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 with some velocity -V, when the ball bounces off it will have a velocity -v - 2V, gaining an extra -2V. (This is easier to understand from the car's passenger's point of view, who will see the ball arriving with a relative velocity v + V and bouncing with -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 shuttle enters orbit around the "incoming" star, the star's gravity will pull it forward mostly 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...

EDIT: typos