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# A Little Math Drives Out Demons

A friend of mine—who will remain unnamed—wrote this comment on a Facebook thread:

“Last night on Coast to Coast AM, Richard C. Hoagland, who studies celestial events, said the confluence of the asteroid passing and the meteor explosion in the Eastern side of the Ural Mountains could not have happened in nature. That the meteor in Russia had to be aimed just right by an intelligence (alien or divine?) to have avoided hitting the hundreds of manmade satellites and to come in at the angle it did.”

I admit I didn’t know who Hoagland is, so I looked him up. Wikipedia describes him as “an American author, and a proponent of various conspiracy theories about NASA, lost alien civilizations on the Moon and on Mars, and other related topics.” That fits, since what he says about the meteor is absolute nonsense. Here’s why.

There are 300 geostationary satellites orbiting the Earth at 22,236 miles above the surface. At that altitude the geostationary satellites appear to stand still in the sky, which is what you want for communications satellites. Let’s think of them as being on the surface of a sphere. The radius of that sphere is 22,236 miles plus the mean radius of the Earth itself, which is 3,959 miles, so the total radius is 26,195 miles.

Let’s figure out the surface area of that sphere. The formula is 4 X pi X radius-squared, which comes out to 8.6 billion square miles. And what about the area that the satellites occupy?

Satellites vary in size, but let’s say that when it’s unfolded, with its panels extended, the average satellite, when viewed in cross section, occupies an area of 200 square feet. Since there are 300 satellites, the total target area is 300 X 200 = 60,000 square feet. This is about 0.002 square miles.

So here’s the ratio: 0.002 to 8.6 billion, which is the same as 2 to 8.6 trillion. So the chance of a meteor hitting a satellite is 2 in 8.6 trillion. For practical purposes, that’s zero.

(Note 1: Remember, the meteor is passing through the sphere occupied by the satellites at an oblique angle; it doesn’t skim along the surface of that sphere as though it were a steel ball in a pinball game looking for bumpers to hit. The meteor may as well be aimed straight down at the Earth.)

(Note 2: I realize there are satellites other than the 300 geostationary ones. Their existence hardly changes the result. Even if there were ten times as many satellites orbiting the Earth—3,000 in all—the odds of hitting one would still be 2 in 860 billion.)

Here’s another way to think about all this: Let’s say all 300 satellites are laid out on the ground in your local park, in 15 rows of 20 satellites. Now look at the park through Google Earth. Start near ground level and pull back.

At 2 miles up your park will be a dinky part of what you can see. At 22 miles up your park will hardly be visible. Now imagine that you’re 1,000 times higher than that, at 22,236 miles above the ground—you might not be able to make out your state, let alone your park.

If this little game were fair, we’d have placed the 300 satellites along a band that stretches around the 25,000-mile circumference of the Earth (because in reality the satellites are positioned above the equator), which means one satellite about every 80 miles. What chance do you think you’d have of seeing the one satellite that’s most directly below you? What chance would you have of hitting it with a projectile that you toss at it from 22,236 miles above the Earth? The area that lone satellite occupies is infinitesimal compared to the area you can see. Even if you tried to hit it, you couldn’t.

I’m not surprised that Hoagland made the claim he did, given that he believes in lost civilizations on the Moon and on Mars. Maybe he read too much Edgar Rice Burroughs when he was young and didn’t realize that Burroughs was writing fiction, not history—that John Carter of Mars, for example, wasn’t a real person.

However that may be, my little story has a moral: We need to be skeptics when we’re told something scary or bizarre, especially if it’s told on a sensationalistic radio program, especially if it has a quasi-religious angle. More often than not, what we’re told is loopy.

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