The first one.

I know we'd all like some scientific actualisation of Star Wars but I mean:

• They made noise in space 'cause that's fun.
• There was always gravity on pretty much any ship.
• I don't really recall any spacewalks so we don't see any instance of 'no gravity'
• There's hyperspace since lightyears is a bit of a long time.
• Stormtroopers seem very scientifically and inefficiently accurate

At this point I think the Star Wars movies (the oldies) pretty much ignored a fair bit of the science.

But if it was a death star literally put there in our universe, I think there would be a bit of structural considerations for gravity, but not huge due to it being quite hollow. Gravity is pretty strong when the sphere is entirely comprised of dense rock and no air. A mostly hollow sphere of air where air is something close to 1/1000 that of rock (yes, used the density of water lol) is not going to get much of a rollicking from gravity.

Edit: an interesting 'expose' on the moon landings claim one thing: why were the photos so relatively boring? Because they were real and that's all they could get for all the limited resources they had at the time.

The construction of the first Death Star

Cross-sections of the DS-1 Death Star.

https://starwars.fandom.com/wiki/DS-1_Death_Star_Mobile_Battle_Station

It's not gravity, it's the Force^TM^

Besides technical diagrams from supplementary stuff, the Falcon lands in a docking bay that's oriented towards the first option. There could be some kind of transition point to the second option, but we don't see it and it'd be really awkward.

Both.

The Millenium Falcon landed in a bay that was oriented with the N/S axis of the station, but was accessed on the equator. So the interior of the station has a gravity well with "up" pointing to one of the polls.

The surface cannons, surface towers, and trench defenses were all radially oriented with "up" pointing out into space, like you'd expect on a moon.

This also suggests the station was littered with gravitational dead spots and areas where you'd have to carefully transition from one gravity well orientation to another. No wonder everyone is wearing a helmet.

There's no way they used that much of the interior. Where do all those giants pits go?

Logic says B but LEGO says A

The second one, but standing on the outside of the sphere. It rotates around the gun.

Probably A. It would likely have used artificial gravity just like any starship. Star-Trek has it built into the deck plates but I dunno how Star Wars does it. Artificial gravity can then be dialed in to compensate for the natural gravity of the structure. Which is probably less than you'd think. Without normal gravity effects, the internal air and water pressure will be mostly uniform across the ship instead of denser towards the core.

Same with the matter making up the structure. It'll largely be hollow and filled with air, so much lower natural gravity than an actual moon of the same size. According to official sources (referenced here: https://scifi.stackexchange.com/questions/92401/is-the-death-star-s-gravitational-force-strong-enough-to-hold-an-atmosphere) it's between 120 & 160 km radius, for a probable gravity of ~0.04g. That's not quite microgravity, but still far too low to be walking around in. For comparison Lunar gravity is ~0.166g.

Get your science out of my Star Wars

The first one because luke fell off the bottom.

i don't know much about star wars, but wouldn't gravity be weaker near the centre as you'd have less mass below you and more above you

B) if their antigrav is like 2001 a space Odyssey. A) if they're using local gravity (eg built in the gravitational orbit of something).

So depends where it was built.

Either way miniaturization is what they really need to focus their efforts on. Hell, they'd save a lot of space if it were an unmanned drone. Which is also true of Elon Musks schemes to get to Mars.