Elon Musk made another characteristic splash recently with his plan to launch a Falcon Heavy into orbit around Mars, with the bonus payload of his personal Tesla Roadster inside.
Of course, it's an experimental launch, and quite possibly might blow up on launch. If it doesn't, it will head into orbit around Mars, apparently indefinitely.
Musk was quoted in the above article as saying it
"Will be in deep space for a billion years or so if it doesn’t blow up on ascent"
Assuming he means Mars orbit when he says "deep space", and assuming the rocket makes it there, how long would it actually stay in orbit, without refueling or any kind of human interference? I would assume the rocket might have some fuel left for correcting its trajectory, and it would need far less than, say, the ISS in LEO, where there's more drag due to Earth's dense atmosphere. But would it really last a billion years? Or will its orbit degrade and its body disintegrate before then?
I admit I am imagining a stereotypical circular orbit around Mars... could Elon be talking about a larger Elliptical orbit akin to a comet? In that case, I imagine there are even more variables that would make a billion-year lifespan unpredictable.