How do capitalists expect to achieve infinite growth on a finite planet?

They don't really.  They just talk as they do.

You know those questions teens ask each other that nobody can really answer?  Would you deliberately run over a three-year-old if it would save a group of five people blocking your path?  That kind of thing.

Well here's a question like that.  Would you like to make a billion dollars if it meant the entire earth would become inhabitable 10 years after you died?  Billionaires in 'extractive' industries have already answered that question.  They simply don't care about long-term consequences.  They want to make their billions, and if people have trouble living on earth after they're dead, that's THEIR problem.

Capitalism itself tends to be totally preoccupied with the short term--the next stockholder's report, the next big deal, etc.--at the expense of the medium-to-long term.  Capitalism doesn't have to be based on unlimited growth forever.  We just do it that way.

Like the rest of us Capitalists expect to die.  What happens after that is no concern of theirs.  Mostly capitalists are old meaning they only have a few years left with which to ravage the planet and not enough time for the consequences to hit THEM.

At the disadvantage of others. 

Innovations can answer those questions.  If we don't have capitalism, there will be no more innovation.  Only de-growth and extreme down grade of quality of life.

No, that's why they are on Mars already

There's plenty more to reap still. We still haven't scratched the surface.