CRATERS in the SOLAR SYSTEM. REMOTE ACCESS ASTRONOMY PROJECT UNIVERSITY OF CALIFORNIA, SANTA BARBARA and CENTER for PARTICLE ASTROPHYSICS

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1 CRATERS in the SOLAR SYSTEM REMOTE ACCESS ASTRONOMY PROJECT UNIVERSITY OF CALIFORNIA, SANTA BARBARA and CENTER for PARTICLE ASTROPHYSICS

2 Craters in the solar system Jatila van der Veen, UCSB Physics Department and Adolfo Camarillo High School Philip Lubin, UCSB Physics Department THE FOLLOWING MAY BE REPRODUCED IN ANY FORM FOR USE IN A CLASSROOM, BUT UNDER NO CIRCUMSTANCES MAY ANY PART OF THIS BE REPRODUCED FOR PUBLICATION WITHOUT THE WRITTEN CONSENT OF THE AUTHORS. Modified by WAC at UNC-CH 6/12/02 References: "The Collision of Solid Bodies", Eugene and Carolyn Shoemaker, in THE NEW SOLAR SYSTEM, Beatty and Chaikin, ed., Sky Publishing, "Killer Crater in the Yucatan", J. Kelly Beatty, in SKY AND TELESCOPE, v.82, no.1, July, *************************************************************************************** In the following activity, you will: * Compare the sizes of craters on some of the satellites of the planets in our solar system; * Calculate the energy released by impacts at an average speed based on crater sizes. *************************************************************************************** Background: Impact cratering is one of the most widely observed geologic processes in the solar system. In fact, there is strong evidence that asteroid or comet impacts have played a role in some of the major extinctions of plant and animal life in the Earth's history. It is estimated that at least 20 craters of diameter 10 km or larger form on the Earth per million square kilometers every billion years, based on craters found on Earth and the number of observed asteroids and comets whose orbits pass close to Earth. On a geologically active planet like Earth, impact craters get eroded relatively rapidly and are difficult to find. On bodies with no atmosphere, water, or active volcanoes, ancient impact craters are preserved. The surfaces of our Moon, Mercury, Venus, Mars, and many of the moons of Jupiter and Saturn are covered with craters. IN THIS ACTIVITY YOU WILL COMPARE IMPACT CRATERS ON TWO OF THE SATELLITES OF SATURN, OUR MOON AND THE EARTH ITSELF.

3 FIGURE 1 IS A PICTURE TAKEN BY VOYAGER I OF MIMAS, ONE OF THE MOONS OF THE PLANET, SATURN. Notice the very large crater in the northeast quadrant of Mimas. This crater is named Herschel, after the astronomer who first discovered this moon of Saturn. Figure 1 I. Estimating the size of the crater Herschel Using Figure 1 measure the diameter of the image of Mimas in centimeters: Diameter of Mimas = cm We know from measurements taken by Voyager I that the actual diameter of Mimas is 390 km. Now we can find the scale of this image in km/cm: Scale factor = (diam. in km)/(image diam. in cm) = km/cm Now we can estimate the diameter of the crater... Find the widest part of the crater, and measure the diameter in the same manner as you measured the diameter of Mimas itself. Diameter of crater = cm

4 Now multiply by the scale factor to find the diameter of Herschel crater in kilometers: diam.(cm) x scale factor (km/cm) = diam. = km What fraction of the diameter of Mimas is the diameter of Herschel crater? Herschel crater is one of the largest craters observed on any body in the solar system. If the impact had been much larger, Mimas would have broken apart. ************************************************************************************* II. Craters on Dione: FIGURE 2 IS AN IMAGE OF DIONE, ANOTHER SATELLITE OF SATURN Figure 2

5 This image does not show the entire moon, but you can get a fairly good estimate of where the center of Dione is by observing the curvature on the sides in the image. Once again, we will need to estimate the scale of this image in kilometers/cm. Try to find the center of Dione from the image. Get as accurate a measurement of the diameter of Dione s image in centimeters as you can, using the same method as before. Diameter of Dione s image in cm = cm. The actual diameter of Dione is about 1120 km. Now you can estimate the scale factor for this image in the same way you did for the image of Mimas. Scale factor = (diam. in km)/(diam. in cm) = km/cm Finding the largest crater on Dione. Look for the largest crater you can find in Figure 2, and estimate its diameter in the same way you did for Herschel crater on Mimas. Diameter of largest crater in cm = cm Diameter of crater in km = (diam. in cm) x (scale factor) (km/cm)= km What fraction of the diameter of Dione is the diameter of this crater? Which crater is actually larger, this one on Dione, or Herschel on Mimas? Which crater is larger IN PROPORTION TO THE BODY IT IS ON? *****************************************************************

6 III. Comparing Craters on the Saturnian Moons with Craters on Our Moon FIGURE 3 IS AN IMAGE OF THE EARTH S MOON TAKEN FROM APOLLO 16. Figure 3 Let s repeat the exercise again. Find the center of the Moon from the image. Get as accurate a measurement of the diameter of the Moon s image in centimeters as you can, using the same method as before. Diameter of the Moon s image in cm = cm.

7 The actual diameter of the Moon is 3476 km. Now you can estimate the scale factor for this image in the same way you did before. Scale factor = (diam. in km)/(diam. in cm) = km/cm Finding the largest crater on the Moon. Look for the largest crater you can find in Figure 3, and estimate its diameter in the same way you did for craters on Mimas and Dione Diameter of largest crater in cm = cm Diameter of crater in km = (diam. in cm) x (scale factor) (km/cm) = km What fraction of the diameter of the Moon is the diameter of this crater? Now which crater is actually larger, this one on the Moon, the largest crater on Dione, or Herschel on Mimas? And, now, which crater is larger IN PROPORTION TO THE BODY IT IS ON? *************************************************************************** IV. Comparison with Craters on Earth The famous Barringer Crater in Arizona shown above (Figure 4) has a diameter of only 1.2 kilometers. This is tiny compared to the large craters on moons that we have been examining. Does that mean that large bodies haven t hit the Earth? Of course not! It simply means that because of erosion on Earth, craters tend to be erased fairly quickly. However, it turns out that evidence for large impacts in

8 earlier times can now be recovered using modern techniques for mapping the density and magnetic field variations of ancient rocks. FIGURE 5 BELOW IS A MAP OF AN IMPACT CRATER NEAR CHICXULUB, YUCATAN PENINSULA IN MEXICO. Figure 5 This impact basin is buried under several hundred meters of sediment beneath the coastal waters of the Gulf of Mexico; thus hiding it from view. The diameter of this buried crater is 170 kilometers! The best estimate of the time of the impact was 65 million years ago (based on the depth of the sediment, dating of the rocks, etc). This is believed to be the event, which caused the last great worldwide extinction in which half of the species on Earth became extinct--including the dinosaurs! How does this Chicxulub Crater compare in size with the large craters we examined on the moons?. And how does the Chicxulub Crater compare IN PROPORTION TO THE BODY IT IS ON?. *************************************************************************

9 V. Going further... Estimating the Energy Released in an Impact Bodies that crash into planets or satellites at high speeds create tremendous shock (pressure) waves that penetrate the surface of the planet or moon. These extremely high pressures cause both the target material and the impacting body to get so hot it is vaporized or melts. This ultra hot material moves outward from the location of the impact, as an expanding shock front, which pushes outward to form a crater rim. After the shock wave passes, some material from the crater rim slumps inward and converges in the center to form a peak. Also there is often an elastic rebound at the center of the crater, which accentuates the formation of a central peak in the crater. An examination of the larger craters in Figures 1 through 3 shows that central peaks are quite common. Much material is ejected from the excavated crater. While the floor of the crater is often smooth due to melting, the ground outside the crater is often littered with debris from the impact. The ejecta consists mainly of material blasted out from the floor of the crater, and sometimes chunks of the impacting body itself (if it was massive enough that it did not all vaporize upon impact!). There are often secondary craters observed around large craters, which are made by the ejecta. Rays are observed around young craters on the Moon and other planets, which are made up of ejecta, which were shot out from the crater. It turns out that the size of a crater depends primarily on the Kinetic Energy of the impacting body. A rough rule of thumb is that the impact energy is approximately proportional to the cube of the diameter of a crater. For example a crater that is twice as big will be excavated by an impact in which the energy (either by making the impact velocity higher or the body larger) is about 8 times bigger! Thus, by studying crater sizes astronomers can estimate the sizes and impact energies of bodies that made them. While this is actually a rather complicated process that involves doing impact experiments under controlled conditions in the lab, we can make some rough estimates of the amount of energy released by impacting bodies from some simple considerations Impact velocity. Impact velocities are estimated to range from about 5 km/sec for colliding asteroids to 40 km/sec for the body that collided with the Earth 65 million years ago creating the Chicxulub Crater. To be on the conservative side, however, let's assume an impact velocity of 10 km/sec. 2. Size of the impacting body. This is a tough one. From our examination of the various sizes of craters on the Moon, Dione and Mimas we can conclude that impactors probably come in a large variety of sizes. Furthermore, since there seem to be many more small craters than large ones we can conclude that there must be more small impactors than large ones. A very approximate rule of thumb is that an impact crater is about 10 times bigger in diameter than the impactor if the density of the target and the impacting body are about the same. If the 1.2 km diameter Barringer Crater was caused by a rocky body, our rule of thumb would imply that its diameter was about 0.12 km or 120 meters. 3. Mass of the impacting body. We need to estimate the density of a chunk of interplanetary material...if it was a rocky piece of material, it could have a density of around 3-5 gm/cm 3, but if it was a chunk of an iron-nickel meteor, its density could have been 8-9 gm/cm 3. If it was a piece of comet, on the other hand, its density could have been around 1-2 gm/cm 3. Let's just assume our craters were caused by asteroidal chunks of rock, with a densities of about 3.0 gm/cm 3. Now let s try to estimate the Energy of the Barringer Meteorite!

10 Make sure your units are consistent: a. Convert density in gm/cm 3 to density in kg/m 3 : kg/m 3 b. Find the volume in m 3 for a spherical body from V = (4 π r 3 )/3 (for the Barringer Meteorite r = 60 meters V = m 3 c. Mass = (volume) x (density) = kg d. Convert velocity to m/sec: m/sec e. Now, let's consider how much kinetic energy is dissipated as heat and other forms of energy when this body of 120 meters diameter, density 3000 kg/m 3, and moving at a velocity of 10000m/sec impacts the Earth (we can neglect atmospheric effects). K.E. = 1 2 mv2 = Joules To get an idea of how much energy this really is, consider that 1-megaton of TNT (that's 10 6 tons of TNT) is equivalent to approximately 4.2 x Joules. How many megatons of TNT are equivalent to the energy released by our typical hypothetical impacting body? Megatons of TNT And this is just a small collision! f. Now, the Chicxulub Crater is 170 km in diameter instead of 1.2 km. Assuming that crater diameter really is proportional to the energy cubed we can estimate the energy of the impact based on the energy of the Barringer event. K.E. (Chicxulub) = K.E. (Barringer) x [diam (Chicxulub)/diam. (Barringer)] 3 = Joules Or Megatons. As a point of reference, the combined nuclear weapons stockpiles of all the Nuclear Powers in the world add up to somewhat more than 10,000 Megatons. No wonder the Chicxulub event caused a widespread extinction! g. Assuming the Chicxulub event was also caused by a stony asteroid of density 3000 kg/m 3 estimate how big it was if it was also moving at a speed of 10000m/s. Diameter of Chicxulub impacter km. Crater Counting and the Spectrum of Impacters (Power Laws in Nature)

11 The SPECTRUM of a set of objects, like Asteroids or Comets, is just the Distribution of the NUMBER of these objects as a function of their SIZE. Now, having looked at the titanic amounts of energy that can be released in the impact of an asteroidal or cometary body on the earth it s important to ask how often such events may occur. Unfortunately this is hard to assess because of the Earth s very active geology. We have weathering and erosion as well as continental drift, both of which tend to erase craters after only a few hundred million years or so (Remember Chicxulub was buried in sediment and only discovered using the sophisticated seismic techniques applied to oil exploration). But our neighboring Moon has no significant atmosphere and is a small body so it also does not have continental drift. As a result the cratering on the moon has been preserved over geological time. Remembering also that the rule of thumb is that the diameter of a crater is about 10 times the diameter of the impactor that caused it, we can estimate the size spectrum of impacters in the vicinity of the Earth by measuring the size spectrum of lunar craters. That is, you are going to sort craters on the moon according to their size and then count the number of craters falling into several size bins. Crater Counting: Go back to Figure 3, which is the Apollo 16 image of the moon. The smallest crater you can see in this figure has a diameter of about 0.2mm. Using the lunar image s scale factor that was previously determined calculate the actual diameter of the smallest visible crater Diameter of the smallest visible crater = km. Compare this with the diameter of the Barringer Crater by taking a ratio. Diameter of Smallest Lunar Crater/Diameter of Barringer Crater = Of course, this DOES NOT mean that there are no smaller craters on the moon s surface. It simply means that we can t see smaller craters in this Apollo 16 image of the moon. Our knowledge is limited by the quality of our observations (in this case the resolution of our photograph). In other words, based on existing data we have no direct information on the number of smaller craters and/or impacters. But we can still estimate the number of smaller bodies by finding the size spectrum of the craters we can see and then extrapolating from that data to the smaller sizes, which we cannot see. To establish the size spectrum we will follow the following procedure: We re not going to count all the visible craters in the image so we first need to choose a couple areas to sample. To do this draw a couple circles on your image with diameters between 3 and 4 cm. Locate these circles slightly off center toward the right side of the image where shadowing makes the craters easier to see. Record the diameter of your sampling circle in the attached table Then divide each of your circles into 8 sectors by drawing 4 lines through the center. This is simply to make the counting a little easier by not having to keep track of large numbers. Now count all the craters in each sector which are 1mm or less in diameter and record your count in the appropriate column of the attached table Next count all craters between 1 and 2 mm in diameter and also record this count in the table Then count all craters between 2 and 4 mm in diameter and record this count Finally count and record all craters between 4 and 8 mm. In the final column add your counts for all sectors to get the sample total for each size bin. Repeat the above procedure for your other sampling circle.

12 You have now established a pretty good estimate for the size spectrum of lunar craters. You should notice that the numbers clearly fall off with increasing size and this has a clear implication The number of small bodies is considerably larger than the number of large impacters AND in all likelihood (by extrapolation) the number of unseen bodies (via craters) is far larger that the number we can see. To clearly see this trend, make a graph of the total number of lunar craters in each bin on the vertical axis against the upper limit on the size of each bin (i.e. 1, 2, 4, 8 mm) on the horizontal axis. Graphically the trend is unmistakable the number of small impacters increases dramatically with each step. The implication is that the Earth and Moon have been struck repeatedly by huge numbers of rocks from space over their history. The moon has preserved the record of this rain of cosmic bodies but the Earth has not because of erosion and continental drift. Crater Size Bin < 1mm 1-2 mm 2-4 mm 4-8 mm Total Craters of All Sizes < 1mm 1-2 mm 2-4 mm 4-8 mm Total Craters of All Sizes Area 1 Area TOTAL Samplin g Circle Diamete r