How Stupid Can You get?

Fig. 1

Fig. 2.

In today's paper there appeared a news story that bordered on the incredible. Under the headline: 'NASA's Pocket Lint Unable to Cushion Blow of Asteroids' it was reported that - while Congress charged NASA with spotting Earth-threatening asteroids four years ago, it never provided the money to build the necessary telescopes to do so! How stupid can you get?

How big a threat are the Earth-crossing asteroids?

First it is instructive to see how they can emerge as a threat, when their orbits are perturbed as shown in Fig. 2 above, for Icarus (Fig 1. shows a large asteroid, Gaspra, that - if it struck Earth - would annihilate all life on it).


What makes any large asteroid dangerous, is its mass in combination with its relativity velocity or speed of approach. Thus, large Apollo objects and other asteroids would typically have relative velocities from 11,000 to 30,000 meters per second, or about 6.8 to 19 miles per second.

For an asteroid with a 1 kilometer (0.62 mile) diameter, at a density three times that of water, this would generate an equivalent energy on impact of one million Hiroshima sized atomic bombs. Since the Hiroshima explosion was equivalent to 13,000 tons of TNT, this means a larger asteroid would generate an explosive force of 13 thousand megatons. This already is roughly equal to the total equivalent of all U.S. nuclear warheads.

For a ten kilometer asteroid (roughly 6 miles across) the explosive equivalent would translate into 13 million megatons. This would dwarf all man-made nuclear stocks and warheads, and is rightfully called ‘planet –killer’. An asteroid about this size is believed responsible for the extinction of the dinosaurs nearly 65 million years ago. For present day inhabitants of Earth, the consequences would hardly be less startling or grave. A Gaspra (12.5 x 7 x 7.5 miles) impact would obliterate all life on Earth - never to arise again.

The crater and blast effects alone would eliminate most of the population on the continent it struck. An ocean strike, creating tidal waves upwards of 2 miles in height, would be even worse. The debris, for its part, would block out most solar radiation and probably usher in massive extinction of oxygen producing plants including sea plankton – that account for ninety percent of our oxygen.


How probable is such a Torino 9 or so impact?

The calculation of the probability is based on an estimated 15 Apollo Objects acquiring an Earth-crossing orbit every million years.

From this it has been reckoned that the odds of a given Apollo Object eventually hitting Earth are 5 in one billion. This works out to one impact, on the average, every 200 million years. But wait. There are about one thousand such objects in all so that the probability that any one will strike Earth is now: (1000) x (5/1000000000) = 5/1000000. This figure: 5 in one million means that time wise, 5 asteroids would be expected to strike Earth every million years, or one every two hundred thousand years.

The problem with statistics like this is that they can lull a person into a false sense of security. It is true that the impact rate is low, relative to the scale of recorded history, but it is comparatively high in the context of geological time (thousands of millions of years). To fix ideas, consider that the most recent crater formed by a true Apollo object (as opposed to a large meteoroid) is at Lake Bosumtwi basin in Ghana, Africa. This is about 1.3 million years old. On this basis, the Earth is certainly long overdue for another hit of staggering proportions. Indeed, from the mean frequency of collisions we have worked out, the Earth should have been struck at least six times since the last impact by an Apollo object.

I should point out that in all of these statistics no account has been taken of the colliding comet factor. However, estimates by the Ames Research Center suggest that- with comets included - there are at least 2,000 objects that can cross the Earth's path. (Recall the recently photographed impacts on Jupiter were from a large comet). Since my calculations were based on 1,000 objects - e.g. asteroids only, the probabilities would increase by a factor two. The time interval between major collisions would be halved.

Of course, statistical behavior does not follow rigid rules. There is no statistical law that pre-ordains an asteroid impact on Earth with the precise regularity of a 200 thousand year interval. By analogy, there is absolutely no reason why I shouldn't get a run of heads if I flip a coin ten times. Maybe I will get six heads in a row in one such run. The point, and it is an important one, is that the string cannot continue indefinitely. Assuming the coin is "true" the probability of heads must average 1 out of every 2 tosses. Looking at 100 tosses, for example, the total heads and tails will probably be very close to 50 each. The run of heads at some stage would have been compensated for by a similar run of tails to balance out the "law of averages".

Somewhat similar conditions apply to asteroid strikes on Earth. The run we are currently experiencing: no major hits over 6 successive periods of two hundred thousand years each, can’t go on indefinitely. As certainly as heads become tails for coin tosses, "no impacts" must become registered impacts for Apollo objects approaching Earth. The next big hit could come at any moment from an undetected asteroid. Or, it may come in the year 2015 when 1989FC is brought into Earth's vicinity, after its 1989 close pass.


In addition, there is always the possibility that the odds could be altered by some external factor. For example, the projected encounter in 2015 may start out a near miss, but the sudden intrusion of a new comet could change it to a direct collision. The comet's gravitational effects would have re-oriented the direction of the asteroid. Of course, this could also work in reverse: the direct hit may be transformed into a 'graze' by the same comet. Or, the asteroid could perturb the orbit of the comet so that the comet nucleus hits the Earth instead.



Let us hope, while congress sits on its hands - no large, threatening asteroids approach or threaten us. We would then quickly behold what real worries can exist, above and beyond our political ones!