Adapted from lecture materials in Physics 5 -- Spring 1997
George H. Lenz, Whitney Guion Professor of Physics and Dean of the College

Introduction

The materials presented here were developed and compiled in the spring of 1997 as a part of the introductory physics course for liberal arts students. Sections of this course deal with energy, Newton's Law's and planetary motion, and processes which affect the evolution of the earth and life on it. At the time, a great deal of excitement and interest was generated by the nightly appearance of the Hale-Bopp comet, and the "discovery" by the media that the earth is under constant bombardment by a variety of celestial objects. This media blitz was highlighted by a feature article in the New Yorker, numerous articles in national and local newspapers, a TV miniseries, and two documentaries dealing with meteor and comet impacts, all within a three month period. In addition, a number of books and websites (see bibliography) addressed the issue of our present knowledge of planetary impactors and of the likelihood of their producing effects which could change the global environment in the future.

Energy of Impactors

Any object which has mass (m) and moves with a velocity (v) has energy associated with it due to its motion. The energy is called Kinetic energy (K) and is related to the mass and velocity by the following expression:

K = 1/2 m v²

When an impactor begins to penetrate the earth's atmosphere, collisions between it and the molecules in the atmosphere begin to transform the kinetic energy of the impactor to heat, light and mechanical (sound) waves. The effect can be explosive in nature, generating heat, light, blast and sound energy sufficient to disrupt the impactor, causing it to "burn up" in the atmosphere before reaching the earth. If the impactor is sufficiently large and strong, it may penetrate the atmosphere largely unaffected and impact with the earth. In this case the impactor can create a crater, which may be up to 100 times the size of the impactor itself. The kinetic energy is transformed again into heat, light, mechanical waves, and kinetic energy of the material ejected from the crater. That material may or may not be melted or vaporized, depending upon the specific structure of the impactor, the ground it hits and the energy it carries.

Since these impacts are explosive in nature, their energy release or transformation is usually measured in units associated with the energy released in chemical explosives such as TNT or plastic explosives. For example, conventional aerial bombs of World War II vintage carried an explosive payload of 500, 1000, or in a few instances, 2000 pounds of explosive. A 2000 pound bomb carries one ton of explosive. It is a very large weapon. For example, the truck bomb used to destroy the Murrah Office Building in Oklahoma City is estimated to have been about 4800 pounds or 2.4 tons of chemical explosive. Nuclear weapons, developed in the last fifty years have a much larger explosive yield than chemical weapons, but their destructive potential is still measured in terms of tons of TNT. For example, the Hiroshima weapon was estimated to have an explosive power equivalent to 18,000 tons of TNT, or 18 kilotons of TNT, where the prefix kilo means multiply by 1000. The energy yield of modern nuclear weapons is measured in units of a million tons of TNT, or 1 Megaton. Mega means multiply by 1,000,000. The most powerful weapon ever tested was set off by the USSR and had an energy release of approximately 50 megatons. The destructive power of these weapons is both enormous and horrific, but, as we shall shortly see, provide the only cognitive bench mark we can use to conceptualize the energy of large earth impactors.

To get an appreciation for the energy magnitudes involved, consider one-half of a cardboard box designed to ship a refrigerator. It has a volume of approximately 1 meter cubed. That is, it is one meter wide, one meter deep and one meter high. If we fill it with the material that comprises a stony-iron meteorite, it will have a mass of about 4,000 kilograms, or a weight of about 8,800 pounds. Now let this box move with a velocity of 23,000 meters per second which is in the range of velocities of some of the rocks moving in near earth space. The kinetic energy of this rock, one meter on a side, is approximately equivalent to 1 kiloton of TNT. Now if we double each dimension of the box, it becomes 2 meters by 2 meters by 2 meters and has a volume which is 8 times as large, and it has 8 times the energy.

In this case, a meteor which has a volume of about 4 full sized refrigerator boxes has an energy a little less than one half that of the Hiroshima weapon. Notice that the energy of the meteor goes up as the cube of its linear size. That is,

K L³

This means that when it comes to earth impactors, bigger is not better.

The table below shows how the size of the "cubic" meteor affects its kinetic energy and explosive potential. If you assume a spherical meteor, the numbers change slightly but it does not affect the overall significance of the argument.

Meteor material: 4,000 kilograms per cubic meter.

Velocity: V = 23,000 meters/sec = 50,000 miles/hour.

The conclusion is that the energy of the impactor rises dramatically with size and for objects of the order of 100 meters, (The length of a football field) it rapidly exceeds anything ever seen in recorded history. As the size of an impactor increases, it reaches progressively lower levels in the atmosphere and the energy transferred to the shock wave can produce damage at ground level even if the object does not survive to impact. For example, in 1908, a body estimated to be 60 meters in diameter broke up about 8 kilometers (26,000 feet) above Tunguska, Siberia, and released somewhere between 12 and 20 megatons of energy. Even though it did not reach the ground, trees were knocked to the ground at distances as great as 40 kilometer (24 miles), and fires were ignited up to 15 kilometers (9 miles) from ground zero. If it happened today over a populated area, many people would be killed or injured. The probability of impacts with even larger objects, of the order of 1 kilometer in diameter, is very small, but such a collision could happen. The effect of this large an impactor striking the earth could be as catastrophic as that which ended the age of the dinosaurs. In 1991 Congress recognized the hazard associated with such an event and authorized NASA to conduct a study of it and to take steps to accelerate the discovery of threatening asteroids and comets. The full text of that study was published in 1992 and called the Spaceguard Survey Report. It is available at the web site: http://george.arc.nasa.gov/sst.

The report recognizes that the Earth has been bombarded throughout its history by large numbers of asteroids and comets, and that thousands of small meteorites penetrate the atmosphere and fall harmlessly to the ground every year. As far as larger impacts are concerned, more than 130 terrestrial impact craters have been identified with sizes ranging up to 200 kilometers in diameter and dating from the very recent geological past (Meteor Crater, Arizona -- about 50,000 years ago) to impacts occurring in excess of 2 billion years ago. Since 70% of the earth's surface is covered with water, numerous additional impacts have yet to be identified, or may have been erased by erosive or crust recycling processes.

The major concern is with incoming objects of stony or metallic composition which are between 100 meters and 1000 meters in diameter or larger. It is estimated that about two thousand such objects with a diameter of 1 kilometer exist in or travel through near earth space, but that fewer than 10% of them have been identified and their orbital parameters determined. It is also thought that between 25% and 50% of these will eventually impact the earth, but that the time between such impacts is greater than 100,000 years. These objects have energies so much larger than those studied in nuclear war scenarios that it is difficult to be certain of their effects, but it is thought that as the size increases, a threshold is crossed where the effects go from being primarily local to being global in character. These impacts can have environmental effects which could threaten the existence of civilization and possibly of life itself.

Fortunately, the number of impactors and the probability for impact decreases as the size of the object increases. On average one anticipates a Tunguska class impact with the earth to occur once every 300 years, and a potentially globally catastrophic impact to occur once every 500,000 years ( Spaceguard Survey Report). The probability of a catastrophic impact on an annual basis is thus 1/500,000. This seems like an extremely unlikely event. On the other hand, it is about 15 times more likely than the chance that you will win the Virginia lottery on one play in a given year.

The Smoking Gun

It is important to understand that the view that catastrophic events triggered by meteor or comet impacts with the earth occur with some regularity, and that these events have had a significant impact on the evolution of life on earth, has only achieved wide acceptance within the last twenty years. Before 1980, the generally accepted notion was that major evolutionary events on earth are characterized by slow, small changes taking place over long intervals of time (millions of years). It is only recently that we have come to think that almost all evolutionary change occurs during brief episodes that occupy a tiny fraction of the total time available, and that gradual changes are separated by brief (years or decades) extinction events in which large numbers of species and genera rapidly disappear despite the fact that they are spatially separated by distances of a global scale. The ultimate test of the validity of this hypothesis is to identify and date an impact crater with one of the discontinuities identified in the stratigraphic history of the earth. In an evidentiary sense this would be like finding a suspect in a criminal case holding the "smoking gun." In fact, this seems to have occurred.

The most dramatic and best studied of the discontinuities is that which marks the end of the era of dinosaurs which occurred some 65 million years ago. It marks the end of the Cretaceous period K, and the beginning of the Tertiary period T, the so-called K/T boundary in the stratigraphic record. At the 100 or so sites where this boundary layer has been studied, there is a millimeters -- thick layer of gray clay that varies little from site to site. It is one to 10 millimeters thick, and of a uniform composition which seems unrelated to the local rock structure which surrounds it. Reasonable estimates suggest that, world wide this layer contains 10 18 grams of clay or about 1000 cubic kilometers of material.

The thinness of the layer and its uniformity suggest that it was deposited in a single event in less than a year. In 1980, Luis Alvarez, a physicist who had previously won a Nobel Prize for his work in particle physics, and his collaborators found in this layer a concentration and pattern of abundance of metals (initially Iridium) which is rare in the earth's crust, but which matches that found in meteorite material very well. It was also found that mixed in with the clay layer are particles of heavily shocked quartz, and that the layer is thicker and contains more and larger particles of fused quartz in the Caribbean basin area than elsewhere. This indicates that tremendous heating occurred producing temperatures high enough to fuse the quartz, and that the epicenter of that heating is likely to be found there. It also indicates that the "event" was not likely to be of volcanic origin.

Worldwide, the geologic record shows that over 90 percent of the existent species vanished abruptly and nearly simultaneously. This means that rock layers beneath the clay are rich in fossil remains whereas they are missing in the layers above it. This includes plants and animals from widely separated geographic regions. The cause of the mass mortality at the K/T boundary remains unclear in detail, but a number of reasonable suggestions have been put forth.

Alvarez and his co-workers pointed out that the immediate effects of the explosion, blast, heat, and the ignition of fires, effects only a small portion of the surface of the earth and are not likely to cause a global kill-off. The most obvious cause of the global mass extinction was the fine grained clay itself, which if transmitted to the stratosphere, would be substantial enough to shut off sunlight from the surface of the planet for several months to a year. Without sunlight the land masses undergo significant cooling. Indeed, computer simulations show that the dust shield created would cut off photosynthesis completely for many months and that the continents could cool by as much as 70 degrees Fahrenheit. Thus most of the land area of the planet is cooled below freezing and is in total darkness. Fortunately, the large thermal inertia of the oceans would limit their cooling to only a few degrees. Others have suggested that the extreme heat generated would produce large amounts of nitrogen and oxygen compounds which would eventually be converted to nitrous and nitric acids in quantities large enough to acidify large land and water bodies and contribute to habitat changes and species extinctions. Computer simulations and laboratory studies suggest that a major impact can eject and accelerate a mass of material a hundred times as large as the mass of the impactor itself to high speeds. For example, a 1000 cubic kilometer impactor can generate 100 times as much matter as ejecta, some of which can achieve speeds approaching escape velocity, can travel great distances, and, upon reentry, can cause fires all over the earth. The energy released in a large impactor (1 kilometer in diameter) is sufficient to cause fires to ignite on a global scale. Interestingly, an identified constituent of the K/T global boundary clay layer is soot.

The specific details of the collision are also important. For example, if the impact occurred in deep ocean, rock ejection would be minimized, destruction due to tidal waves thousands of feet high would be important, and damage due to global firestorms minimized. Much depends on the details of the impact, and it is clearly important to locate the crater associated with it. Also, since roughly seventy percent of the earth's surface is water-covered, we might expect that only a small fraction of the likely impactors would leave a signature on the ground. As good fortune would have it, a likely candidate has been identified. In 1990 Alan Hildebrand, David Kring, and Bill Boynton suggested the K/T impact site might be a large roughly circular, sediment-filled basin on the north slope of theYucatan Peninsula in Mexico. Called the Chicxulub crater, it was produced 65 million years ago, is 180 km in diameter, and required an impactor of 1000 cubic kilometers to excavate a crater with a volume of 100,000 cubic kilometers. In short, it fits the bill for the "smoking gun."

In conclusion, it appears clear that the impact of asteroids and comets with diameters greater than one to two kilometers in diameter has significantly altered the evolution of life on earth in the past and will likely continue to do so in the future. Fortunately, the technology exists to identify potential major impactors and to take action to modify their orbits if it is determined that a collision is likely to occur.

Bibliography

"Is this the End" by Timothy Ferris, The New Yorker, January 27, 1997 pp(44-55)

Rain of Iron and Ice: The Very Real Threat of Comet and Asteroid Bombardment, John S. Lewis, Addison Wesley Press, 1996

Century's End, An Orientation Manual Toward The Year 2000, Hillel Schwartz Currency , Doubleday , 1990, 1996

Asteroid and Comet Impact Hazards, NASA Ames Space Science Division

Comets and Meteor Showers, Gary W. Kronk