No, the Death Star Isn’t Impossibly Big in the Rogue One Poster. We Did the Math

People are complaining about the size of the Death Star in the Rogue One poster. Here's how you could actually make that picture.
RogueOnePoster.jpg
Disney

I've made it clear that I am super excited about Rogue One: A Star Wars Story. It seems obvious that others are equally excited. But what about this new poster for the movie? Here's a common reaction:

"Wow. The Death Star is huge. If it was that big or that close to the planet, wouldn't its gravitational force rip things apart?"

Yes, the Death Star looks a bit large. But it doesn't mean it's actually that large. Yes, I realize I just said that as though the Death Star is a real thing. It's not real---even I know that. But let's say you replaced the Death Star with the moon and the planet with Earth. I can explain how you would make a photo like this poster.

It starts with angular size. When you look at something, or especially when you take a photo, you don't see the size of an object but its angular size. The angular size of an object depends on two things: its actual size and the distance from the camera (or human observer).

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In this diagram you can see that the two balls have the same apparent angular size even though they are different actual sizes. You can calculate the angular size in radians as:

La te xi t 1

Here L is the length of the object and r is the distance from the object to the observer.

Now let's take a picture of a person with the moon in the background. The moon has an angular size of about a half a degree, so it's going to look rather small. The angular size of the person will depend on the distance to the person. Let's say this human is 1.75 meters tall and I am 40 meters away. This would make an angular size of 0.044 radians or 2.5° (which is a larger angular size than the moon---just to be clear).

Next I will take another picture of the person and the moon. But this time, I am going to move back 160 meters so the total distance to the human is 200 meters. This also will make the distance to the moon 160 meters greater than it was. However, since the distance to the moon is 384 million meters an extra 160 meters doesn't make much difference. So, by moving back the human now has an angular size of about half a degree and so does the moon.

After making the human smaller (but the moon stays essentially the same) I can use a zoom lens to make both human and moon increase in apparent angular size by the same amount. Thus the trick to a big moon is to get far away from an object with the moon in the background and use a telephoto lens.

And that's how you would make a cool picture of the Death Star. If the Death Star was real.

Oh, but what about gravity? Could the Death Star orbit so close to the planet that it would look that big? I don't think so. It probably would be too close to have a stable orbit. Would it get ripped apart by the planet's gravity? My first guess is no, but someone could do a quick calculation and check for certain.