In a billion years we will be living well off Earth, probably out to the Oort cloud. We may even have the tech to move Earth out to the edge of the solar system.
That was one of 2 scenarios they put forth, using the gravitational pull of meteors to gradually move Earth's orbit further away. The other was just getting the heck out of Dodge. Either way I won't be around to worry about it.
Better take the Moon with us. That thing is slipping away from us at about and inch or two every year.