Chelyabinsk Update

      1.      Yield:  Current evidence suggests an explosive yield of a little less  than 1 megaton of TNT, comparable to an ICBM warhead.  We should be very grateful that it did not detonate closer to the ground, or we would be looking at tens of thousands of civilian deaths.

2.      Optimum burst height:  The nuclear weapons literature, including the classic 1977 analysis entitled The Effects of Nuclear Weapons, shows that the effective range of destruction from an aerial explosion depends sensitively on the altitude of the explosion.  An explosion at sufficiently high altitude strikes a very large area with a weak shock wave, rattling windows but doing negligible damage.  In the daytime, or in cloudy weather, there may be no sightings of a fireball.  A little lower, and the same explosion would break windows.  Glass shards accelerated by the blast wave are the principal hazard.  This is the Chelyabinsk event.  Move the explosion a little closer to the ground, and radiant heating of the surface becomes important.  Fires can be ignited by the flash, especially clothing, window curtains, and automobile upholstery.  In rural areas, trees and brush ignite.  This is the Tunguska event of 1908, which flattened hundreds of square kilometers of forest and burned 2200 square kilometers.  A little closer to the ground, and blast overpressures become high enough to cause structural failure of reasonably well-constructed buildings.  The “premature” failure of the factory building in Chelyabinsk probably owes more to its Soviet-era construction quality than to the severity of the blast.  At about the same explosion altitude, the air blast that follows the flash (traveling at the speed of sound rather than the speed of light) hits hard enough to blow out many of the fires, but potentially fanning others into a firestorm.  In this sequence from high altitude to very low altitudes, each successive blast strikes with greater intensity (higher blast overpressure) over a smaller target area.  A body that reaches the surface either intact or as a compact swarm of high-velocity fragments can excavate a crater, depositing almost all of its kinetic energy in an area about 100 times the actual area of the crater by means of high-speed explosive ejection of debris from the crater.  This is Meteor Crater in Arizona.  Very large impacts eject vast quantities of dust and vapor and shock-produced nitrogen oxides in the form of a mushroom cloud, which lifts them to high altitudes and spreads them widely over the Earth.  The very biggest impacts seen in the geological record actually blast away the atmosphere above a plane tangent to Earth’s surface at the point of impact, hurling crater eject worldwide.  This is the Chicxulub event at the end of the Cretaceous Era, the famed dinosaur-killer.  For a given explosive yield there is an altitude, called the “optimum burst height”, at which the area of devastation is maximized.  For a 1-megaton explosion the optimum burst height is about 1700 meters (a mile) and widespread structural damage occurs for any blast below about 5000 m (3 mi).  For a 10-megaton explosion the optimum burst height is near 5000 m and the threshold for structural damage is near 12000 m (7 miles).  At yields of 1000 megatons (1 gigaton), a 10,000-year event, severe surface damage occurs at just about any plausible burst height. 

3.      Entry Angle and Velocity:  It is aerodynamic pressure that causes an entering body to crush and shear itself into fragments.  The aerodynamic pressure is proportional to the density of the atmosphere and to the square of the velocity.  The density of the atmosphere drops off roughly exponentially with altitude, and is therefore very low at 100 km altitude.  As a general rule, bodies that enter at lower speeds penetrate deeper than those that enter at higher (cometary) speeds.  They contain less kinetic energy per ton, but are more efficient at delivering that energy to the ground.  Bodies that enter the atmosphere at shallow grazing angles (nearly horizontal motion) spend a relative long time at high altitudes where the atmosphere is thin and crushing is least probable.  They tend to decelerate rather gently and therefore are traveling slower at any altitude; therefore they penetrate deeper before exploding than a vertically-entering body of the same size and speed.  Note that, for any given material, the higher the velocity, the higher the altitude of explosion: the faster the bullet, the less its penetration.  There is also a huge range of strengths for asteroidal and cometary material: cometary “fluff” fails at high altitudes; iron meteorites (M-class asteroids) often penetrate all the way to the ground before exploding, and hence deliver their full original kinetic energy to a crater (or small cluster of craters) with high efficiency.  This is the Sikhote-Alin meteorite fall in eastern Siberia in 1947.

4.      Linear Explosion:  The energy dissipated by a strong, deeply penetrating bolide is often released nearly in the form of a point explosion, with almost all the original kinetic energy being given off in the same moment.  But many smaller bodies deposit their energy along a lengthy path through the atmosphere as they break up in many stages.  This is especially true of bodies with shallow entry angles.  Since the impactor may be traveling at 20 km per second, its speed is about Mach 30.  We think of the shock wave from a supersonic aircraft traveling at Mach 2 or 3 as a cone with an opening angle of, say, 30 degrees originated at the nose of the aircraft.  But at Mach 30 the opening angle is only about 2 degrees: the energy released is very nearly in the form of a linear explosion.  Some theorists talk of the “exploding wire” model, which is not a bad way to picture it.  Imagine a “wire” stretching across the sky that detonates nearly instantaneously.  The first sound to reach you is not from the point where the explosion began but from the segment of the wire nearest to you.  That sound reaches you as a strong, sharp blast, a “sonic boom”, after which the sound reaches you from ever more distant locations on the wire.  Thus after the first sharp boom you hear simultaneously the noises emitted both before and after the body passed closest to you.  These explosions and “rumbling” continue until, at last, you hear the first sounds given off during entry.  The first sounds, having traveled so much farther, reach you last.

5.      Crater:  There have been reports on the internet, some illustrated by photos of a burning crater, that purport to show the impact point of the Chelyabinsk bolide.  The photos are simply a hoax, showing file pictures of a natural gas fire that has been burning for decades in an oil field in Kazakhstan.   If there is an impact crater, it is a hole found in the ice of a lake.  That suggests a low fire hazard.

6.      Meteorites:  Meteorite recovery from the bolide would be enormously valuable, and this morning’s news claims over 50 stones recovered to date.  My guess is that there is a potential for recovery of hundreds or even thousands of stones, and that they will prove to be ordinary chondrites (the most abundant types of meteorites, of H, L, and LL classes).  Much weaker (carbonaceous) material would explode at high altitudes; strong (iron or stony-iron) meteorites could penetrate to the ground intact and make a huge crater.  Let’s keep our eyes on this: as the many images of the event are carefully studied we should soon know the precise path of the bolide and hence know where to look for any other meteorites it may have dropped. 

7.      Russian Defense Ministry Spokesman: A high-ranking Russian military officer has been quoted as saying that “this was no meteor; it was an American military test.”  If you can see any military advantage to breaking windows in Chelyabinsk, you’re more imaginative than I am.  Also, Russian scientific sources are quoting entry speeds of 18-20 kilometers per second, which is far above entry velocity for return from the Moon (about 11 km/s) and insanely larger than the top speed of any military weapons system ever devised.  The energy content of the explosion suggests a mass of 10,000 tons, 100 times the lifting ability of a Saturn 5 or the Space Shuttle (neither of which is in service), and about equal to the displacement of a guided missile cruiser such as the Ticonderoga.  This officer would profit from conversing with the Russian scientists who investigated the Tunguska event, and who actually do know something about these events.  Besides, if we take his explanation seriously, we would have to credit those aggressive Americans with having had even higher technology in 1908.