How much relativity effects occur at 0.2c? A sci-fi book series I'm reading has warships unable to hit other ships if their relative velocity is above 0.2c. I was wondering if that was realistic.
The gamma factor at 0.2c is only 1.02, which isn't much of an effect. The main difficulty with aiming at something moving that fast wouldn't be time dilation, it would be light travel time delay.
For example, suppose the other ship is one light-second away from yours and is moving at 0.2c. You're seeing the other ship where it was one second ago, and in that time it has moved 1/5 of a light second. Plus, supposing you're firing a laser at it, the laser will take another second to get to the target, so you have to aim 2/5 of a light second away from where you're seeing the other ship. And during that time the other ship could change direction and spoil your aiming calculation. The sci-fi book series probably is making some assumptions about how fast the ships can change direction, how fast and accurately they can aim, and typical distances between ships during combat to come up with the 0.2c number.
As the lorentz factor calculated above, not much!
Time would only be dilated by that much, and length by the the same amount. It'd definetly be hard to hit something at that speed, but not due to relativity!
