Viewing imaginary spacecraft from the ground

I read and watched a lot of science fiction when I was young. I don’t much any more, mostly because I’m too busy, but every now and then I have a relapse. Also, for the most part, real science is more fun these days. But they aren’t necessarily mutually exclusive.

For example, this evening, I was thinking about the International Space Station. Under optimal viewing conditions, the ISS is the brightest thing in the sky, aside from the sun and moon. But while the station is surprisingly large (about the size of a football field), it is generally smaller than most science fiction spacecraft which are capable of interstellar travel.

Science fiction generally depicts people walking around on the ground, or starships floating close above a planet, but with little connection between the two; The only time I can recall people on the ground seeing spacecraft above are when the Death Star explodes in Return of the Jedi, and when the remains of the Enterprise re-enter the atmosphere in Star Trek 3. But if you can see the ISS from here on Earth, then surely a larger science fiction (or alien) spacecraft would be brighter still.

Figure 1. Since you can see the ISS from your backyard, you don’t need the force to detect something much bigger in the same orbit. Click for larger image.

Thanks to Jeff Russell’s Starship dimensions, scaled profiles of most major starships can be easily compared to the ISS. That’s all well and good, and we can estimate areas and visual magnitudes in the -7 to -10 range for various popular starships. But since there isn’t anything of that brightness in our skies, it doesn’t mean much, except to tell us that they would be easily visible from the back yard of anyone looking for them (assuming they aren’t in Earth’s shadow). But there is a useful celestial yardstick.

Figure 2. relative apparent sizes of various spacecraft (and the ISS) when directly overhead in a 350 km low Earth orbit, when compared to the apparent size of moon. The moon is of course 1000 times larger and 1000 times farther away. Click for larger image.

The Moon, which has a radius of about 1740 km, is about 1000 times farther away than low earth orbit. So a spacecraft 1000 times smaller- say, a flying saucer with a 1.7 km radius- would have the same apparent size when directly overhead. Thirty degrees above the horizon, it would appear half a big. In other words, the shape of kilometer-scale spacecraft, such as a Star Destroyer, or a Babylon 5 capital ship, would easily be discernable to people below. The 24 km-wide flying saucers from Independence Day would appear to be seven times larger than the moon, and would blot out the sun for up to 4 seconds as they passed in front of the sun.

So forget all the garbage you hear about radar jamming and government cover-ups. When the alien invasion fleet comes for us, we’ll be able to watch it from the back yard.

Figure 1 is from STS 118 and Return of the Jedi.