[Spaceships] How should a large station... duck?

[Anthony]

The general case of dodging is that you have to move by more than the diameter of your object, in less time than the object has to correct.

This will usually not be possible for a competently designed impactor, as it will likely have as good course correction as the target, except in the extreme relativistic range, where light speed lag causes problems for both the defender and the attacker.

At 0.99c, in the reference frame of the target, it takes light 500s to cross 1 AU, and it takes the impactor 495s, so you have only 5s warning. This generally makes detection not very viable. However, the impactor has the same problem: you probably don't know the target's position with more accuracy than 'orbiting that planet', so if you've got 5 km/s delta-v available for course correction, you need to know the target's position something like 1,250s before impact, which means you need to be able to detect the target (and distinguish it from possible decoys) at 250AU.