TOTW: Aliens

To add, this is what I meant by my first comment that it is just not credible that the Pentagon would put these videos out there genuinely being flabbergasted and thinking it could somehow show strange craft defying the laws of physics. The variables (target_distance, horizontal_angle, vertical_angle) define at each point in time the position of the target relative to the plane (to be precise they form a spherical coordinate system, the full math is a bit more involved with transformation matrices and stuff, nothing that shouldn't be easy-peasy to any professional in this though) and it's trivial to check that there's nothing even close to defying the laws of physics going on here, what is actually shown in the video is perfectly mundane. If one analyst at the Pentagon somehow fails to analyze this then one could wonder how he even got the job, but if supposedly *all* analysts at the Pentagon fail at this then it's simply not credible. They're just pumping out bullshit to scare people into giving them more money, or trying to divert attention from whatever they don't want people paying attention to.

So apparently (judging by googling an article about it) people thought that this object must be moving at high speed because it looks like it's zooming fast over the ocean. This is just parallax though, and is actually unrelated to the speed of the object, it's simply an effect of 1) the camera moving at high speed and 2) the camera constantly rotating to keep focusing on the object. It's quite easy to see this effect for yourself:

Look in front of you and consider an object in the background somewhat to your left (we'll call this the "left mark") and an object somewhat to your right (we'll call this the "right mark"). I currently have a computer screen in front of me so I'll take the left edge of the screen to be the left mark and the right edge of the screen to be the right mark. Now put your finger in front of your face, like about 20 cm or something, and close one eye and look at your finger. Move your head left until your finger lines up with the right mark. Now move your head right until your finger lines up with the left mark. Now do it again but fast. Notice how it looks like your finger is zooming very fast relative to the background, even though your finger hasn't moved at all, the effect is just because of the camera (your head) moving very fast while keeping to focus on your finger.

Ok I actually think I figured out what the deal with those videos is, after looking up the originals here: https://www.navair.navy.mil/foia/documents?page=1 My hypothesis is that these are training videos, like exam questions for their analysts. My reasoning for this is based on the names they gave to the files, like this:

1) GOFAST

This is the video I analyzed above of something that is, quite distinctly, not going fast at all (about 130 km/h by my calculation). But if you weren't careful about thinking about the camera's movement and just looking at the parallax you'd easily be misled that it's actually going fast. So it seems like a tricky exam question, where they give you this video calling it "GOFAST" but to get the solution you actually have to ignore the video title as well as the parallax effect and just calculate the speed based on the numbers on screen, to see that this thing isn't actually going fast at all.

2) GIMBAL, on youtube here https://www.youtube.com/watch?v=2TumprpOwHY

This video purportedly shows a craft sharply rotating in mid-air. The trick here is to realize that this rotation happens right when the camera's horizontal angle passes 0° (top-middle of the screen). The camera is mounted on a gimbal which means the camera needs to rotate quite significantly when passing through the 0° angle (technically the camera always has to rotate but just by a tiny bit which is corrected for by a derotation system, it's when it passes the 0° that it needs to rotate by quite a lot). That is, the object isn't rotating, it's the gimbal mounting of the camera that is rotating - it's a phenomenon called gimbal lock. What this video is showing is artifacts of the gimbal mounting, and the video is called...GIMBAL. Again sounds like a training/exam video.

3) FLIR, on youtube here https://www.youtube.com/watch?v=lWLZgnmRDs4

Supposedly that one shows a craft suddenly accelerating fast at the end. In reality this thing isn't accelerating at all, it's been moving to the left relative to the plane all along, it's just that the camera has been rotating to keep it in the center of the screen (again see the horizontal camera angle at the top-middle of the screen) and at the end the camera simply loses the lock and so the object moves left out of view.

Given that the first video was named GOFAST even though the object isn't moving fast at all, and the second video was named GIMBAL while the solution was indeed a gimbal mounting artifact, this seems like training/exam videos to me. So I suppose they figured they'd throw some tricky exam videos out to the public and scaring them about "ufo's invading their airspace" so they'd get more money or something like that.

what do your astronomy studies say about the collapse of empires