drops in from hyperspace
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.
Possible Puzzlers
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:
- 1a). How fast and in what direction was the enemy ship traveling, in map-distance per unit time on enemy-ship clocks?
- 1b). How many "gees" (net proper-force per unit mass) did the battlecruiser experience during the rendezvous maneuver?
- 1c). How long, in battleship and in map years, did the "ignition to docking" leg of the detour take? Note that we are not asking how long it took on enemy ship clocks. Why?
- 1d). Where (relative to an origin when first-light from the enemy ship arrived) did the docking take place?
- 1e). How much kinetic energy and momentum per unit mass did our battlecruiser gain during the speedup, from the map-frame perspective?
- 1f). Just after ignition and just before the docking event, what were the apparent forces and rates of energy increase per unit mass to our battlecruiser from the map-frame perspective.
- 1g). Assuming that the battleship does a final rightward constant acceleration burn to return to its original trajectory, how much ship time is lost or gained as a consequence of the detour? How much map time is lost or gained, as well?
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:
- 2a). Before the beginning of the chase, what was the velocity (magnitude and direction) of the enemy ship with respect to the battlecruiser.
- 2b). Before the beginning of the chase, what was the velocity (magnitude and direction) of the battlecruiser with respect to the enemy ship.
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?