Artist’s impression of 2012 DA14 approaching Earth. Credit: NASA/JPL.

You may have heard that an asteroid called 2012 DA14 will pass close by Earth this Friday, dipping below our ring of communications satellites at just 28,000 km (17,000 miles). At 50 meters wide (half the size of a football field), this is the largest asteroid ever recorded coming this close. However, the asteroid Apophis, which is about the size of a football stadium will come just as close on April 13, 2029.

How bad would it be if something like 2012 DA14 actually hit Earth? We’ll get ready, because I’m about to do some math here. A sphere of rock 50 meters in diameter weighs about 200,000 tons, and 2012 DA14 is moving at 12.7 kilometers per second. From this, you can calculate the kinetic energy–one half the mass times the square of the speed:

1/2 x (2 x 10^8 kg) x (12,700 m/s)^2 = 1.61×10^16 joules.

A megaton of TNT is about 4×10^15 joules, so 2012 DA14 packs a wallop of about 4 megatons. That would be a bad day if it happened to hit near populated area. Luckily, 2012 DA14 will stay safely out in space where it can’t hurt anyone, except in the extremely unlikely event that it takes out your satellite TV.

But there are a lot of other asteroids out there. How much risk do they pose? That gets a little complicated. NASA has been tracking potentially hazardous objects larger than 1 kilometer (0.6 miles) wide for some time. These are the asteroids in the “global catastrophe” category, though not in the “dinosaur killer” category. They’ve found 154 of them. They suspect that there are about 10 that we missed because they spend most of their time in the glare of the Sun. (Comets are a separate problem, but they’re quite a bit rarer.)

Astronomers estimate that about a third of these 154 asteroids will hit Earth in the next few tens of millions of years. The rest will either hit Venus or be kicked out of the Solar System. Maybe a few will hit Mercury or Mars. This means that one of these big asteroids hits Earth every 200,000 to 2,000,000 years–unfortunately, we can’t estimate much better than that. Chaos theory prevents us from predicting the appearance of the Solar System over longer time periods.

On the small end, we know things pretty well from radar and eyeball observations. Meteoroids of about 4 meters (13 feet) in size hit Earth about once a year, burning up as fireballs high in the atmosphere. In between is a big gap, where we don’t know how many asteroids there are. They don’t hit often enough to measure directly (which is a good thing!), and we can’t see them well enough to track them in space (which is not so good).

But we can estimate. If meteoroids 4 meters wide hit Earth once a year, then objects 250 times larger impact between 200,000 and 2,000,000 times more rarely. If this relation is governed by a simple equation called a power law, we can calculate how often we will be hit by asteroids of any size:

(average time between impacts) = (size of asteroid / 4 meters)^(log(200,000-2,000,000) / log(250))

You only get a range, but if you do the math, you find that asteroids the size of 2012 DA14 impact Earth between once every 250 years and once every 700 years, on average. The most recent such impact was Tunguska in 1908, but that doesn’t rule one out in this century.

The good news is that there seem to be fewer of these medium-sized asteroids than we expected, so the rate might be as low as once per 1,000 years. Even so, if you have to use the word “megatons” to describe them, you do have to wonder if maybe it’s worth more than the $5 million per year we’re spending to look for these things.