Star Wars Used to Explain the Concept of Angular Size
via WIRED
The resistance is trying to make a quick getaway before the First Order arrives. Then—boom! It’s too late. They’re already here—two Star Destroyers just arrived near the planet in space.
This is the scene that opens Star Wars: The Last Jedi, which just came out on DVD. Having the whole movie means I get to do lots more fun physics analysis, including answering this question: Could you actually see those destroyers from the surface of the planet?
The first question to consider: How far can a human see? Well, that’s a simple question with an easy answer. I can see the moon—that’s more than 200,000 miles away. Better yet, I can see a galaxy (if it’s really dark) and that is over 2 million light years away. So, humans can see really far. Distance isn’t the problem.
Really, the key idea here isn’t “how far” but rather “angular size.” The angular size of an object depends both on the actual size and the distance from the observer: The reason you can see something like the moon even though it is super far away is because it is big. If you put the moon much farther away, you couldn’t see it. You can calculate the angular size as just the object size divided by the distance (in radians). If you want to convert to degrees, you need to also multiply by 180 and divide by π.