Without a spinning core, Earth would be like Mars.
Of course you can live in caves instead of trying to terraform Mars, but doesn't sound so fun.
I.e. Breathing is of limited utility, if the solar weather still gives you cancer.
Sorry for the overly blunt answer, because I know this isn't the question you're asking, but IMHO the question you're asking is based on a ridiculous premise.
We are polluting the Earth. Yeah, this is really bad for the Earth, and for us, but it isn't going to kill all life here. The thing that a "backup planet" is here to protect against is something like being struck by a meteor, or a plague, or nuclear war. Something where everybody dies very quickly, not something where life changes radically.
I am also not sure that it is possible to 'terraform' Earth. 'Terraform' means 'to make like Earth', and Earth is as Earth-like as is possible, no matter how hot or cold it is.
For example, Elon's speech about Mars colonization gives one answer. Maybe you've got great reasons to disagree with him. Maybe there's someone else you'd like to reply to?
(Hint: folks advocating for Mars think the atmosphere is not unusable.)
To hide from Radiation, one plan is to have 16 feet of soil on top of the habitat [1], and limit outdoor time to just 2 hours a day. Given those levels, I'd argue that it would make better sense to build entirely underground on the Moon. The Moon has a shallower gravity well, much stronger solar flux for power, and is much closer for resupply.
[1] http://www.space.com/21813-mars-one-colony-space-radiation.h...
/ducks to avoid projectiles
Apathy is on its way to winning.
(Don't tell Jen.)
Isn't this the next step after turning it off and on again.
Back when we had more mechanical drives, daughterboards, socketed chips and the like, it worked a surprising amount of the time.
Apathy... Maybe that comes with age.
P.S. Not to mention tubes. Yeah, I'm that old.
P.P.S The grandparent was making a reference to a show, and Jen is a character in that show. In case that was confusing anyone.