But I guess that comes down to the velocity of the object in question, and after repeated trajectory adjustments due to gravitational pull, it could quite conceivably end up aiming directly at a massive body in space that exerted the pull in the first place...
On the other side of the orbit, that becomes almost directly at Earth.
Go round and round a few million times, and Earth might actually be at a point in the orbit where it can exert a significant gravitational pull on the passing Tesla.
The difference is virtually meaningless compared to orbital perturbations from other sources. Either way, it's close enough for Earth to affect the Tesla's orbit if it were at the right place at the right time.
After a few interactions, the orbit becomes more funky, and interactions decrease in frequency.