Imagine that a spaceship in deep space is approaching a space station at a constant speed of v = 2/3. Let the space station define the position x = 0 in its own reference frame. At time t = 0, the spaceship is 16.0 light-hours away from the station. At that time and place (call this event A), the spaceship sends a laser pulse of light toward the station, signaling its intention to dock. The station receives the signal at its position of x = 0 (call this event B), and after a pause of 0.5h, emits another laser pulse signaling permission to dock (call this event C). The spaceship receives this pulse (call this event D) and immediately begins to decelerate at a constant rate. It arrives at rest at the space station (call this event E) 6.0 hours after event D, according to clocks in the station.
a) Carefully construct a spacetime diagram showing the processes described above. On your diagram, you should show the worldlines of the space station, the approaching spaceship, and the two light pulses, and indicate the time and place (in the station's frame) of events A through E by labeling the corresponding points on the spacetime diagram. Scale your axes, using the hour as the basic time and distance unit, and give your answers in hours.
b) In particular, exactly when and where does event D occur? Event E? Write down the coordinates of these events in the station frame, and explain how you calculated them (reading them from the diagram is a useful check, but is not enough.)
c) Compute the magnitude of the average acceleration of the spaceship between events D and E in natural SR units (s^-1) and in g's (1g = 9.8m/s, for example 10g, 50g, ... ) Note that a shockproof watch can typically tolerate an acceleration of about 50g.