A starfleet battleship traveling upward which, on seeing light (dot-dashed magenta circle) from an enemy cruiser dropping out of hyperspace when its FTL-drive failed (lower left "event"), accelerates rightward in order to intercept. The enemy trajectory is in gray, while the starfleet ship trajectory is in white.
Proper-time intervals are marked on both trajectories in intervals of 2 traveler-months. Animation frames are separated by 2 map-time months for a time-lapse speedup on your screen (at one frame per second) of about 5,256,000 times.
Units: (a) for distance are map-lightyears, (b) for proper-velocity vectors (green) are map-lightyears/traveler-year, and (c) for proper-acceleration (red) is in lightyears/year^2 or (to first order) "gees". The battlecruiser then reverses acceleration direction in order to (following a 2nd reversal ¾ of the way through) recover its original trajectory, amazingly about 3½ months of ship time ahead of schedule following a 4 traveler-year detour that took it more than a lightyear off path!
The dots in upper left and lower right represent stars separated by distances seen in our part of the galaxy.
All you need to know from the animation above is that when our starfleet battleship (black trajectory), while traveling "north" at 1.0 [ly/ty], detected that constant-velocity enemy cruiser after dropping in from hyperspace (gray trajectory) it began accelerating "eastward" at 1.0 [ly/y^2] to dock with the enemy ship 1.0 [battleship-clock year] later. It then reversed thrusters so as to begin a return to its starting trajectory.
Set 1: Questions to ask, using only the "consensus" bookkeeper frame pictured to define simultaneity between spatially-separated events, might include:
Variations on this type of problem might involve different numbers, non-orthogonal starting velocities and accelerations, and (even more challenging) thrust recommendations by shipboard computers for rendezvous given only data on the moving target. What else?
Set 2: Questions to ask which involve more than one map-frame might include:
These multi-frame problems, like traditional special relativity problems involving multiple Lorentz transform frames, because of the need for multiple definitions of extended simultaneity seem to have more potential for confusion. N'est-ce pas?