Confederacy presidential campaigns that would allow the ignition of Jupiter. The ignition would mean that heat would warm the four Galilean moons, which until then had been heated by a thick layer of greenhouse gasses over sea level, keeping weak solar heat inside their atmospheres. The atmospheres would likely have to be scrubbed, but keeping the sea levels clear of excess oxygen would no longer be necessary.
There is much controversy surrounding the proposed project. Many who are opposed are the inhabitants of Jupiter's floating cities as well as those of the Jovian moons and even many of the Kya. The opposition points to the disastrous Metallica Incident in which a botched ignition caused the disruption of the entire star system, including a populated human colony world. Many of the planets in the system were thrown out of orbit. The other reasons for the opposition are that Jupiter is a historic landmark, so to speak. It is one of the oldest worlds known to humanity and many believe igniting it would be akin to destroying something like the old Statue of Liberty on Earth.
Due to the controversy and opposition, the project was put on hold indefinitely. Instead, the technology was used to continue and ignite many large gas giants, creating new inhabitable worlds out of the moons.