[kijin]

Currently, the Tesla is aimed almost directly away from Earth. After all, it was launched from Earth!

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.

[mnw21cam]

The point was made in the paper - since the Tesla was launched from Earth, its orbit has its closest approach to the Sun very close to the Earth's orbit, and this increases the chance of it being affected by Earth's gravity. This is because for part of its orbit, the Tesla will be effectively travelling along approximately the same path as Earth, just a bit faster. This means that it will approach Earth approximately one in every ten orbits. Hence the first interaction in 2091.

After a few interactions, the orbit becomes more funky, and interactions decrease in frequency.

[cyberferret]

I hope that other members more in the know can clarify, but I thought that the launch into deeper space was done as a 2 stage thing - first, they got the car up into earth orbit, THEN they did a second burn to break orbit. i.e. the second burn was done while the vehicle was moving tangential to the Earth, and not radially away from it?

[kijin]

That just means that when the Tesla returns to the same point in its orbit, it will pass a few hundred miles above Earth's orbit (where the final burn was performed) instead of directly intersecting Earth's orbit.

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.