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In Episode V, when looking for the Falcon, Vader tells Admiral Piett:

Admiral Piett: Lord Vader, our ships have completed their scan of the area and found nothing. If the Millennium Falcon went into light-speed, it'll be on the other side of the galaxy by now.
Darth Vader: Alert all commands. Calculate every possible destination along their last known trajectory.
Admiral Piett: Yes, my Lord. We'll find them.

In terms of a hyperspace travel, from one specific point, how many destinations it is possible to have? Does this phrase even make sense? How can they calculate every possible destination, and what would they do with it? It's not like they can travel to every possible destination...

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    That should depend on a particular departure point -- i.e. if there are ten planets on that trajectory line before that line leaves the galaxy then there are ten possible destinations. If there's only one planet and then the trajectory line runs into a star, then there's only one possible destination. – Null♦ Jul 20 '16 at 17:55
  • @Null well, two possible destinations, but that second one is kind of deadly. – CBredlow Jul 20 '16 at 18:05
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There are hyperspace lanes in Star Wars. Which means you can't travel wherever you want in lightspeed. There are safely charted routes which you can take, which do not lead you close to gravitational bodies and other dangerous anomalies. In fact, pirates are known to hide out near big hyperspace lanes and pull ships out of hyperspace using gravitational devices.

Based on the Falcon's last known trajectory, they can probably check which possible hyperspace routes they could have taken (assuming you can't turn 180 degrees in lightspeed, they had to have taken a lane in that general direction). Just check the highway map.

"Calculate all possible destinations" means check every system or stop they could possibly make which lies on the hyperspace lanes in that direction.

And by "alert all commands", he means: tell everyone and their mother to be on the lookout in those locations.

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  • I believe there are also mentions of certain points along hyperspace lanes where ships will drop out of lightspeed to adjust their course providing opportunities to pirates without 'gravitational devices' – IG_42 Jul 20 '16 at 22:52
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They can see what direction the ship left the system in, and then based off of known systems, predict where a ship of that size with the fuel, hyperspace engines and other parameters could go.

Also, they aren't planning on visiting every possible destination, it's even said in the quote

Vader: Alert All commands

He's saying, alert all command posts, fleets, etc about the Falcon escaping and to be on the lookout.

Think of how in crime shows they often do "BOLO" for a car. The same thing is happening here. Hyperspace computers will often route a ship through known hyperspace routes and then make the jump, and I'm sure the Executor has more powerful computers that allow it to process aforementioned data and return possible system destinations. (After all, it's only a graph traversal problem, I'm sure it's not that hard to solve!)

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