Wednesday, August 14, 2024

Can A Novel Power Law Scale For Cosmic Impacts Predict More Realistic Effects Of Asteroid Strikes?

                                                                                     

                   Gaspra (19.2 km long) would impact Earth at extinction level 

By way of background it is useful - for the purposes of this post  - to understand the Torino scale for gauging the energy magnitude  for asteroid impacts on Earth. Some of the more important Torino scale levels and gradations (registered by mass and velocity) are as follows:


i) Regionally devastating impact, e.g. June 30, 1908 Tunguska impact. Devastation range approx. 10,000 sq. kilometers, killing crops, humans, animals.

Size of object: 20 m (~ 66') to 100m (~330') diameter .

Explosive release: 1 Megaton to 100 megatons TNT equivalent. Collision probability between ~ 1 in 100 yrs. and 1 in 1000 yrs

ii) Mass extinction impact: e.g. KT-boundary impact of 65 million years ago . Devastation range ~ 10 million sq. km., killing all extant dinosaurs and hundreds of other species.

Size of object: 100m (~330') diameter to 1 km (3330') dia.

Explosive release: 100 Megatons to 100,000 megatons TNT equivalent.

Collision probability: between ~ 1 in 1000 yrs. and 1 in 100,000 yrs.

iii) Earth Sterilizing Impact: Example......not yet. 

Would annihilate every last species on the planet and sterilize it for thousands of years to come. Devastation-affected area: > 50 x
 10  sq. km.

Size of object: >> 1 km (3330') dia. (Likely source: any of one hundred Apollo asteroids whose orbits intersect with Earth's)

Explosive release: >> 100,000,000 megatons TNT equivalent.

Collision probability: Unknown but at least one asteroid specialist (Dr. Basil Booth) has predicted an Apollo asteroid collision some time in the next 250,000 yrs.

It is interesting to compare the preceding with new research that has resulted in an emergent asteroid impact template: a power-law size distribution, i.e. as the basis of an impact scale. Clark Chapman and David Morrison, in their 1989 book Cosmic Catastrophes, described the nonuniformity of asteroid sizes as an inherent property. Basically, the chances of collisional fragmentation of a given asteroid depends on how large it is. When a big asteroid breaks up, the total surface area of material increases, and the more numerous fragments have a higher total chance of being involved in other collisions, which would cause them to break up into even smaller pieces.


                                      Figure 1 (From Physics Today, July, 2024 p. 54)

Figure 1 shows the size distribution of near-Earth asteroids. The biggest ones, shown on the right-hand side of the graph, collide with Earth every few hundred million years on average. In this field would be the asteroid Gaspra (see top image) which has a length of 19.2 km.  By any reckoning a collision with this monster would see the extinction of all life on Earth, not just one species. (On the Torino scale, which registers the magnitude of asteroid devastation we are talking about a Torino scale 9 - the maximum.)

It would mark the very tail end of the graph line shown, below Chicxulub.

The latter, about 10 km in diameter, wiped out the dinosaurs 66 million years ago and changed our planet forever. The probability of a similar impact catastrophe in a given year is about one in a hundred million, i.e.  the reciprocal of the mean impact interval. That’s greater than the odds of winning a Powerball jackpot.  For a Gaspra collision we are looking at one in several hundred million odds for a given year. 

At the other end of the spectrum are objects a few meters in diameter, which U.S. government sensors observe exploding in the atmosphere as fireballs, also called bolides, several times every year. They are frequent but inconsequential in terms of risk—the most likely victim being a person, car, or house. Fast forward to a violent encounter, known as the "Mount Tenantry event", which denoted a 0.5m bolide that struck Barbados in 1990 near the village of Mt. Tenantry.  An event -which I helped investigate, and which thankfully didn't hit car, house....or country shopping center.

On the continuum of asteroid size, a threshold exists in which the explosions might be in the low kiloton range (as with the Mt. Tenantry event) or  attain the scale of nuclear detonations. Also, close enough to Earth’s surface to kill people and destroy infrastructure. The latter are generally low-altitude airbursts, like the simulation graphic shown in Figure 2. These are rare on the time scale of human lives. 

(From Physics Today, July, 2024 p. 55)

The meteor that fell over Chelyabinsk Oblast, Russia, in February, 2013, e.g.

           Image of the Chelyabinsk asteroid's exploded over Chelyabinsk, Russia,  in 2013.


was estimated at 66 ft. diameter and packed an energy equivalent of 30 Hiroshima -scale atomic bombs.  The energy was sufficient to injure over 1,000 in the Russian city - mainly from the shock wave produced - with flying debris and shattered windows the culprits. It released about a half megaton of explosive energy and injured more than a thousand people (see Physics TodaySeptember 2014, page 32). Airbursts of that size happen once every 50 years on average.

The 1908 explosion in Russia known as the Tunguska event is probably an order of magnitude more energetic (and likely several megatons), but that estimate is uncertain because the event happened at a time and location for which observational and instrumental data are sparse. We can expect events of that size to happen with a mean interval of about 500 years.

Meanwhile, about a year before the Chelyabinsk air blast , an asteroid identified as DA 14 2012, could have caused mass calamity. It packed a mass of 130,000 metric tons  (» 2.9 x 10 kg) and potential for an explosive release equivalent of a 20 megaton nuclear bomb.  That would be enough to wipe out New York City, or an island nation like Barbados. 

To meet such threats we’ve had Projects Space Watch and Spaceguard – which remain on funding life support, though a bit more largesse has come through in recent years. Space Watch  had been based at the University of Arizona, and featured generous grant allocations in its early years when it  discovered over 1,300 approaching asteroids by 2002.  Later, as the austerity mindedness infected all science research areas, that capability wound down a lot.  

Spaceguard extends asteroid detection to focus more on NEOs (near Earth objects) as opposed to singling out near Earth asteroids (NEAs).  Again budget limitations have loomed and imposed truncated observation time frames and selectivity. As reported in a recent issue (July, p. 54) of Physics Todayauthor Mark Boslaugh notes the first attempt at a quantitative probabilistic NEO risk assessment was published in 1994 by Chapman and Morrison.  E.g.

Their estimates of airburst damage were based on nuclear weapons’ effects and scaling laws. But that method breaks down for larger asteroids because such climate change effects come into play. Chapman and Morrison extrapolated their estimates up to a global-catastrophe-threshold asteroid size between 0.5 and 3 km in diameter, above which they assumed a quarter of the world’s population would die. That estimate has provided a crude framework for deciding how to begin reducing the danger.

By integrating their risk curve, the pair estimated a few thousand fatalities per year. That result, as Boslaugh observes  "is counterintuitive because there is no direct evidence that anyone has ever been killed by an asteroid." We are basically confined to a realm for which the risk is dominated by low-probability, high-consequence events. But the thing is, even if a 1 in 300 million probability seems low (say for a Gaspra hit) the result is complete annihilation of life on Earth, so we need to take it seriously.

The best way then to reduce the risk from these 'celestial swords of Damocles'  is to prevent large impacts. Preventing a catastrophic impact requires finding all the NEOs above the global catastrophe threshold, so a survey program was established by a 1998 NASA directive to discover 90% of NEOs greater than 1 km in diameter. Fortunately, there are only about 1000 NEOs of that size. Because they are the biggest and brightest in the sky, they are also the easiest to discover.

Meanwhile, the current method of choice for planetary defense is to deflect an asteroid from its collision trajectory by sending a spacecraft to collide with it and changing its velocity. That option is plausible only if the asteroid is discovered well in advance, because there must be sufficient time for the asteroid to drift away from where it would otherwise be at the time it crosses Earth's path. But I've already queried such efforts in earlier posts, i.e.

The DART Mission To Deflect A "Killer Asteroid" - Why I'm Not 'Betting the Farm' On Its Success 


Astronomical surveys may have reduced our assessment of the likelihood of a global- or continental-scale catastrophe by an order of magnitude, to an estimate of about 100 fatalities per year.  But let's be clear that much more severe consequences than we've imagined might be triggered by smaller asteroids  (like DA 14 2012) than we had thought.  With that threat in mind, a new space-based IR telescope, the Near-Earth Object Surveyor, will be an essential tool for reducing the remaining risk and providing early warning.

Challenge Problem:

In the early morning hours of June 14, 2002, the Earth had a remarkably close encounter with an asteroid (2002 MN) the size of a small city. It remained undetected until three days after it had passed the Earth. At its closest approach, the asteroid was 73,600 miles from the center of the Earth—about a third of the distance to the Moon. Observations indicate the asteroid to have a diameter of about 2.0 km. Estimate the kinetic energy of the asteroid at closest approach, assuming it had an average density of 3.3 g/ cm 3


See Also:

Amazingly, Newly Discovered Asteroid Appears To Be A 2nd Earth "Trojan"

And:

The DART Asteroid Mission: Will It Really Succeed ?..

And:

    Asteroids: The Celestial 'Swords of Damocles'

 

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