When a (perfect) ball is thrown at a (perfect) car, it will bounce off with the same velocity, v, but with its direction reversed. If the car is moving towards the car with some velocity V, when the ball bounces off it will have a velocity v + 2V. (This is easier to understand from the passengers of the car, who will see the car arriving at v + V and bounding at -v - V, or -v - 2V relative to the ground).

In the ball-car collision the electromagnetic forces are the ones responsible for changing the direction of the ball. But in the binary system, it is gravity. In particular as the shuffle enters orbit around the "incoming" star, the stars gravity will mostly pull it forward when it completed half orbit.

I hope I make sense.

Overall, such a joy to read this paper. With basic physics it makes you dream of sci-fi...