Modeling Impact Craters

Modeling Impact Craters Lab

Name: ______This lab is due on or before ______

Adapted fromLesson 6, Impact Craters - Holes in the Ground! Exploring Meteorite Mysteries, A Teacher’s Guide with Activities for Earth and Space Sciences. NASA EG-1997-08-104-HQ.This publication is in the Public Domain and is not copyrighted. Permission is not required for duplication.

GOALS:

Investigate the effect that velocity (speed and direction) has on the cratering process

Identify and describe the relationship of mass to crater formation.

Background Information

Impact craters are geologic structures formed when an extraterrestrial object such as a meteorite, asteroid or comet smashes into a planet or other solid body. Extraterrestrial objects such as meteors move very fast in space. Gravitational force causes change in velocity of the mass as it moves toward the planet surface. Interaction with Earth’s atmosphere causes transfers of energy that contribute to changes in the meteorite velocity.

When the solid portion of the meteorite strikes the surface, depending in part on the amount mass remaining, the large velocity change can cause a huge amount of energy transfer. In an impact, the meteorite kinetic energy is transformed, into thermal energy that melts rocks and energy that pulverizes and excavates rock.

1. Choose a partner. Write your partner’s name here: ______

1. Obtain the following items. Check them off as you find them.

Projectile Set A (four marbles of the same mass and size)

Projectile Set B (three spheres of roughly equal size but not equal mass)

Metric ruler (12-inch)

Meter stick (1 meter)

Lab balance

Dry material box—this is filled with sand in roughly equal proportions but they have different colors to simulate the different types of soil/rock.

1. Record the masses of the projectiles from each set.

DATA TABLE 1 Projectile Set A Masses

Projectile
SET A / Mass (g) Measure to the nearest 0.01 g / Describe the object? round? Flat? 3-D? / Dimensions (length x width x height) or Diameter
1
2
3
4

DATA TABLE 2—Projectile B Descriptions

Projectile SET B / Mass (g) Measure to the nearest 0.01 g / Describe the object? round? Flat? 3-D? / Dimensions (length x width x height) or Diameter (in cm)
1
2
3
4

1. Prepare to drop the projectiles into the dry material box. Measure the height at which you dropped the projectile using the meter stick.

DATA TABLE 3—heights of drops and characteristics of craters formed by Projectile Set A

Projectile A / Height of drop (in cm) / Length of longest ray in crater (in cm) / Depth of depression (cm) / Observed effects on layers of sand
1 / 25
2 / 50
3 / 75
4 / 100

DATA TABLE 4—height of drops and craters formed by Projectile Set B

Projectile B / Height of drop (in cm) / Length of longest ray in crater (in cm) / Depth of depression (cm) / Observed effects on layers of sand
1 / 75
2 / 75
3 / 75

1. Answer the questions below.

Based on experimental results write complete answers for the following:

1. What is the physical evidence that the energy of the falling projectile was transferred to the dry material?

1. How does the mass of a projectile affect the cratering process?

1. What effect does the height of the projectile have on the velocity?

1. How does the velocity of the projectile affect the cratering process?

Based on additional research write complete answers for the following:

1. Identify the variety of objects that become meteorites. Describe the types of physical evidence that scientists use to identify the source of a meteorite.

1. What is the relationship of the gravitational force to the mass of the meteorite and the distance to the meteorite from the planet? Describe the effect that gravitational force has on the velocity of a meteorite. Describe the resulting effect on the shape of the path that a moving meteor typically travels along. How does gravitational force govern the observed characteristics of the model impact craters?

1. What is the relationship between the kinetic energy, mass and velocity of a moving meteorite?

1. What do scientists tell us about the approximate typical range of meteorite velocities?

1. Based on this information, if a meteorite is assumed to be 10 kilograms in mass, estimate the average kinetic energy of this meteorite.

Additional Information:

1. From (3-16-2006)

Meteorites are bits of the solar system that have fallen to the Earth. Most come from asteroids, including few are believed to have come specifically from 4 Vesta; a few probably come from comets. A small number of meteorites have been shown to be of Lunar (15 finds) or Martian (13) origin.

One of the Martian meteorites, known as ALH84001 (left), is believed to show evidence of early life on Mars.

Though meteorites may appear to be just boring rocks, they are extremely important in that we can analyze them carefully in our labs. Aside from the few kilos of moon rocks brought back by the Apollo and Luna missions, meteorites are our only material evidence of the universe beyond the Earth.

Meteorite Types
Iron / primarily iron and nickel;
similar to type M asteroids /
Stony Iron / mixtures of iron and stony material like type S asteroids /
Chondrite / by far the largest number of meteorites fall into this class;
similar in composition to the mantles and crusts of the terrestrial planets /
Carbonaceous Chondrite / very similar in composition to the Sun less volatiles;
similar to type C asteroids /
Achondrite / similar to terrestrial basalts;
the meteorites believed to have originated on the Moon and Mars are achondrites /

A "fall" means the meteorite was witnessed by someone as it fell from the sky. A "find" means the meteorite was not witnessed and the meteorite was found after the fact. About 33% of the meteorites are witnessed falls. The following table is from a book by Vagn F. Buchwald. Included are all known meteorites (4660 in all, weighing a total of 494625 kg) in the period 1740-1990 (excluding meteorites found in Antarctica).

Meteorite Statistics
Type / Fall % / Find % / Fall Weight / Find Weight
Stony / 95.0 / 79.8 / 15200 / 8300
Stony-Iron / 1.0 / 1.6 / 525 / 8600
Iron / 4.0 / 18.6 / 27000 / 435000

A very large number of meteoroids enter the Earth's atmosphere each day amounting to several hundred tons of material. But they are almost all very small, just a few milligrams each. Only the largest ones ever reach the surface to become meteorites. The largest found meteorite (Hoba, in Namibia) weighs 60 tons.

The average meteoroid enters the atmosphere at between 10 and 70 km/sec. But all but the very largest are quickly decelerated to a few hundred km/hour by atmospheric friction and hit the Earth's surface with very little fanfare. However meteoroids larger than a few hundred tons are slowed very little; only these large (and fortunately rare) ones make craters.

A good example of what happens when a small asteroid hits the Earth is Barringer Crater (a.k.a. Meteor Crater) near Winslow, Arizona. It was formed about 50,000 years ago by an iron meteor about 30-50 meters in diameter. The crater is 1200 meters in diameter and 200 meters deep. About 120 impact craters have been identified on the Earth, so far (see below).

A more recent impact occurred in 1908 in a remote uninhabited region of western Siberia known as Tunguska. The impactor was about 60 meters in diameter and probably consisting of many loosely bound pieces. In contrast to the Barringer Crater event, the Tunguska object completely disintegrated before hitting the ground and so no crater was formed. Nevertheless, all the trees were flattened in an area 50 kilometers across. The sound of the explosion was heard half-way around the world in London.

There are probably at least 1000 asteroids larger than 1 km in diameter that cross the orbit of Earth. One of these hits the Earth about once in 300,000 years on average. Larger ones are less numerous and impacts are less frequent, but they do sometimes happen and with disastrous consequences.

The impact of a comet or asteroid about the size of Hephaistos or SL9 hitting the Earth was probably responsible for the extinction of the dinosaurs 65 million years ago. It left a 180 km crater now buried below the jungle near Chicxulub in the Yucatan Peninsula (right).

Calculations based on the observed number of asteroids suggest that we should expect about 3 craters 10 km or more across to be formed on the Earth every million years. This is in good agreement with the geologic record. It is more difficult to compute the frequency of larger impacts like Chicxulub but once per 100 million years seems like a reasonable guess.

Here are educated guesses about the consequences of impacts of various sizes:

Impactor Diameter (meters) / Yield (megatons) / Interval (years) / Consequences
< 50 / < 10 / < 1 / meteors in upper atmosphere most don't reach surface
75 / 10 - 100 / 1000 / irons make craters like Meteor Crater; stones produce airbursts like Tunguska; land impacts destroy area size of city
160 / 100 - 1000 / 5000 / irons,stones hit ground; comets produce airbursts; land impacts destroy area size of large urban area (New York, Tokyo)
350 / 1000 - 10,000 / 15,000 / land impacts destroy area size of small state; ocean impact produces mild tsunamis
700 / 10,000 - 100,000 / 63,000 / land impacts destroy area size of moderate state (Virginia) ocean impact makes big tsunamis
1700 / 100,000 - 1,000,000 / 250,000 / land impact raises dust with global implication; destroys area size of large state (California, France)
from 'The Impact Hazard', by Morrison, Chapman and Slovic, published in Hazards due to Comets and Asteroids

2. From (3-16-2006)

Cratering in Theory

The largest and most terrific impact feature is the meteorite crater. The theory of cratering is logical, however, the mechanics of the process is quite unique and intricate. Imagine the consequences of an impact that produces more energy than 1000 atomic bombs the size of those dropped on Japan to end WWII (Grieve and Personen, 1992).

An iron-rich meteorite traveling over 50 km/s enters the earth's atmosphere as a fiery ball with a thin layer of melt due to the heat from air friction. Travel through the earth's atmosphere is approximately the same as traveling through 4 feet of solid rock (LeMaire 1980).When this meteorite comes in contact with the earth a fantastic shock wave is produced in both the meteorite and surface rocks. This is referred to as the compression stage by Melosh (1980), or the "early stage" by Holsapple and Schmidt (1987). During this process the target material is accelerated downward by the shock. Because the tremendous pressures produced within the target by the shock wave are adjacent to the "outer limit" of impact, which is still only subjected to the earth's atmospheric pressure, material is catastrophically forced out the sides of the impact area. This squishing of material out the sides of the impact is called jetting. The material ejected forms a hydrodynamic jet that has a velocity several times that of the meteorite itself, and is composed of an incandescent liquid or superheated vapor spray (Melosh, 1980). A complicated system of shock waves and rarefaction waves envelop the target and projectile. One of the main results of this process is the transfer of kinetic energy from the meteorite to the target in the form of internal and kinetic energy. The rarefaction waves catch up with the initial shock wave several projectile distances from the impact, greatly reducing the shock intensity. After only a fraction of a micro-second, the compression stage ends with the complete transfer of energy in the form of a shock wave and latent heat.

The crater excavation stage (Melosh, 1980) overlaps somewhat with the compression stage. This stage is likened to an atomic explosion, and is characterized by rapid crater expansion. Materials leave the crater in two ways, ballistically, or plastically (Melosh, 1980). The most highly shocked rock nearer the surface is unloaded so rapidly it has a net upward force that propels the rock from the opening crater. Slightly deeper rock is pushed laterally from the crater. During this stage, depending on exact P/T conditions the target rock may be melted, partially melted, brecciated, or vaporized. Commonly a large amount of impact melt is formed. Several authors have attempted to calculate the decay rate of the shock wave, one estimate by Gault and Heitowit (1963) (form Melosh, 1980) indicates that pressure decrease was proportional to the 1/radius2.6. Another estimate given by Hollsapple and Schmidt (1987), indicates the shock decreases at a rate of 1/radius6 to 1/radius2. Crater growth finally stops when the net upward propelling force at the crater rim is not large enough to eject any more material.

The final stage of crater growth, the modification stage, lasts only 20 s to 30 s (Melosh, 1980). Small simple craters (basically craters that are symmetrically bowl shaped) don't undergo much modification, but they may fill themselves, at least partially, with impact breccia or melt from the impact. Large craters, however, often undergo tremendous modification (they are called complex craters). This modification often produces raised centers and double rings. Although the exact mechanism for is debated, Melosh (1980) indicates that gravitational collapse is the main driving force. At least three main theories for central uplift of craters exist, but it seems intuitively obvious that the rebound from shock is the most likely of these. This process could be likened to the initial upward movement of water droplets when a stone is tossed in a pool. The development of a second ring around a complex crater is also is poorly understood. Ideas like "frozen" shock waves, fault scarps, and material differences have all been suggested (Melosh, 1980), however second rings appear to be related to normal faulting found around impact sites.

The cratering process represents the greatest release of energy per unit time known to man. The mechanisms are complex, and the results are spectacular. It is little wonder we do not fully understand the cratering process. In the past, experiments that model cratering by shooting projectiles at great speeds into different materials (Hollsapple and Schmidt) have been performed. Although these experiments paved the way for further research and modeling, they are fundamentally flawed. We simply do not have the ability to shoot projectiles at hyper-velocities equivalent to those of meteorites, and the extrapolation or scaling from moderate velocities to hyper-velocities is not adequate. Experimental limitations coupled with the huge number of mechanical factors involved in theoretical calculations is a real problem. Perhaps it is better to grossly oversimplify all of these problems, and try to rely on the fact that some of these factors may, in effect, cancel each other out. Therefore the simplest way to look at a meteorite impact may also be the best.

Quantifying the Cratering Process

First we will consider the kinetic energy of a meteorite. The variables mass and velocity become unknowns, however, we can put realistic limits on each of these. For example a meteorite must be traveling at least 11 km/s. This is equal to the minimum velocity needed for a projectile shot from earth to overcome gravity and reach space. Logically, anything falling from space to earth must achieve the same velocity. According to Middleton and Wilcock (1994), 72 km/s is near the upper limit of meteorite speed. The density of an iron meteorite is 8000 kg/m3 and for a stoney meteorite is 3500 kg/m3. Although the diameter of a meteorite remains an unknown variable, it's density must lie between these two endmembers. Let us assume that the meteorite is roughly spherical in shape. Now taking an iterative approach, we can plug in various reasonable speeds, reasonable densities + reasonable diameters (thus reasonable masses) into the formula,

1/2Mv2 = Total Kinetic Energy.

Consequently, we will receive a reasonable total kinetic energy estimate over a wide range of conditions (Table 1).

This is a valuable approach to cratering, because slight variations in the angle of impact can be (for the most part) entirely neglected. In other words an impact at 75 degrees is approximately the same as using a diameter 3/4 as big as the original diameter or using a density that is 3/4 the original density of the meteorite.

Because most impact features (melts, shatter cones, etc.) are often hidden under sediment or eroded away, the only real impact features we can measure directly is a crater. Can one estimate the size a meteorite from the size of its crater? The answer is yes, to a first approximation. Lets assume for a minute that 100% of the meteorite's energy goes into the formation of a simple crater. This can now be likened to the energy needed to excavate a bowl shaped volume (a simple crater). In other words Energymeteorite = Potential Energyexcavation. The potential energy is equal to the volume of rock that will be displaced (V) multiplied by that rocks density (d), the gravity of the planet the meteorite is impacting (in this case, earth) (g) and the height of excavation (h). If we call the hemispherical radius of the crater, R, and we let the height needed to move the rock (h) be equal to R, it is easily seen that Energymeteorite = K*Rcrater4 , where K is a constant equal to 2/3pi*d*g (Table 1).

Of course not all of a meteorite's energy is used to crater, in fact some of it is used to produce a huge shock wave, and most is lost as latent heat (Melosh, 1985). These are two important considerations, but how can we consider them? Holsapple and Schmidt (1987) and Melosh (1985) treat this problem at length. Melosh (1985) estimates that about 80% - 95% of the meteorite's energy is expended as a shock wave and heat, leaving only a small percent to excavate a crater. Calculating the energy of the shock wave, and the amount of heat produced is not straight forward. Calculations for shock propagation speed and particle velocity depend heavily upon the property of the target rock itself. The amount of heat produced and the resulting amount of melt is also very complicated to calculate and varies only roughly as a function of impact energy (or crater diameter) (O'Keefe and Ahrens, 1994). Because of these problems, the seemingly easily calculated relationship Emeteorite = Ecratering + Eheat + Eshock wave doesn't do us much good.

Implications of Results

The calculations above show us that even a small meteorite impact can release the energy equivalent of a nuclear arsenal (many megatons of TNT).

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