Some have argued that the Death Star is capable of accelerations of 100g, or about 1,000m/s2. This data is based solely on the Rebel screen in the moonbase, and the presumption that it is positionally accurate.
However, the figures derived by the originator of that idea are false.
He suggests that we trust the Rebel screen over the Imperial readout in order to determine the speed of the Death Star. Take a look below at the Imperial readout. Notice the curvature of the gas giant, and the motion of the Death Star?


The argument that we must trust the Rebel screen over the above Imperial screen makes no sense, and ignores the canon facts. Shortly after the Death Star entered the system, we are told that the battlestation will be in firing position in 30 minutes. More importantly, we are told that the Death Star is orbiting the planet at maximum velocity, and we're shown the shot captured in the first picture above.
(The idea of maximum velocity is peculiar here, but could refer to the simple orbital trajectory, or something to do with the repulsorlifts.)
The original proponent of the 100g figure, meanwhile, shows us the Rebel screen readout at 15, 5, and 0 minutes from the Death Star's reaching of firing position. While we cannot see on this screen where the ship was located at 30 minutes out, we can certainly see that if the Rebel screen is positionally accurate, and given that the DS was already at maximum velocity, the Death Star would have been in a prime firing location 30 minutes prior, but from the other side of the planet. Further, given the max velocity line as compared to his assertion that the DS must have accelerated afterward, the proponent is asserting that they must've slowed down and then re-accelerated for no reason whatsoever.
In other words, instead of simply turning around and shooting, they made an orbit of the planet for no good reason. If they had, in fact, needed to turn around to target the moon, they could have simply dropped out of hyperspace sooner. You can see this below:


So, pick one: Either the differences between the Rebel screen and the rest of the canon facts indicates that the Rebel screen is not positionally accurate (and that therefore you cannot derive acceleration from the Rebel screen), or the Empire is utterly stupid when it comes to navigation.