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4. Part I Craters on the Surface of the Moon 4.1 Curvature of the Moon Begin viewing the Lunar images PowerPoint. Figure A is an image of the Lunar Highlands taken with a telescope. There is a three inch by three inch grid overlaid on the image for reference. Remember that impact craters are all roughly circular in shape when viewed directly from above. Now compare the looks of the craters in the three inch grid to those farther out at the edge of the Moon (on the limb). From your viewing point do the craters on the limb appear circular or oval in shape? • Use this piece of viewing evidence and state and argument for the Moon being spherical 4.2 Relative Age of Clusters of Craters When impacts occur the new craters will be made obliterating any older craters that were already there before. This can make clusters of craters appear layered. By surveying the damage that new craters make to older existing ones, we can tell the younger craters from the older. • Choose a cluster of craters in Figure A in which you can determine the relative age of a minimum of four craters. • Draw the cluster in the box below and label the craters from oldest to youngest. 64
4.3 Cratering Rate Counting craters is a way that astronomers estimate the age of celestial surfaces. The Moon is of particular interest because in this one case we actually have verified the age of the Lunar Highlands and Maria by radioactive dating of samples of rock brought back by the Apollo and Luna Missions. Scientist found that the Highlands are nearly as old as the solar system itself. Their scars contain a record of the conditions of the solar system early in its formation-up to 4.5 billion years ago. The Maria, by contrast, formed about one billion years later. At their formation, lava flows masked over the old scars making a smooth surface. Consequently they contain only the impact record of the last 3.5 billion years and have lost the record of the first 1 billion years. Now we contrast these two surfaces and we ask the question has the rate of meteor impacts been constant through out the history of the solar system, or is it changing and if so how? To contrast the Highlands and Maria, two images are marked with a three by three grid. Figure A has a grid for the Highlands image, and Figure B has a grid for the Maria. The two grids cover the same square kilometers of moonscape. Choose the tiniest crater that is still clear to see and count all craters in the three by three grid that are that tiny size or larger. If a crater extends out of the grid, count it if the center of the crater is on or inside the grid lines and leave it out if the center falls outside. • Number of craters in the grid on the Maria (Figure A) = Number of craters in the grid on the Highlands (Figure B) = Scientist believe that impactors strike the Moon's surface at random and no particular region of the Moon is more favorable to impacts than any other over time. Consequently we can get a gauge of the number of craters that formed in only the first 1 billion years if we subtract the number of craters in the Maria grid from the number of craters in the Highland grid. Thus the average cratering rate for the first 1 billion years is: Craters in Highlands - Craters in Maria craters/billion years And similarly the average cratering rate for the last 3.5 billion years is:
craters/billion years Craters in the Maria = 3.5 Compare these two cratering rates. What can you conclude about the cratering rate in the early history of the solar system versus the rate in the last 3.5 billion years? What does this mean about the conditions that existed in the first 1 billion years after the solar system's formation? Suggest a way to improve the calculation of the average cratering rates for the highlands and Maria of the Moon: 4.4 Relative Sizes of Craters In this section you will try to get a feel for whether the size of the average impactor is changing over time. First you need a way to measure the size of craters. To do this Look at Figure C in the PowerPoint. The large crater is Plato and it has a diameter of 109 km. Use a ruler to measure the diameter of Plato in millimeters on your computer screen. Note the crater looks oval in shape. • Why is the long axis the true measure of the crater's diameter? Now divide the known diameter of Plato in km by the measured diameter in millimeters: this will give you a scaling factor. Scale = Diameter in km = km/mm Diameter in mm This is the scale of km/mm measured on the image. Now return to image A and pick the five largest craters whose center at least falls in the grid marks. Measure their diameter with the ruler and multiply this by the scale factor to determine their actual diameter.
Five Largest Craters in the Highlands (Figure A) Diameter on image Actual Diameter Largest Craters In millimeters In km Crater 1 Crater 2 Crater 3 Crater 4 Crater 5 Now do the same for Image B which is the Maria. Five Largest Craters on the Maria (Figure B) Largest Craters Diameter on image Actual Diameter In millimeters In km Crater 1 Crater 2 Crater 3 Crater 4 Crater 5
Now survey the five largest craters in each group and find the crater with the median size diameter. This will eliminate the stray, one-time, large impact that might skew the data. Compare the median crater's size for the Highlands to the median crater's size for the Maria. How do their diameters compare? Remember that the diameter of the impactor is about one tenth the diameter of the crater that it makes once it strikes the surface. Using this fact what can you conclude about the size of the average impactor in the first 1 Billion years of the solar systems formation compared to that of the last 3.5 billion years? 5. Part II: The Height of a Lunar Mountain By measuring the length of a shadow cast by a mountain on the Moon and using simple geometry we can calculate the height of the mountain. In Figure D the large crater is again Plato which has a diameter of 109 km. Measure the diameter (long axis) with a ruler in millimeters. Again calculate a scale factor just as in section 4.4. = km/mm Scale = Diameter in km Diameter in mm Next measure the length of the shadow, S, of the large mountain below the crater on your image in millimeters and convert to km by multiplying by the scale factor. S = Length of Shadow = mm = km. Study the following diagram:
To calculate the height of a Lunar Feature consider the following geometry: Sun Light h = height of Mountain S = length of shadow Stan (0) Where for in degrees: @ Distance to Terminator 360° 2TR Terminator Notice the height of the mountain his given by h = Stan (0) You measured S and still need to determine e. Study the diagram and convince yourself that the angle between the direction of the sun's light as marked and the shadow is the same angle between the terminator and R an arrow with length equal to the radius of the Moon extending from the center of the Moon to the base of the mountain. A simple ratio will allow us to determine e if we can measure the distance separating the mountain and the terminator of the Moon. Let t = the distance from the base of the Mountain to the terminator. Measure t on the image and convert to km using the scale factor: t = mm = _km Use the following ratio to calculate in degrees: in degrees = 360° 21TR the Moon, is 1738 km. Where t is in km and R, the radius Solving for e 60
e = degrees Now the height of this mountain on the Moon is h = Stan (0) h = km Compare the height of this Lunar Mountain to the heights of mountains in these ranges on Earth: Himalayas are about 8 km in height. Rockies are about 3 to 5 km in height Appalachians are about 1 to 2 km in height. Texas Hill country hills are about 0.5 km in height Mountains of which range would have similar heights as the Lunar Mountain? Bonus: Use this same technique to determine the maximum height of the crater wall for Plato crater. Length of the longest part of the Shadow, S: S = mm = km Lett = the approximate distance from the base of the crater rim to the terminator. Measure t on the image and convert to km using the scale factor: mm km Use the following ratio to calculate e in degrees: in degrees = 360° 2TR Now the height of the crater wall is h = Stan (0) h = km How does the height of the crater wall compare to the height of the Mountain? 70