Crunching the Numbers on the Chelyabinsk Meteorite

(Credit: Calgary Times)

Let me say this up front: I do not want at all to make light of a tragedy.  Hundreds of people have been injured as a result of this event, and of course my thoughts and prayers are with them.  But at the same time my ASD mind has been busy ever since then running the numbers on this event.

According to Russian authorities, the mass of the object was around 10 tons, and it was moving at roughly 30 kilometers per second at the time of the explosion.  The formula for kinetic energy (energy of movement) is as follows:

KE = .5(m)(v^2)

That is, kinetic energy (in joules) is equal to one half the product of the mass (in kilograms) and the square of the velocity (in meters per second).  Assuming the Russians are using the metric ton, this works out to (.5)(10,000 kg)(30 000 m/s)^2 = 4.5E12 joules, or or 4.5E09 kilojoules (that's 4,500,000,000 kilojoules).

The conversion factor between kilojoules and megatons is 4.18E12, giving us a yield of approximately 1 kiloton.  That's ten times greater than the estimated energy released by the explosions at the World Trade Center during the 9/11 attacks, or one-tenth the strength of the Hiroshima bomb.  It's a good-sized tactical nuke comparable to that used in the AIR-2 Genie air-to-air missile (designed to destroy Soviet bomber formations during the Cold War).

(Above: detonation of a live AIR-2 Genie during the Plumbbob John nuclear test, July 19, 1957.  This took place at around 15,000 feet--approximately half the altitude of the Chelyabinsk meteorite. Credit: U.S. Air Force file photo.)

A one-kiloton explosion has a zone of total destruction about .15 kilometers in radius.  At the .5 kilometer radius most standard housing is destroyed, although reinforced concrete structures will remain.

Now, to put that into a perspective involving human beings: I tried to get the population density of Chelyabinsk online but wasn't able to find it, so I'll use that of a city of similar size in the United States: San Diego, California (4000 people/square kilometer; if anything the population density in Chelyabinsk is likely higher given that Russian cities are much more centralized than American cities, but we can take this number and run with it).  The explosion as it occurred if it had occurred at ground level would have resulted in at minimum 3,100 deaths and injuries.  More depending upon the circumstances of impact: residential area versus industrial area; speed and competency of emergency response; secondary damage from fire, release of industrial toxins, etc.  Given that Chelyabinsk was once a center of Russian weapons-grade plutonium production and is regarded as one of the most polluted cities on Earth as a result, this could have been very, very bad.

Look at the formula above.  Mass is important, but velocity is even more important because you use the square of the velocity.  A little faster and not only would the meteorite made it all the way to the surface, the energy released would have been a lot greater.

Now, take that meteorite and drop it on San Diego, right over City Hall.  Here's what you get with a ground burst:

http://meyerweb.com/eric/tools/gmap/hydesim.html?dll=32.71533,-117.15726&yd=1&zm=14&op=156

Pretty much everything between Balboa Park and the Convention Center is trashed.  The Padres aren't going to be playing at PETCO Park anytime soon, as it and the Gaslamp Quarter have been pretty well demolished. You don't get the same level of secondary damage from dispersed industrial pollutants as Chelyabinsk, because San Diego's heavy industries aren't located in the city core, but you do lose a lot of infrastructure you'd need to respond to the disaster: police and fire department assets, several hospitals, disruption of communications, etc.  Likely in either Chelyabinsk or San Diego you'd be looking at tens of thousands of deaths, to be realistic.  And then there's the economic damage: billions of dollars just to repair and rebuild, with a longer-term impact due to the loss of infrastructure and vital industries.

Again, this is the same object that exploded at roughly 10,000 meters above Chelyabinsk (about the altitude of a commercial airliner).  An object that could actually break through the pressure front of the air in front of it and reach the ground would be a lot more energetic and do that much more damage.
Still don't think we need a space program?  Our only hope of preventing a huge tragedy is to get out there, find out what these things are really made of before they impact, and learn how to stop them.

Chelyabinsk is a wake-up call, or it should be.  Thank God it wasn't any worse.

(Credit: IBI Times. I don't know this man's name or I'd include it too. All things considered, he got off lucky!)