I was originally going to use a video similar to the shot from above. It shows a moving shadow from the intensely bright meteor. Well, it seems someone beat me to it.
Well done, Stefan Geens. I salute you. However, instead of just stopping I think I will repeat the analysis using Tracker Video Analysis. I always say, if it's worth doing once - it's worth doing twice. Actually, I don't always say that but maybe I will start.
Originally, I was going to use this Russian meteor video:
The only problem is that it isn't in HD and some of the shadows are difficult to see. You should watch it anyway. In particular, watch the pedestrian crossing the street at the lower left. The whole sky lights up but it seems like this person is just "meh" - unimpressed. Ok, well here is the video that Stefan used. It's much better.
As Stefan points out (by the way, he did an excellent job at the analysis - make sure you check out his post), you can find this location in Google Maps.
Assuming Google Maps has an accurate scale, I get the distance between the center lamp posts is 31.9 meters and the distance across the road (from light post to light post) is 38.8 meters. I will use this to correct the perspective issues in the video.
Here is the plan. I want to get a plot of the tip of one of light post shadows as it moves along the street. So, the first step is to download the video from YouTube (I use the Chrome extension Chrome YouTube Downloader) and drag it into Tracker video.
The next thing I do is to adjust the video clip properties. We only want the part of the video with the meteor shadow - this starts around frame 714. Also, I chose to skip every other frame - just because I think that will still give plenty of data.
Now we need to scale and adjust for perspective. Click Video - Filters - New - Perspective. This will place a red box that you can move the corners to locations that you know. Then you tell Tracker where these corners are supposed to be. For this case, I assume the following shape is a rectangle that is 31.9 m by 38.8 meters.
Once you do that, Tracker will automagically transform your video to something like this:
It took me a while to figure it out, but you can adjust the shape of your perspective rectangle both in "input" mode and "output". After you get the perspective the way you like it, you can scale the video. Notice that the four light posts now make a rectangular shape. It looks like we are in business to do some serious stuff now. All I need to do is to create a new "point mass" and start clicking on the end of the shadow.
I used the base of one of the light posts as the origin for my coordinate system. With that, I can make a plot of the length and angle of the shadow as a function of time.
What do these two things tell us? Well, imagine you were at the end of the shadow and moved along with it. If you looked at the top of the light post (actually, there seems to be a thicker part that goes thinner that I used to mark the locations) then this light post would be covering the meteor. The θr value is the "heading" to the location of the meteor and the r value gives the of the angle of the meteor above the horizon. Here are two diagrams that might help where the red arrow points to the location of the meteor.
So, I get two angles (the h angle is the "heading" and the a is the altitude angle). If I use these I can make a plot of the angular position of the meteor in the sky.
This might look a little funny - but that's just because of the different scales in the vertical and horizontal directions. That dip in altitude angle at the end isn't very large - just a couple of degrees. The heading angle has a much larger range than the altitude angle, but the graph doesn't display it to scale. It would look really wired if it did, but I know you want to see that anyway. Ok, you asked for it.
Here is the Tracker zip file if you want to answer the following homework questions (you will need to install Tracker Video Analysis). If you don't want to use Tracker Video, here is a spreadsheet with the data in it.
- Using the data from this light post and the location of Chelyabinsk, make a picture of the path of the meteor in the sky.
- If you assume the meteor was 20 km away from the light post, how fast was the meteor moving?
- What if the meteor was only 10 km way? How fast would it be moving then?
- Can you estimate if the meteor was moving at a constant speed or not?
- See if you can reproduce Stefan's results with this video analysis data.
That is your homework.
Another video
Why stop there? Why not look at another view of the same meteor? Here is the video. I'm not sure why, but it is embedded restricted. Well, here is a picture.
This is what the trajectory looks like from the camera. This is unscaled video - so the dimensions would be in pixels.
Here is a spreadsheet with the data from the video and here is the Tracker zip file.
And of course there is homework for this video also. There are quite a few things that you don't know. If you estimate or assume some values, you can find the other things. Which values do you estimate and which do you calculate? You pick.
- The angular view of the camera.
- The location of the video.
- The angle of the trajectory with respect to the view - was the motion perpendicular to the camera view?
- The meteor speed.
- The meteor distance.
- I didn't include the data, but you can estimate the brightness of the meteor as a function of time. This would be a little tricky since it seems that the camera has some automatic adjustments for brightness.
Yes, I know that is a lot of homework. You don't get better at physics without doing physics. Actually, one cool thing would be to compile trajectories of the meteor from many different video locations. With this you could really pinpoint the actual position and speed of the meteor. Who needs radar when you have Russian dashboard cameras?
