This show's science is terrible. Basically magic *spoilers*

Their gravity simulation explanation makes sense in regard to centripetal force early in the show. Thrusters are used to maintain the rotation of the ark and the centripetal force required for artificial gravity-like forces on the occupants. We see the entire construct of stations rotating along a central axis. This means their sensation of gravity would be away from the central axis down, inward up. As you climbed toward the center eventually there would be an increasing sensation of weightlessness and in the center axis standard microgravity.

It works on the same idea as swinging a pail of water- the water can remain in the bucket despite gravity pulling it down because of centripetal force.

This is an important thing to note because it means every time we see someone standing, their feet are aimed at the outermost point of the station in regards to the axis.

So what the hell is going on after most of the ark stations go to planetfall and Jaha is left up there? We know he is left with a ring-shaped system of modules that are damaged. We know he has gravity while he is on the station- everywhere, so his ring station must be rotating. An object in motion will tend to stay in motion unless another force acts upon it. So it would continue rotating until maybe earth's gravity began to have a significant effect- for an orbital object that could be decades or centuries or more.

So his station is rotating. He finds imaginary son-baby. He finds a spacesuit. he is too stupid to realize that duct tape or really any tape is a great short term measure for a crack on even pressurized glass so does not try that for THE ONLY PRESSURE SUIT LEFT ON THE STATION (which is weird all by itself, there should be many in every station.) Decides to try to do a no-tether, no propulsion EVA that amounts to jumping in the general direction.

Here's where things get weird. We don't see the station ring rotating in relation to earth or stars or anything at this point and even for a giant object like that, it has to rotate pretty fast to generate 1G of force, visibly noticeably at least. It should be. For him to be standing in the airlock like that, we should see that.

So he decides to take a leap. Now you have to consider that even were it rotating, because of the direction he perceives as down because of the centripetal force, it would have to be rotating in the OPPOSITE direction. This is actually a different direction than it would have been rotating when it was attatched to that central axis when it was the full Ark. In the earlier case it would be along what we think of the common rotation axis of a ring. To make it like the way it shows gravity as he looks out of the lock, it would have to be along a z-axis rotation. So not only is it rotating, it's rotating in a way that he is now shooting at a target going continually downward from him, not right in front of him. Once again, we don't see this.

So he leaps, unaided, manages to thread a 2 meter needle over what, 500 meters maybe? and then deftly hits the airlock door as he floats in. He immediately hits the floor as the lock pressurizes. Legit LOL here. The presence of air is not what creates the sensation of gravity here or anywhere.