Jonathan McDowell, an astronomer at the Harvard-Smithsonian Center for Astrophysics and a noted space analyst, says two forces acting on the car will limit its lifetime.
One is Jupiter. The giant planet's gravity perturbs bodies in the asteroid belt and, over time, will have an effect on the Tesla's trajectory. The other effect is a subtle acceleration produced by tiny temperature-related forces over extremely long periods that also would act to change the orbit.
"It's tiny, but over timescales of millions of years it's enough to shrink the orbit and make the thing fall into the sun," McDowell said. "So it's a race between does that happen before some Jupiter perturbation ejects it from the system.
"On timescales of centuries, it's going to be pretty much in the orbit it's in now. On timescales of thousands of years, it's going to be in a not-horribly-different orbit, but Jupiter will mess it around some. And then on timescales of millions of years, it won't be there anymore."