Homework Set 4
DUE: Friday, June 21
One of the first things planetary astronomers do when they get pictures of a newly explored planetary surface is try to determine how old it is. They do this by counting all the craters in a given area, and comparing it to the number of craters found on a surface of known age. If the newly explored surface has more craters than the known surface, then it is older. If the newly explored surface has less craters than the known surface, it is younger. This is because planetary surfaces collect impacts continually. If the craters get wiped out by volcanic lava flows or the action of water, then the surface is 'young'. A surface of known age would be Apollo landing sites, where samples were taken, and their age determined by radioactive dating. Recall that there are many more smaller rocks impacting, more frequently, than larger impacts. Therefore, there are many more smaller craters than larger ones. Smaller craters can be wiped out by volcanism or water more easily than larger ones.
So if we keep track of the number of smaller craters compared with the number of larger craters on a newly seen planetary surface, we can perhaps determine the processes that wiped out the craters, making the surface young.
For this Homework Set, you are going to determine the age of a particular area of the Moon, by counting craters of different size ranges on the attached photocopy of an image of part of the Moon. The area is a Mare, called Oceanus Procellarum. By keeping track of the number of craters in four different size ranges, you will create a 'size-frequency' plot. The size-frequency plot you generate will be compared with those of parts of the Moon that have known ages. By comparing them, you will be able to determine the age of Oceanus Procellarum.
1. What is the area of the image, in square km? Use Flamsteed crater (21 km diameter), labeled 'F' in the image, for scale.
2. Carefully count all the craters that are on the image that have a size between 16 and 32 km. How many are there?
3. Carefully count all the craters that are on the image that have a size between 8 and 16 km. How many are there?
4. Carefully count all the craters that are on the image that have a size between 4 and 8 km. How many are there?
5. Carefully count all the craters that are on the image that have a size between 2 and 4 km. How many are there?
6. Calculate the SURFACE DENSITY of craters for each size bin (16-32 km, 8-16 km, 4-8 km, and 2-4 km). That means, how many craters in a given size range are there per square km?
7. Present results from 1-6 in a table, with one row for each size bin. One column for the size bin, one for the number of craters you found in that size bin, and one column for the crater density.
8. Plot the crater density vs. crater diameter. The vertical axis is the crater density, and the horizontal axis is the diameter. The horizontal axis should go from 0 - 32 km. For each size bin, choose the middle of the bin to plot the point. That means that the point for the bin from 16 - 32 km should be at 24 km, the point for the bin from 8-16 km should be at 12 km, the point for the bin from 4-8 km should be at 6 km, and the point for the bin from 2-4 km should be at 3 km. Notice that this is a log-log plot, which is why the scales for the horizontal and vertical axes are not linear. But you don't have to worry about this; just use the scaling provided in the plot, and plot the four points you have calculated. Remember, plot crater desnsity on the y-axis vs. center of the size bin on the x-axis. Refer to the attached size-frequency plot to see how it's done.
9. Compare your plot with the one provided. Is Oceanus Procellarum older or younger than Average Lunar Mare? Is it older or younger than the lunar highlands?
10. What is your best estimate of the age of Oceanus Procellarum, and how did you arrive at it?
6/18/96