Satellites have a lot of room

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I saw an animation this morning showing how the space above our planet is dangerously crowded with satellites. That motivated me to do a little back-of-the-envelope math.

The vast majority of satellites are in low earth orbit (LEO), which extends from 160 to 2000 km above the earth’s surface. The radius of the earth is about 6400 km, so the volume of the LEO region is

frac{4pi}{3} left((6400 + 2000)^3 - (6400 + 160)^3right) text{km}^3 = 1.3 times 10^{12} ,text{km}^3

There are about 12,500 satellites in LEO, so the average volume of LEO per satellite is about 100,000,000 km³.

Now this isn’t the last word in collision avoidance—there are lots of complications we’re not going to get into here—but it is the first word: there’s a lot of space in space.

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