Impact Processes: Meteor Crater, Arizona
What was the size of the bolide that formed Meteor Crater?
Understand the Problem:
A bolide falling toward the Earth is propelled by gravitational attraction.
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Because it is moving, the bolide has an energy of movement or kinetic energy (KE), which is described by the equation: KE = 0.5 m s2 where m is the mass of the bolide and s is its velocity. |
If the bolide is accelerating downward, its KE must be increasing as the square of the velocity! If the bolide is big enough, it will pass through the atmosphere without burning up completely. When it strikes the surface of the Earth, its velocity and KE go to zero in an instant, but the law of conservation of energy holds that the energy is not simply lost; it is transferred to the surroundings as heat, light, and work, sending out shock waves and excavating a crater far larger than the bolide itself.
Consider the factors that would determine how “large” a crater is formed. In part, this would depend on geological conditions specific to the impact site, such as the mechanical properties of soils and rocks. However, one might also assume that KE of the bolide is a more important factor: the more energy delivered upon impact, the “bigger” the crater that is excavated. (We will use diameter to represent crater “size,” because as a crater is eroded away through time, its diameter changes far less than its depth.)
If KE is the most important (controlling) factor, and we can find a mathematical relationship between KE and crater diameter, we can take the dimensions of Meteor Crater and calculate the KE, and then the mass, of the offending bolide. From the mass, we can then calculate the "size" (more precisely the volume) of the bolide, because volume and mass are related by density, and we have actual fragments of the bolide on which density has been measured.
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Gather Data:
What data are available to help us solve this problem?
The impact that formed Meteor Crater is beyond history; evidence suggests that it occurred about 50,000 years ago. An impact of this size has not been observed on Earth in recorded time (and most would likely consider that a good thing!). But in the last century, for better or for worse, human beings have devised and experimented with a process of comparable destructive power: nuclear explosions. Until the advent of treaties restricting the practice, nations tested nuclear weapons by detonating them at or just beneath the surface.
Sedan, NV nuclear testing explosion and resulting crater. Image source http://rst.gsfc.nasa.gov/
In the United States, most nuclear weapons testing took place at the Nevada Test Site, in the Mojave and Great Basin Deserts of south-central Nevada, on the homelands of the Newe (Western Shoshone) people. The Newe had no say in the testing, and continue to work for restoration of these lands.
Nuclear explosions often excavated craters identical to those attributed to bolide impacts. The KE released in these blasts was known to the weapons designers, so here was a relationship between energy and crater size. This information was eventually made public, and planetary geoscientists made use of this relationship to estimate the KE needed to excavate impact craters of various sizes and ages, on Earth and other planets.
Some of these data, for what are thought to be actual bolide impact craters are tabulated here. Crater diameter is reported in meters (m) and KE in joules (J).
| Crater | Diameter(m) | Kinetic Energy of Impact (J) x 1018 |
| 3800 | 2.461 | |
| 12000 | 15.85 | |
| 23000 | 310 | |
| 32000 | 1000 | |
| 70000 | 14500 | |
| 140000 | 205000 |
Source: Roddy: Dence et al., 1977.
We can use mathematical regression on these data to derive an equation relating these two variables:
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Notation:
D = diameter (in m) of the resulting crater |
This will enable us to calculate KE of impact for any Earth crater of known diameter, such as Meteor Crater. However, our ultimate target (so to speak!) is the volume of the bolide, and for that we will need two more equations:
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Information: This equation models kinetic energy (KE):
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Information: This equation models density,
ρ = density of the bolide in kilograms per cubic meter (kg/m3) V = volume of the bolide in cubic meters (m3) |
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Solve the Problem:
Use the online applets or your calculators to answer the questions below.
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PROBLEM 1: Make points from the data provided in the table: the first coordinate should be the diameter of the crater and the second coordinate should be the kinetic energy. Write the second coordinate as shown in the table, just remember that the real value for KE must be multiplied by 1018. Use the power regression applet. |
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PROBLEM 2: Use power regression to find the equation of best fit. Round constants to 3 decimal places. |
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Notation: The equation as given by the applet has the general form y = axbIn this problem
'a' and 'b' are constants determined by the regression of the data. The coefficient 'a' should be in scientific notation (in this case, a = c x 10-12 with c in the form x.xxx). We can express this equation as:
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Information: Meteor Crater is about 1,200 meters in diameter. |
We will use this equation for craters with
diameters between 500 and 140,000 meters, 500 < D < 140,000.
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PROBLEM 3: Now you are ready to determine the size of the bolide that formed Meteor Crater. |
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STEP 1. Use the regression equation you developed to find the kinetic energy (KE) of impact. You can do this calculation in the Math Pad in the Math Tool Chest. [Use Math Pad] |
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STEP 2. Use the kinetic-energy equation to find the mass of the bolide. As noted above, use v = 20,000 meters/sec. Record your answer. [Use Math Pad] |
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STEP 3. Use the density equation to find the volume of the bolide. The iron-nickel fragments found at the site have a density of about 7,800 kg/meters3. Record your answer. [Use Math Pad] |
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STEP 4. Find the diameter (in meters) of this significant bolide. [Use Math Pad] |
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STEP 5. Compare the size of this bolide to that of something else familiar to you. [Use Math Pad] |
ASSUME: Assume that the bolide was approximately spherical as it plunged to Earth.
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Information: You can find its radius using the equation for the volume of a sphere, V = (4/3) π r3where V = volume of the bolide in cubic meters (m3) r = radius of the bolide in meters (m) π ≈ 3.14159, In Math Pad type 'pi' for π |
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PROBLEM 4: Another bolide impact, one that occurred about 65 million years ago, was much larger than the Meteor Crater impact. It is thought to have caused (or at least hastened) the extinction of the dinosaurs. The KE released in this impact was probably equivalent to 100 million megatons of TNT exploding |
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STEP 1. Given that 1 megaton TNT = 4.185 x 1018 J, convert this KE value to joules. [Use Math Pad] |
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STEP 2. Determine how many times more KE was released in this impact than in the Meteor Crater impact. [Use Math Pad] |
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STEP 3. Determine the diameter (in meters) of the crater that could have been formed by this impact. [Use Math Pad] |
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STEP 4. Find the diameter (in meters) of this significant bolide. [Use Math Pad] |
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STEP 5. Again, compare the size of this bolide to that of something else familiar to you. [Use Math Pad] |