GEOL212 Due 10/1/18 Homework V

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1 GEOL212 Due 10/1/18 Homework V General instructions: Although you are allowed to discuss homework questions with your classmates, your work must be uniquely your own. Thus, please answer all questions in your own intelligible words. (When in doubt, use complete sentences.) If calculations are involved, show all work (so that I will have some basis for giving partial credit.) Be sure to use appropriate units and significant digits, where appropriate. Impact geochronology: It is intuitively obvious that the older a landscape is, the greater its opportunity to accumulate impact craters. Thus, the counting of impact craters is a useful means of comparing the ages of regions on planetary bodies that can be photographed from space. For questions 1-4, refer to the attached images from Google Mars showing: a.) Gusev Crater (Where the Spirit rover operated from 2004 until 2010) and its surroundings. b.) Part of the margin of Amazonis Planitia northeast of Gusev. 1.) Begin with the Amazonis image. Identify all unambiguous craters. Using a ruler, measure their diameter to the nearest km (you will have to approximate in many cases), and note the diameter in km in a list. (You will want to use Excel for this.) Draw an X over each crater that you measure. Measure only unambiguous craters. If you re not sure a feature is a crater, ignore it. You ought to be able to identify craters down to 4 km in diameter. (2mm in the image.) Plan to spend some time on this. When you are done, sort your list by crater size. NOTE: Everyone will do this slightly differently, depending on which craters you identify and how you measure them. Still, do your best to collect good data. If you don t, your answers to later questions might be distorted. (GIGO) In the table below, indicate, for each diameter category, the cumulative number of craters equal to or larger than that amount. (For diameter 2, you would indicate actual the number of craters on your list with diameters greater than or equal to 2 km.) Then indicate the cumulative frequency of craters. Obtain this by dividing the cumulative number by the number of square kilometers in the image. (Each image covers 40,500 km 2 ). Use scientific notation where appropriate.

2 Crater diameter (km) Cumulative number Cumulative frequency ( = cumulative number / 40,500 km 2 ) =>4 =>5 =>6 =>7 =>8 =>9 =>10 =>20 =>30 =>40 =>50 =>60 =>70 =>80 =>90 =>100 STOP AND CHECK, are your numbers cumulative? If any cumulative number is smaller than the number in the row below it, it is wrong! For example: If there are 6 craters => 8 km., then there must be at least that many => 7 km. 2.) On the attached log/log graph paper, plot the cumulative frequency / km 2 against crater diameter. Be careful not to get confused! 2 x 10-4, for example, is twice as big a number as 1 x x 10-3 is ten times as big.

3 3.) Now repeat the above steps for Gusev. This will take longer because there are more craters. Crater diameter (km) Cumulative number Cumulative frequency ( = cumulative number / 40,500 km 2 ) =>4 =>5 =>6 =>7 =>8 =>9 =>10 =>20 =>30 =>40 =>50 =>60 =>70 =>80 =>90 =>100 4.) Plot these cumulative frequencies on the log/log graph. 5.) For any size class, which region has the higher cumulative frequency values, Gusev or Amazonis? In very simple terms, what does this imply about their relative ages? 6.) As plotted, are your cumulative frequency curves for these regions roughly the same general shape? What does this suggest about the size distribution of available impactors during Gusev and Amazonis times? I.e. was the size distribution the same, or did it change between these times? If it changed, describe the change in simple terms.

4 7. Figure 4.27 of your text (page 151) shows calibrated cratering curves for the Moon and Mars, allowing us to infer numerical ages of landscapes. What kind of data is used to calibrate the lunar cratering curves? 8.) How are the Martian curves calibrated? Which calibration do you consider more trustworthy? 9.) Your text s 4 Ga (billion year) and 3 Ga curves from figure 4.27 are indicated on the graph paper provided for the interval of km diameter. Based on your crater counts, is the Amazonis region younger or older than 3 Ga? 10.) Based on your crater counts, is the Gusev region older or younger than 4 Ga or 3 Ga?

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