What could cause Earth to drift out of orbit over a period of months to years?
I would like to have Earth slowly move away from the sun, taking somewhere between several months and a couple of years to reach the point where human life on the surface is no longer possible. (The story revolves around efforts to get protected in time and the resulting conflicts. So yes, we have some level of spaceflight, but not FTL -- the people who get out will be taking their chances on something like generation ships. Or, as pointed out in the comments, by building shelters on earth to give them longer to come up with a permanent solution.)
My problem is that I don't know what could cause this. I can think of ways to knock the earth out of its orbit quickly that involve killing most or all of the inhabitants, but I need something that leaves many people alive and gives them time to stew about what's next. I want them to be slowly freezing, not slowly cooking -- moving away from, not falling into, the sun. Is this possible? If so how?
It's ok to vaporize a region if that's needed. I'm not fussy about which people survive, only that many do.