During Rogue One, we saw that the Death Star was able to aim and directly target
the city of Jedha.
So why, an the end of the movie, did they not
fire directly at the archive? They hit what seems to be a location far out in the water, next to the island.
I think it was because they didn't want to wait to get into ideal position.
The Death star was rising from the horizon and positioning itself to attack. Turning huge battle station like that even for few degrees may take a long time (if we take into consideration the firing at the rebels base in ANH, where they managed to deploy a whole squadron and destroy the Death star before it could emerge from behind the planet).
Tarkin knew exactly from previous attack what the blast radius is, and he probably didn't want to wait to get into position to hit the dead center of the target, when he knew he would hit the target anyway.
(out of universe answer: so we get a more emotional ending)
Scarif shot was perfectly aimed. Did you see the shot went right through Scarif facility giant antenna, killing Director Orson Krennic prior to impacting the ocean ?
Perhaps, the Death Star was aiming at the bright radio-source as a good approximation of the Scarif archive location.
Although, that green ray should have deposited about 40 tonnes TNT of explosive energy into the antenna it went through. Sadly, the filmmakers haven't thought about this bit.
The angle was much more difficult.
The death star was shooting straight down onto Jedha. This was a planned destruction to demonstrate its power and to remove some rebels.
The shot at the archive wasn't planned. They didn't know that the rebels would attack. You can see that the laser hits the top of the archive and continues in a flat angle to the ground. In some scenes you can see the explosion from top as you have seen on Jedha, but that wasn't the view from the death star, rather it was shown from above the portal.
That issue has been nagging me. Probably the thing that makes the least sense in the movie (well, together with Xwing not hitting a big fat shuttle standing in the front of the base that they target. Please).
I believe that this has to do with the reshots. If you look at the screenshots of the trailers, tv ads and such, you'll quickly discover that the first cut of the movie did not end the same way.
First, on this still from a scene that did not make it into the final cut, you can see what I believe to be the archive building without the antenna on top of it (in the distance, on the far left):
It seems that in the initial cut there was no antenna on the archive building.
Second, there are numerous shots of Jyn & the gang running on sandy beaches with the death star plans.
Example (there plenty of others):
See that thing in Jyn's left hand? Detah Star plans. So they were out of the archive building, in the open, with the plans.
Third, as clearly visible on that still from the same deleted scene, there was at least a dish antenna somewhere else on scarif in the first cut of the movie (see on the top right corner):
Hence my belief that, in the initial cut, there were two distinct locations. The building were they steal the plan from and a communication complex with the antenna that they send the plans from. That would explain why the death star does not target the archive building itself (despite the line cited above that is indeed spoken in the movie - which was the cause of my initial issues with this scene as it doesn't fit with what we see), its target would have been further away : the antenna complex. I am aware that this does not explain everything, but I still think that's quite a fun theory :).
There's an old joke that goes like this
Close only counts in horseshoes and nuclear war
They didn't have to hit the archives at all. Just get it close enough and the shockwave will do it for you
They definitely aimed for the Citadel.
From the movie dialogue:
General Romodi: Permission to target their fleet?
Tarkin: “Lord Vader will handle the fleet”. "Your target is the Citadel"
The soldier tasked with the targeting is Hurst Romodi, the same soldier who pulled the trigger on Jedha. Having observed the Battle Station's destructive potential and under pressure from Tarkin to fire as soon as humanly possible, it certainly doesn't seem beyond the realms of reality that he simply took the shot he had, factoring in the position of the Death Star in relation to the Citadel.
Meanwhile, Tarkin would put the Death Star to better use by employing it for its stated purpose. He gazed down at Scarif. Such a beautiful place, and he would be among the last to see it.
“You may fire when ready,” he informed Romodi.
The general immediately set to carrying out his world-ending orders.
and
“Lord Vader will handle the fleet,” Tarkin said. “The plans must not be allowed to leave Scarif, at any cost.”
Romodi understood. “Yes, sir,” he replied, and began calling orders to his aides.
Let's be honest here. Missing by a thousand miles isn't that big of a deal when a miss of that magnitude is still a hit. And heck, they managed to shoot the top of the Citadel off. How close do you want to get it?
I think it was a simple case of trajectory and angle as listed above, but also as a means to do more damage. The Death Star's destructive potential is exponential, which is how it can destroy whole planets. Targeting the city directly would destroy it, but firing into the ocean would destroy the base as well as send a tsunami to clean up the remains and anything left behind.
Short answer - they wanted to fire fast and still destroy the Citadel.
Unfortunately, the real answer has nothing to do with logic, Imperial tactics or the Death Star's capabilities.
The Death Star shot wide so that we could watch the explosion roll in over the horizon as Jyn and Cassian held each other on the beach, knowing that they were about to die. They were going to die heroes, and we got to watch it happen - slowly.
It was incredibly emotional. Why? Because you watched the explosion coming right at them - and so did they.
Thousands of people died when the Death Star blew up Jedha City. Did you feel for them? Nope. Because you didn't see them.
Billions people died on Alderaan. Meh. It was just a planet on a monitor.
Over a million people were killed on Death Star 1. No one cared. Same with Death Star 2.
This was the first time we saw a Death Star explosion that was not instant death, and it was dramatic - but it made no sense.
They justified it by having the Death Star's beam destroy the dish and Krennic. But, any TIE Striker, TIE Fighter of AT-ACT could have done that earlier.
Why would Tarkin destroy all Imperial architectural plans (no backups) and the Scarif base, just to kill 30 rebels and a guy he is mad at? I don't think that would go over well with the Emperor. Scarif is where the Empire built its war machine, so they say.
Tarkin only uses the Death Star, and aims wide, to create a movie moment.
Bear in mind this is a franchise where the Force does not awaken. Details like this will drive you mad unless you remind yourself that it was only a movie.
Also, you might as well ask why the Empire would build an archive to store TAPES (or hard drives) of architectural plans - and design it like a tower vs. a regular building with normal shelves - when we know they have an Imperial computer network?! Again, this was just designed for a cool action scene that was straight out of a video game.
