The big news of the day--actually last night--is that a large meteor has apparently fallen on the city of Chelyabinsk in central Russia. The event caused serious damage and resulted in injuries to between 500-1000 people, with estimates still being tallied. This type of event is rare, but not without precedent: In 1908, an even larger meteor fell near the Tunguska river, also in Russia, and leveled more than 2000 square kilometers of forest. Adding to the intrigue, a near-Earth asteroid named 2012 DA14 is currently being monitored by scientists and has just made a close passage to the Earth today. With its closest approach distance projected to be 27,700 kilometers, and with an estimated diameter of 46 meters, the DA14 asteroid flew closer to the Earth than any large asteroid since scientists began monitoring these objects 15 years ago.
[youtube:sl_RknL9G-Q, 560, 340]
(This dramatic footage was uploaded to Youtube by Russia Today, courtesy of Alexsandr Ivanov.)
Taken together, these three events raise the question of how often our planet should suffer destructive impacts from the skies. Of course, small rocky bodies hit the upper atmosphere on a regular basis, whereas larger bodies, with significant destructive potential, are quite rare. Incoming meteors obey a scaling relationship, where the frequency of聽impact is almost a perfect power-law function of the size, so that the聽frequency is proportional to the inverse square of the diameter, D, i.e.,聽
[equation]frequency = (1 per year) (D/1 {\rm meter})^{-2}[/equation]
This law apparently holds over a wide range of sizes, down to the tiny dust particles that hit orbiting satellites and up to the 10 km asteroid that killed our dinosaurs. Note that the impact frequency for 10 km asteroids would be about one event every 100 million years (which is about right). While different sources tend to agree on the power-law behavior of this scaling law, the normalization is uncertain, perhaps by an order of magnitude.
If we ignore all uncertainties, the above scaling relation shows that impacts by asteroids as large as DA14 are expected every 2100 years. Near misses, like today's, are more common, so that the DA14 close passage should perhaps be considered as a 'once a millenium' event.
The Tunguska event has been estimated to have an impact energy of about 10 megatons, comparable to a modern nuclear weapon. If this event was due to an asteroid impact, how large would it have to be? Note that the escape speed from Earth is about 11 km/s and the orbit speed of Earth around the Sun is about 30 km/s; impact speeds are thus expected to be of order 20 km/s. In order to attain 10 megatons of energy, the projected mass of the Tunguska asteroid must be about 2 x 1011 grams. For a density of 5 g/cm3, the corresponding diameter is 43 meters. In other words, the Tunguska asteroid is roughly the same size as the DA14 asteroid. In fact, the Wikipedia page lists the frequency of Tunguska events at one every 300 years.
How about the Chelyabinsk event from earlier today? 聽The reports that I have seen to date do not specify the size of the rock, but we can make a rough estimate: Although the injuries are serious, the blast was not as large as the Tunguska event. If the impact energy were as small as one kiloton, the asteroid size would be about 2 meters; if the impact energy were as large as 100 kilotons, the asteroid size would be nearly 10 meters. Taken at face value, the scaling law predicts that 10 meter bodies should hit the Earth once a century. However, these energy estimates specify the size of the incoming body near the surface of Earth, whereas the scaling law holds for bodies striking the top of the atmosphere. As a result, the initial size must be larger, so that the frequency of impacts would be correspondingly lower.
The bottom line is that both Tunguska and DA14 events should occur only once or twice every millennium, whereas Chelyabinsk events could occur more often, perhaps every 100 years (where these estimates should be considered highly approximate). The smaller asteroids that lead to smaller, but still destructive, Chelyabinsk-like events are both relatively common and hard to detect. Larger asteroids like DA14 can be detected, but remain difficult to stop if they are on a collision course with Earth.
We thus continue to face adversity from above.
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Fred Adams is an FQXi member and astrophysicist at the University of Michigan.