If there is a prize for over-analyzing a trailer, I should get at least a nomination for the the most recent Star Wars trailer. I will take this image from the international trailer for Star Wars: The Force Awakens and determine the location of these TIE fighters. It's a cool shot that makes me even more excited to see this movie.
When things are farther away, they "appear" smaller. We can call this the angular size. If I know the angular size and the actual size of the object, I can find the distance to that object. Let's call the angular size θ, the actual length L, and the distance r. For small angles, I get the following relationship:
Here is the plan. Using a TIE fighter width of 6.4 meters (the same dimension used in my last TIE fighter analysis) I can measure the angular size to determine the distance to each spacecraft. But two problems remain. First, what is the angular field of view for the camera? Second, what is the left-right, up-down position of the spacecraft.
For the angular field of view, I am going to use the size of the sun (well, it's a sun, not the sun). Our sun has an angular size of 0.53° or 9.25 x 10-3 radians. I'm just going to assume this sun is like ours. Of course that would mean this shot from the trailer is using a zoom lens to make the sun appear very large. That's OK.
Now, what about the up-down, left-right position? Imagine each TIE fighter is on the surface of a sphere that is centered on the camera. If this sphere is large enough, each spacecraft will have an x and y coordinate based that I can calculate from the distance (r) and the angular distance from the center of the frame. So, after I calculate the spacecraft distance I measure the horizontal and vertical angular size to calculate the actual position.
Now for some measurements. I will take that frame from the video and scale based on the size of the sun. The simplest way to get angular data from an image is to use Tracker Video Analysis—yes, it's designed for videos but it works just fine for images too. After scaling the image to the angular size of the sun, I can get the angular positions of the TIE fighters as well as their angular size. From there, I can calculate the position (x,y,z) of each one.
My plan was to create a GlowScript model showing the location of all the TIE fighters. However, this doesn't work. There is a problem—the fighters are not even close to one another. Perhaps this plot showing the z-positions of the 7 spacecraft will help (I am calling the z-direction towards the sun).
The number of the TIE fighters is completely arbitrary. But look at those spaces. The closest fighter is 4.5 km away from the camera and the farthest is just under 25 km. That is like 20 kilometers between the first and last TIE fighter. If you ever wanted to call something a lose loose formation, this is it.
But why are they so far apart? The problem is the angular field of view. If you want the sun to look that big, the camera has to zoom in quite a bit. Even if the sun is twice the angular size of our sun, the spacecraft are still super far apart. Really, if the TIE fighters are relatively close (let's say 500 meters apart) then when zooming in, they are all around the same angular size (just imagine distances of 4.5-5.0 km). But what if you don't zoom in? What if the TIE fighters are much closer? In that case, the sun would be very small (look how small the Sun appears when you take a photo).
OK, you know I can't leave this alone. I have to fix it. What if I just ignore the angular size of the sun and pretend like this is a typical video camera with an angular field of view of 39.6°. In that case, the nearest TIE is only 116 meters away and the farthest is 800 meters (note, I think I might have messed up with one of my previous measurements of position). Now this is something I can model.
Try zooming in to see the TIE fighters a bit better (zoom with the scroll wheel on a mouse or however your trackpad scrolls). Also, if it makes you happy you can rotate the view to see it from different angles.
In the end, either the TIE fighters are very far apart or the sun is huge. How huge would the sun be? In my model, the angular size of the sun is about 19° (or about 35 times larger in appearance than our sun). People like to talk about the super moon like it's a big deal—this sun would be a big deal. It would be fun to think about how hot a planet would be with the sun of this angular size (maybe that will be a future post).
Is that double eclipse? That would be crazy. What are the chances of a lunar eclipse? For Earth, it's not so common since the orbital plane of the moon is not the same orbital plane of the Earth around the sun. The moon only comes in between the Earth and sun every once and a while. If the Earth-sun-moon orbits were flat, there would be an eclipse once a month. What about two moons? I suspect that two moons that large (since they are huge like the sun) would gravitationally influence each other to make an unstable system (that's just a guess). Also, you could have one moon small and very close and then another moon larger and farther away so that they appear to be near the same angular size.
Maybe the bottom "moon" isn't a moon and instead is a space station—or a hill.
