The space tug and its load / target are on the same trajectory at the time of rendezvous. Once they're synced up, they're drawn toward each other, with the tiny

The space tug and its load / target are on the same trajectory at the time of rendezvous. Once they're synced up, they're drawn toward each other, with the tiny gravity of each affecting the trajectory of the other. But while the load is passively traveling through space, the tug can reposition itself. This way, the tug determines the ultimate trajectory of the load while also having some control of its own trajectory, which it uses to continually bend the load's trajectory.