Given that the Millenium Falcon was using sublight ion drives when careening at the bridge of the Avenger (Captain Needa's ship), why could they not track the ion drive emissions and see where it stops? If the ion trail just ceases to exist on the "back" of the bridge area, send a TIE fighter to take a look.

Alternatively, there should also have been some fairly substantial sound from the hull when the manual grapple (And or magnetic grapple) was employed to bring the MF to the sudden halt necessary. (or even some stormtrooper looking out a random porthole)

Vader

Alert all commands. Calculate every possible destination along their last known trajectory.

That would seem to indicate to start at point of origin and go out from there.

Given that the Millennium Falcon was using sublight ion drives when careening at the bridge of the Avenger (Captain Needa's ship), why could they not track the ion drive emissions and see where it stops? If the ion trail just ceases to exist on the "back" of the bridge area, send a TIE fighter to take a look.

Alternatively, there should also have been some fairly substantial sound from the hull when the manual grapple (And/or magnetic grapple) was employed to bring the MF to the sudden halt necessary. (or even some stormtrooper looking out a random porthole)

Vader

Alert all commands. Calculate every possible destination along their last known trajectory.

That would seem to indicate to start at point of origin and go out from there.