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Name:______Date:______
Partners ______
Astronomy Exercise #2: The Moon's Surface
by Mary Lou West
Purpose: to become familiar with the major features of the Moon and to measure some of their dimensions. To make a simple model and then modify it to fit new observations.
Equipment: small photo of the full moon, plastic overlay, transparent tape, 3 different colored permanent marker pens, large photo pair of first and third quarter moon (in large tan envelope with Explore the Moon map, and Probes and Landings (Rukl p 193), and 5 cm cardboard window), meter stick, straight edge or ruler, Lunar Orbiter Photographic Atlas by David Bowker,
Procedure: The naked eye easily sees the dark maria on the Moon, while binoculars and telescopes reveal craters, mountains, rays, rilles, domes, and wrinkles. You will examine several lunar photographs and maps.
1. Mare Regions
A. Names of major maria (small photo)
Examine a photograph of the full moon carefully. Overlay it with the clear plastic and add some tape so that the plastic can flip up easily.You will be putting three types of labels on this plastic, so write small. Use one color pen to label the major mare regions as seen by the naked eye (Mare Crisium is on the right side). Include the mare Serenitatis, Tranquillitatis, Crisium, Imbrium, Humorum, Frigoris, Nubium, and also Oceanus Procellarum.
B. Diameters of Maria (large photo pair) Moon radius = r =______
Measure the diameters of the mare regions Crisium, Imbrium, and Tranquillitatis. These are thought to be circular regions. (But are they?) Each mare region should be measured twice, once in the tangential direction (parallel to the nearest edge of the moon) and once in the radial direction (toward the center of the moon's face). Also measure how far the center of the mare is from the very center of the moon's face. Please do not bend the large photos or put any marks on them.
Because of foreshortening on a spherical surface, the radial measurement needs to be corrected. The correction depends on how far the region is from the center of the moon's face (distance x) as compared to the radius of the moon (r). The correction (a’) to the radial diameter (a) is
a' = corrected a = a______
( 1 - (x/r)2)1/2
Make a table with columns for Mare name, b (diameter tangent), a (diameter radial), x, a', average diameter ((b+a')/2), average diameter in km, accepted value, and % error.
Note that you can use a proportion to convert the average diameter in centimeters (image) to the average diameter in kilometers (real).
any size in km = (size in cm on image) * 1738 km
(r in cm on same image)
Compare these with the accepted diameter values (Crisium 450 km, Imbrium 1080 km, Tranquillitatis 720 km). Be mindful of significant figures.
2. Craters
A. Names of Major Craters (use the small photo and overlay again)
On your small photo of the moon find the craters Copernicus, Kepler, Eratosthenes, and Tycho (note the long rays). On the plastic overlay label them with a different colored pen than the one you used for the mare regions.
B. Diameters of TwoCraters (large photo pair again)
Measure the diameters of the craters Copernicus and Eratosthenes. Convert them to kilometers and compare to the accepted values. (Copernicus 93 km, Eratosthenes 58 km)
C. Height of crater rim and central peak
For tall features near the moon's terminator (edge of daylight) the height (h) of the feature can be determined from a measurement of the feature's shadow length (s) and the distance (d) of the feature to the terminator.
h = s * d * 1738 km
r * r
On crater Eratosthenes you can measure the shadow of the crater rim on the floor, and also measure the shadow of the central peak on the floor. Convert these to kilometers and compare with the accepted height values (rim 3 km, peak 1 km)
Look at other craters. Are the crater floors the same level as the surrounding terrain or are they depressed? ______
Look at other craters with central peaks. Do the peaks extend above their rims or are they shorter? ______
3. Cratering Rate
Since direct dating of rocks (by their radioactive decay) is possible for only a very small sample of material from other worlds, we must calibrate and use an indirect method such as crater density to get a rough idea of the ages of various areas on the moon.
A. Apollo Landing Sites: Simple Model (small photo again)
Mark on your overlay of the small photo the landing sites of Apollo astronauts. Use yet another color pen. Why is there no Apollo 13 site?
Use the Lunar Orbiter Photographic Atlas by David Bowker (QB 595 .B67 1971, oversize) to count the craters visible in a 10 km x 10 km area near the Apollo 14, 15, 16, and 17 sites.
If a region gets resurfaced by lava or by erosion sediments then the old craters on it get erased. Since new craters form randomly, a young surface should have fewer craters on it than an old surface has. How many craters should a really fresh surface (age = 0 years) have? ______
After the Apollo 14 astronauts returned to Earth, physicists dated their moon rocks at 4.0 billion years old. A simple model could then be made to calibrate cratering rate with age. Make a graph with the horizontal axis being time from 5 billion years ago to now, and the vertical axis being craters/area. Plot the points for age = 4 billion years, and for age = 0 years. Use a ruler to draw a straight line through these points. With this model we can predict the ages of rocks returned by further Apollo missions. Put these "simple model ages" in your data table.
B. Apollo Sites: Modified Model
After the Apollo 15 astronauts returned rocks to Earth and their ages were determined radioactively, astronomers realized that the simple linear model of crater density vs. age was inadequate (wrong). Missions 16 and 17 corroborated these findings. From the instructor get the actual radioactive ages for the Apollo 15, 16, and 17 regions, and plot these points on your graph. Connect the five actual points with a smooth curve rather than a straight line. Since the rate of cratering is the absolute value of the slope of this curve, what has happened to the rate of cratering over the last several billion years? ______.
C. Applying the Modified Model (large photo pair again)
We can apply this modified model (curved line) of crater density vs. age of surface to both mare and highland regions at other places on the moon than just where the Apollo missions landed. Use a 5 cm x 5 cm cardboard window to count craters on a highland region ______,
and also count the craters on a mare region ______.
The ratio of mare craters/ highland craters is ______. If the heavily cratered highland region is 4.0 billion years old, then how old is the mare region you just examined? ______.
Hint: on the curved line (modified model) how long did it take for the number of craters/ km2 to fall to the same fraction?
4. Discussion Questions
A. Make a small sketch of the Man-in-the-Moon, the Lady-in-the-Moon, and the Rabbit-in-the-Moon.
B. What are the English names of the major maria?
C. Discuss reasons for your errors in mare and crater diameters and in rim and peak heights.
D. Make a scale drawing of the side view of the crater Eratosthenes.
E. Why do you think the cratering rate changed over the last several billion years? How could we check out this idea?
F. What assumptions are you making in 3C above (applying the modified model to different regions of the Moon)?
Nearly full moon taken in Burlington, Vermont, July 21, 2013, by David West