Sounds similar to the old Panoramic movie dome they had at Astroworld years ago... It was REALLY cool (literally and figuratively-- they kept the air conditioning in there at like 60 degrees-- NICE on a hot humid Houston afternoon!)
You went in and laid down or sat on the floor, there were no seats. The "screen" was a hemispherical dome above you. It was ringed by like 6 projectors, each projecting film which was taken from a special camera setup using a ring of 6 cameras mounted in a fixed housing. The film started with someone walking along with this setup on a dolly in front of them, giving you the perspective of walking along with them through town. Then it switched to mounted on top of a car, so you were 'riding on the roof' and it was neat because you could look any which way around you and see anything as if you were driving by it in the car. Then they switched to the last 3/4 of the movie, which had the camera rig slung under a helicopter as it flew under a bridge, over water, circled and hovered and did aerial tricks and stuff... the view was exactly what you'd see if you were riding in a lawn chair slung ten feet beneath a helicopter, and because of the peripheral vision effects, you actually felt as if you were taking G-forces as the helicopter banked and turned sharply-- it felt like the floor was moving and the image on the screen was standing still. I recall some kids even got airsick from it and ran outside. It was WAY kewl though. Crappy Six Flags ripped it out a couple years after they bought Astroworld (which itself is long gone now).
I see the setup you're contemplating. I think the cameras would need to be mounted in the nosecone of the rocket, looking out and down at like a 45 degree angle (or whatever depending on the camera's field of view-- the FOV's would have to overlap the bottom of the rocket SLIGHTLY but not like most rocket vids where the fins are nearly in the middle of the screen! They would need to be just barely visible at the very bottom edge of the 'screen', and of course you'd have to know the camera's field of view to the sides and divide that by 360 so the camera's FOV's just overlap or abut (as little as possible to minimize processing power required to stitch the images together). You'd get a "360 degree" "planetarium" view of the ground and surroundings as the rocket ascended, which would look like you were looking down from the camera's position from just ahead of the rocket without the nosecone on ascent, much like most flying video games where you're 'behind' the plane 'flying' it, but in this case "in front of" the rocket, looking back as it "flies towards you" as you "ride in front of it" and the ground drops away.
Now, I'm not sure how perspective effects would work with this, because usually these sort of camera setups are filming with a lot of the motion being primarily fore/aft, side/side, and NOT up/down in relation to the axis of the camera setup. Of course putting this setup on a rocket, with the camera mounts' axis of symmetry aligned with the rocket's flight axis would result in mostly an up/down motion in the video, which might be more prone to distortion effects from perspective. Mounting the camera mounts axis of symmetry at a right angle to the rocket's flight axis would of course minimize this, but it would also result in the view changing to a 'pilot's view' similar to what a shuttle commander might see out his windows-- a view straight ahead, out each side window toward the horizon, but with the added view aft toward the ground, much like a fighter pilot in a straight up climb might see behind him. Of course that would also restrict the "side views" which would no longer be in the 360 degree view axis, and the straight up view would be boring (unless you were flying toward something!) but it would minimize any such perspective distortions in the final footage.
As for software to integrate it all together into a seamless 360 degree movie, that's TOTALLY another issue. I'd tend to think the software would have to create a 'panorama' from each matching frame from each of the cameras, frame by frame, then play them to create the panorama movie. Sounds like a LOT of computing power and memory! The setup I referred to earlier used simple film cameras in a housing which was constructed with a certain geometry with the cameras mounted together LOOKING OUT, which was then duplicated in reverse by placing the projectors in a ring around the wall mirroring the geometry of the cameras, PROJECTING INWARD and onto the hemispherical dome. Display of such a video on a flat screen would give a VERY weird perspective, as it would be a "flat" representation of a "spherical" view, much like a Mercator projection map of the Earth... Not exactly the immersive experience one would hope for....
OK I just thought of a way to do this "on the cheap"... and the display would even work right too... install six gum cams or fob cams in the "hex housing" and put it on top of the rocket. Borrow five more laptops (and use your own as the sixth) and load each of the six cams videos individually into each of the six different laptops, arranged in the same way around you as the cameras were arranged in the housing. Arrange the six laptops in a circle around you and play the vid on all of them at the same time... :y:
That's the only way I can think of to get the '360 degree view' on the screens as it was meant to be seen with video equipment rather than film projectors... nobody makes a spherical screen you could put over your head. Maybe virtual reality would work, but again, it would take MAJOR computing power to be able to 'look around' in realtime in the 360 degree view you'd have, because VR works by calculating where you're looking and then displaying the appropriate view onto the VR glasses/viewscreen.
Don't see how you could do it realistically without access to a military combat simulator... (Hmmm.... that could work).
Later! OL JR