Impact Craters
| List the names of all participating team members for this lab. _______________________________ _______________________________ _______________________________ _______________________________ |
Big Idea: The Moon is a beautiful example of the tumultuous beginnings of our Solar System. The surface of the Moon is littered with impact craters, from a time when smaller Solar System objects called planetesimals impacted the surface of the Moon. Because events like these occurred in the early Solar System, many millions of years ago, we don’t have direct observations of the processes or objects that formed them. Astronomers rarely have an opportunity to perform direct experiments, but today you will study the process of cratering by forging your own impact events. You will simulate an impact crater by dropping a small metal “impactor” into a bin with sand.
- Laptop or computer with web browser
- Box of sand, rulers, impactors, colored powder
- Digital scale (located at the back of the classroom)
Part 1. Exploration
Depending on the specific circumstances, an impactor will create a crater in a target material principally due to one of four processes:
- Splash (avalanche): crater diameter set by how much material falls in around impactor.
- Thud (surface crack/pulverization): crater diameter set by surface disturbed by impactor.
- Crunch (compression): crater diameter set by material crushed beneath impactor.
- Spray (excavation): crater diameter set by material thrown outwards by impactor.
- Carefully observe a stainless steel ball falling from 50 cm onto the sand in the bin, as measured from the top of the sand surface. Try this several times. Be sure to drop (don’t throw) the impactor from above the bin. Before each impact “reset” your sample sand surface by covering and shaking the sandbox vertically up-and-down several times (without spilling sand). Be sure to shake the sandbox vertically up-and-down and not side-to-side. To view the crater structure, it can help to shine a light from the side to cast shadows (just like how we view craters on the Moon).
Discuss in your team the hypothesized process(es) of crater formation (“splash, thud, crunch, or spray.” Briefly explain what you observed to support your choice(s). Do not worry about guessing the “correct” answer, this is just a preliminary hypothesis. Note any dissenting opinions amongst your team.
| Sand crater process hypothesis: Explanation of your choice: |
- How to measure an impact crater is a qualitative decision, but it is important to be consistent with how you measure. Briefly describe a step-by-step procedure for measuring the diameter of impact craters that you can apply consistently and use throughout this lab. You can include a sketch of how to identify the crater edge.
- Choose a single metal ball and measure its mass. Drop the impactor into the sand box from several different heights ranging between 10 cm and 2 meters or more. Make at least three drops for each height in order to test for consistent results. If results are not consistent, make more drops. List all your trials from the same height in the column “Crater diameters (cm).” Be sure to use these units throughout!For each drop height, calculate the impact energy (in kiloergs) = (mass, in g)*(height, in cm), and the average crater diameter. (Example, a 50 g impactor released from 20 cm would have 50*20 = 1,000 kilergs of impact energy.) Try enough drop heights that you complete the entire table.
| Mass of impactor (g) = | |||
| Drop height (cm) | Impactor energy (kiloergs) | Crater diameters (cm) | Avg. crater diameter (cm) |
- Create a plot with “Impactor energy (kiloergs)” on the vertical (y) axis and “Avg. Crater Diameter (cm)” on the horizontal (x) axis and attach it to this lab. You may use the graph paper on the next page, or a spreadsheet such as Excel or Google Sheets. In Excel, after you make a scatter plot, right click on the numbers on each axis, choose “Format Axis” and select “Logarithmic scale” to change from a linear to log scale.)
Astronomers often search for relationships that span large ranges (many factors of 10). Often a simple line (y = a x + b) does not describe that relationship well, but instead there may be a power-law relation between two variables (y = a xp). When a power-law relation is plotted on a log-log graph it appears as a straight line. If you take the log of both sides of a power-law relation you get log y = p log x + log a, which shows a linear relation between log x and log y.
- Use a trendline or a ruler to fit a straight line to your data. Determine the log-log slope and y-intercept of this line on the log log plot and record it below.
Part 2. Does the Evidence Support a Hypothesis?
Consider the research question: “How is the energy of an impactor related to the diameter of an impact crater?” The “splash, thud, crunch, and spray” models describe different crater formation processes, but they can also be expressed mathematically.
Imagine a simplistic model of an impact where the impactor excavates a volume of material in a vaguely spherical shape, a “spray.” The volume of materials is proportional to the diameter of the crater. The amount of energy used to lift the material is proportional to the mass of material and the height that material was lifted. As mass scales with volume, and the crater height scales with diameter (larger craters are also deeper), the energy used to lift the material will scale as D3 x D = D4. For a “splash” we would expect that energy is proportional to crater diameter, E ~ D4, or a power-law with a power of 4. A plot of log E vs log D for the “splash” process would be a line with a slope of 4.
Similarly, the “crunch” process will compress the crater volume beneath the impactor. In this case the energy scales as the compressed volume which scales as the crater diameter cubed: E ~ Volume ~ D3. The “thud” process is defined by the case in which the energy scales with the surface area of the crater: E ~ D2. And for the “splash” process the material that falls in scales with crater diameter, so E ~ D1.
- Suppose a fellow student proposes the generalization, “The diameter of the crater is proportional to the energy of the impactor.” Based on the data that you collected, do you agree or disagree with the generalization? Explain your reasoning and provide specific evidence from the data to support your reasoning.
- Examine the power law (or log log slope) of your “Impact Energy vs. Crater Diameter Log-Log Graph” from Part 1. Does the data that you collected support or refute your original cratering process hypothesis? Explain your reasoning and provide specific evidence from the data to support your reasoning.
Part 3. What Conclusions Can You Draw From The Evidence?
Say that a student tried to determine, “What is the effect of changing the mass of an impactor on the diameter of a crater?” by dropping different mass impactors from the same height of 20 cm, and recording the following data in the table below.
| Impactor mass (g) | Crater diameters (cm) |
| 10 | 3.0, 3.0, 2.8, 3.0, 2.5 |
| 20 | 3.0, 3.8, 3.3, 3.5, 3.5 |
| 50 | 3.5, 4.2, 4.9, 5.1, 5.0 |
| 100 | 5.2, 5.0, 5.5, 5.0, 5.4 |
| 250 | 6.0, 7.0, 6.2, 5.8, 5.9 |
| 500 | 7.0, 8.8, 8.2, 7.5, 8.0 |
- What conclusions and generalizations can you make from just the data in the table above? Explain your reasoning and provide the specific evidence you are using, with sketches or graphs if necessary, to support your reasoning. Also state any assumptions in your reasoning.
- Which factor — impactor mass or drop height — is more important in determining the diameter of the resulting impact crater? Explain your reasoning and make reference to your previous answers.
Part 4. What Evidence Do You Need to Pursue a Question?
Recall that you covered your sandbox and shook it vertically up-and-down between each drop to consistently “reset” your sample. Consider the following claim: “If the sandbox is shaken side-to-side between each drop, the sand grains will sift and settle, becoming more tightly compacted for the next drop from the same height.” Describe precisely what evidence you would need to collect in order to answer the research question of, “How does a ‘side-to-side reset’ for medium-grain sand affect the results of each subsequent drop from the same height?” Do not actually do the steps in the procedure, only describe them below.
- Create a detailed, step-by-step description of the evidence you would need to collect and a complete explanation of how this could be done. You might include a table and sketches. The goal is to be precise and detailed enough that a classmate could follow your procedure.
Part 5. Formulate a Question, Pursue Evidence, and Justify Your Conclusion
Your task now is to 1. design an answerable research question about the characteristics of impact craters that you have not completed before, 2. propose a procedure to pursue the evidence you need, 3. collect data using the tools you have previously used in this lab, and 4. create an evidence-based conclusion. The format for your research investigation is provided below.
Your instructor must read and approve your research question and procedure before you begin collecting evidence.
Specific research question:
Step-by-step procedure, with sketches if needed, to collect evidence:
Data table and/or results (use additional pages if needed):
Evidence-based conclusion statement (including assumptions):
