The Saturn V wouldn't be anything like enough. But there are ideas for ways to move the Earth over a half billion year period. One approach involves repeatedly sending a giant asteroid to do close flybys of Jupiter and Earth. If you plan its trajectory just right, this will pull Jupiter in towards the sun a tiny bit, and move the Earth out by a larger amount. Only a tiny amount for each flyby, but over half a billion years that all adds up to be enough to move Earth. Not much fuel is needed, just course corrections from time to time. Jupiter does all the heavy lifting in this approach.
But that's obviously dangerous if you get it's orbit wrong for one of its many millions of flybys and it hits the Earth.
The science fiction writer David Brin came up with another approach which seems safer, in his Let's Lift The Earth!
Not necessarily 4 billion years, even half a billion years from now, then the sun will warm up and it may be too hot for life on Earth.
But to put this into perspective, it took half a billion years to evolve from tiny microscopic creatures to humans. Including evolution of worms then the very first creatures with primitive backbones, fish, transition to land, the dinosayrs, mammals and ourselves.
So - there's no hurry here. Many other human civilizations and probably other technological species will probably arise between now and then, surely.
And- might be the answer is to save the Earth. If we can think of a couple of ways to do it with present day technology (though one is quite risky) - surely there must be many other ways to do it with technology developed for millions of years into the future. I'm sure that we haven't discovered everything in science, at least there is no sign yet of the pace of discovery slowing down - and probably there are many discoveries still to be made that would seem as bewildering to us as our radio and lasers etc would be to eighteenth century science.
Or maybe the answer it is to move to Mars as it gets warmer, and then to Jupiter's moons. Or free flying space stations. Or goodness knows what. Might well be methane breathing octopuses or goodness knows what who face this issue anyway :). Some creature evolved half a billion years into the future from us.