Technology won! Humans managed to advance technology fast enough that they circumvented any global warming apocalypse and by some sheer miracle (maybe God's intervention) they got their population under control and all agreed to stop killing each other.
So they are now in the familiar post-scarcity era and everyone's settled down nicely. There is a new problem, the sun's battery is running out. Let's set the scene several thousand years from now. I know the sun has a very long time left comparatively, but you know what humans are like, they worry.
It was decided that sending small groups of humans off to nearby habitable planets (which have been 100% confirmed) would be logistically difficult, favor some humans over others, unlikely to succeed and be hard to populate the planets for a myriad of reasons. "How could we take the whole of Earth to a new star?" they asked. "We could build the biggest Solar Sail ever?" suggested one naive proto-scientist.
OK enough of the theatricals. Is it possible to build a giant solar sail, big enough that the sun propels it and its gravity (and/or other forces) counteracts the propulsion so that it pulls the whole solar system with it? Basically we are trying to turn the whole solar system into a ship.
Imagining we have all the resources of the solar system, what would be the logistical problems in achieving this? Can we make it to another star, let's say 10 light years away before our Sun's "battery" runs out? Would it be possible to detach the sail and aim Earth so it starts orbiting the new star safely? Answers should be science-based but do not necessarily need citations.
If we cannot take the solar system with us, is there a way we could incubate the Earth while it travelled alone by solar sail to the new star? The majority of life would have to be present when we arrived.