When a canon shoots a ball straight up (one dimension), the ball only accelerates as long as the nongravitational force of the canon acts on it. After that, the ball decelerates in the gravity field until the point it turns back and accelerates in the opposite direction as it falls back on earth. So is it right to say that according to GR, not only the freely falling body, but also the upmoving and 'turning point' frame are inertial, since no non-gravitational force acts on them? But doesn't the ball notice the direction change of its motion? Is that because there are (at least) three local inertial systems?