Proposal 1--Deep Impact: Meteoric Effects on the Lunar Surface

This topic submitted by Charlotte Bornhorst, Robyn MacConnell, Sara Robinson, Kate Weiland (bornhocs@muohio.edu, macconrs@muohio.edu, indygrl581@msn.com, weilankl@muohio.edu) at 9:09 PM on 9/27/02. Additions were last made on Monday, November 21, 2005. Section: Cummins

Natural Systems 1 Fall, 2002 -Interdisciplinary Studies-Miami University

Deep Impact: Meteoric Effects on the Lunar Surface

The question that our student generated lab poses is as follows: do the size, mass, velocity, and angle with which meteors strike the moon determine the shape, size, and complexity of lunar craters? Using basic mathematical principles, we have made several predictions to answer our question. We predict that the size, mass, and velocity of the meteor affect the size (diameter and depth) of the lunar craters. We also predict that the angles at which the meteors strike the moon determine the shape (elliptical or circular) of the lunar craters. We propose that those meteors with a higher velocity and greater mass will result in deeper and more complex craters upon impact with the moon. In order to stay focused, we will be researching five craters: Aristoteles, Copernicus, Tycho, Timocharis, and Theophilus. By studying the impact that meteors have on the moon, we hope to understand which factors affect the way craters are created. We primarily want to discover which, if any, of the factors including size, mass, angle, and velocity of the meteors affect the size shape and complexity of the craters they form. We chose this topic because our group had a common interest in astronomy, and we all agreed that the moon would be a highly visible subject. Instead of viewing the moon as an aesthetically pleasing object that is only useful to werewolves and the hopeless romantics, we hope to realize the science and history of its rocky past.

Crater History:

Craters have been a source of fascination for moon gazers for centuries. When observing these formations, one must take into consideration that there are two ways in which lunar craters are formed. Some were formed by volcanic explosions, which blew the rocks of the moon outward and resulted in lava flows and craters. However, the topic of our experiment will focus exclusively on the second type of craters, which were formed by meteorites striking the surface of the moon.

Compression Stage
When a meteor strikes the moon, it trnsfers its kinetic energy to the surface it hits. The equation KE=1/2 mv*v shows us that the kinetic energy is conserved during impact, which means that the energy is not lost, only transferred. The results of this energy transfer cause a shock wave through the lunar surface, melting or vaporization of both the impactor and target material, and the energy and momentum move and disrupt the lunar surface material. For a meteoric crater to form, three stages must be fulfilled. The first stage is the compression stage. When the meteor impacts the surface, it punches a small hole, which results in a shock wave through the lunar surface. The pressure that is created by the conversion of energy from simply kinetic energy to a combination of kinetic and heat energy causes material from the impact site to become fluid like. During the compression stage, very little material is actually projected out of the impact site. The compression stage is the shortest of the three stages, and the time of impact can be calculated by taking the impactor's diameter divided by its speed at impact, or D/d.

Excavation Stage
The second stage in the formation of a crater is called the excavation stage. During this stage, the crater grows to a very large size in a very short amount of time. The shock wave that was produced in the first stage rises to the surface of the moon, and transfers its energy with it. When the wave reaches the lunar surface, the material is ejected upwards in a cone shaped form. This material is called ejecta, and it is composed of hot vapor, melt droplets, and fine debris. Also included in this mix is breccia, which is different lunar rocks melded together. The original cone is then dispersed in a hyperbolic pattern and lands around the crater forming the ejecta blanket. The excavation stage lasts longer than the compression stage, and it equals the square root of the diameter of the impactor divided by the acceleration due to the gravity of the target.

Modification Stage
The third stage in this three-part process is the modification stage. In this portion, the loose material that was ejected from the crater will slide down the rim of the crater resulting in the possible formation of terraces and/or a central peak. The modification stage will last for approximately the same amount of time as the excavation stage. Basically, the modification stage is simply the settling of the ejecta from the impact.
There are different types of craters that vary due to shape, size, and complexity. Larger craters generally have a diameter of 20 to 30 km and have flat floors and wavy edges. Craters that are between 30 and 40 km in diameter are either regarded as simple craters or complex craters.

Literature Review:
Other scientists have researched lunar craters and have come to a conclusion that the average velocity with which a meteor strikes the moon is 20 km/sec. This high velocity causes the size of the crater to be 10 to 20 times larger than the size of the object that caused it. Due to the fact that scientist believe that the surface of the moon has remained unchanged for the last 4,000 million years, they are able to record data on craters which were formed years ago, but remain the same today.
The earliest scientist to view the lunar surface with the help of a newly invented optic tube was Galileo (1609). This tube allowed him to see the lunar surface in more detail and be able to make descriptive observations for his data charts. He challenged long-held Aristotelian beliefs regarding the perfect nature of celestial spheres, which resulted in extreme friction between him and the Catholic Church. Galileo published five books with rough sketches of lunar craters, which spurred on the development of more accurate moon maps by other scientists. Thanks to Galileo's pursuits, scientists were able to view the moon through a telescope and research its surface more precisely.
In 1829, a German scientist by the name of Franz von Paula Gruithuisen made predictions about the cause of craters on the lunar surface. He was the first to suggest that the craters were formed through meteoric impact. He believed that spherical bodies hit the moon and then sank into the surface under their own weight to cause the depressions we can see from earth. He believed these objects to be circular because the edges were scraped off leaving circular walls.
The American geologist Grove Gilbert created experiments with clay in order to represent the formation of lunar craters. As an experiment, he dropped balls of various sizes and shot bullets from a pistol into a clay and sand target. The resulting indenture was a mini model of the craters one can find on the moon. He computed that the average angle of meteoric impact on the moon would be about 45 degrees. He argued that due to this fact all the moon craters would be elliptical or oval.
Eugene M. Shoemaker, a well-known scientist focusing on the moon, gave reasoning in 1969 for the formation of craters on the moon by impacting meteors. Even today, it remains a controversial issue among some scientists as to whether the craters were formed by meteoric impact or through volcanoes. By comparing craters formed by volcanoes on earth to lunar craters, he gathered much data on the differences of these two types of craters and proved his point that the lunar craters were mainly formed by meteoric impact. His argument included that the size differentiation of the meteoric craters varied greatly, whereas volcanic craters are generally within the same size range. Shoemaker also pointed out that volcanic craters are in a systematic formation, whereas moon craters are scattered randomly.

Library Sources:
1) North, Gerald. Observing the Moon: The Modern Astronomer's Guide. Cambridge:
Cambridge University Press, 2000. This book provides background information and
maps which are helpful in finding craters. It also gives information along with tips on how
and when it is easiest to view each crater through a telescope.
2) Hoyt, William Graves. Coon Mountains Controversies: Meteor Crater and the
Development of Impact Theory. Tucson: The University of Arizona Press, 1987. This
source gives information about scientists in the past who have researched and/or made
discoveries about the moon.
3) Cook, Jeremy. The Hatfield Photographic Lunar Atlas. London: Springer, 1999. It
provides detailed maps of the moon.
4) Cooper, Bonnie et al. The Moon: Resources, Future Development and Colonization. Chichester: Praxis Publishing Ltd., 1999. This book provides us with useful
information about physical features of the moon. These features range from craters to
mountain ranges and basins.
5) Wlasuk, Peter T. Observing the Moon. London: Springer Verlag, 2000. This book
provides a map key with latitudes and longitudes in order to find the craters we will be
studying.
6) Moore, Patrick. The Moon. New York: Rand McNally and Company, 1981. It
contains photographs and maps of the moon. It gives us a reference point when we are
searching for the craters through the telescope. It also includes information on craters on
the visible side of the moon.
7) Kitt, Michael T. The Moon: An Observing Guide for Backyard Telescopes.
Waukesha: Kalmback Books, 1992. Each of our craters is described in this book. It
includes the best times to see the craters and special features of each one.
8) Spudis, Paul D. The Once and Future Moon. Washington: Smithsonian Institute
Press, 1996. It gives background information on craters and detailed descriptions of how
craters are made. There is also some information about scientists who have studied
craters.
9) Leonardi, Piero. On the Origin of the Lunar Craters. Italy: Universita di Ferrara,
1967. It describes the origin of craters and how they are formed and how different factors
impact its formation.
10) Waters, Aaron Clement. Moon Craters and Oregon Volcanoes. Eugene: Oregon
State System of Higher Education, 1967. It had a lot of articles concerning the controversy
over the origin of moon craters (e.g. either volcanic or meteoric).
11) Adams, Peter Joseph. The Moon: the nature of its surface, its geology, origin and
history, as inferred from recent researches with telescope, spacecraft, and astrophysical
techniques. London: H.M.S.O., 1968. This book is a very useful source because it
describes in depth about the surface layers of craters. It has numerous photos and
information on various semi-recent published research.
12) Pike, Richard J. Geometric Interpretation of Lunar Craters. Washington: US
Government Print Off, 1979. This book is useful because it has detailed plans about the
structure and shape of certain craters. There are also many pictures with specific
details.

Internet Sources:
1) "Craters." The University of Michigan Astronomy Department. Online. 26 Sept. 2002. http://www.astro.lsa.umich.edu/Course/Labs/craters/cr_intro.html It explains how the flour lab works and gives important equations that should be used to fill in the data charts.

2) "Impact Craters on the Moon."Enchanted Learning. Online. 7 Sept. 2002. http://deepimpact.jpl.nasa.gov/science/cratering.html">http://deepimpact.jpl.nasa.gov/science/cratering.html">http://deepimpact.jpl.nasa.gov/science/cratering.html This is a very good source of pictures and it also explains the different stages of crater formation very well.

4) "Planetary Impact Craters." NASA. Online. 17 Sept. 2002. http://rasc.larc.nasa.gov./rasc_new/rasc_fy01_top/CAPS_Overview.html This is the NASA website that gives information about current NASA goals, missions, and real threats of striking meteors.

5) Marsden, Brian. "Eugene Shoemaker (1928-1997)." NASA. Online. 25 Sept. 2002. http://www.jpl.nasa.gov/s19/news81.html It has a detailed description of the life of Eugene Shoemaker, who is mentioned in several other important literatures.

Materials and Methods

Our experimental design involves: careful observation using the Miami University telescope, several experimentations which require launching projectiles against a flour bed, and in depth research on other scientists and their studies.
We will use the university telescope to view our five craters and use the micrometer to take measurements of them. We will take pictures using the telescope, which will be incorporated into our class presentation and final report.
Our flour lab will be used to represent the formation of craters on the moon. We will place a bed sheet on the concrete outside and spread a five centimeter layer of flour on top of it. The projectiles we will use are: an irregular marble, a spherical marble, two random rocks, a sticky-tack ball, a ping-pong ball, a golf ball, a billiard ball, a tennis ball, and a medicine ball. We are using balls of varying weight, shape, and size so that we can get a well-rounded data chart that will show us how these different factors affect the shape of the resulting craters. The ratio we are planning on using is 1km: 1cm. We derived this ratio from the fact that a crater's diameter is about ten times that of the impactor and its depth is 1/5 of the craters diameter. At first, we will drop the objects from a height of 30cm, 60cm, and 90cm directly perpendicular to the flour base. After recording the data, we will throw the objects from an angle of 30 degrees and 60 degrees and use a stopwatch to record the amount of time it takes for the object to hit the flour. After each throw we will measure the diameter and depth of the resulting crater and make a few quick sketches of its shape. We know that the size of the crater is related to the energy of the impacting object. Therefore, we will use the Power Law (D=k*E^n) where D is the crater diameter, k is an unknown constant, E is the energy (KE and PE) of the meteor, and n is an unknown factor that describes the dependency of the crater diameter on the energy of the meteor. To find out how the diameter of the crater scales with energy, we can use the equation E=mgh. Through this data we can make a graph and table of the crater diameter as a function of energy. Because a simple graph of this relationship would result in a curvy line since n is the exponent, we will plot it using log(diameter) vs. log(energy) so that we get a straight line. This would make it easy for us to find n, which would simply be the slope of the line. To find the constant k, we will take one data point on the graph and plug it into the equation D=k*E^n. At the end of our thorough experiment, we will have extensive data charts, sketches, and graphs.
At the beginning of class, we will give a quick multimedia presentation on the background of moon craters and how they are formed. Thereafter, we will ask the class to perform an easier version of our experiment as part of our interactive class presentation. We will divide the class into four groups and give each group different objects. One group will be assigned the ping-pong and golf ball. The second group gets the tennis and the billiard ball. The third group gets the marble and the irregular marble. The fourth group is assigned the sticky-tack and the irregular rock. We will explain how to do this experiment during our presentation and pass out a data chart as an aid (see attachment).

Flour Lab Data Chart

We will also do extensive research on other scientists' observations and research. We will use some of the precise data they have collected over the years and compare their results to the data we collect through our own independent experiments and observations. Through this comparison, we will be able to see how accurate our data results are.

Larger Relevance
The larger relevance of our research is to understand and show how meteoric impacts affect land surfaces. We could take our collected data and information and see how it would relate to surfaces on the earth. We would be able to hypothesize what would happen if a meteor would hit the earth and what shape, size, and complexity the crater would be. Even though we are not going into detail about the dust cloud that would result from such a large impact, we would still be able to understand the basic physics behind the formation of such a large crater. We could take our research data and show how the size of a meteor affects the resulting crater and what that would mean in relation to the size of the earth. In a less abstract take on it, we will learn how much velocity, size, shape, and angle at which an object hits a target actually affects the surface it strikes. In context of the moon, we will be able to figure out how large the meteors were that formed specific craters that we are studying. This data could also help us to hypothesize how large a meteor would have to be to wipe out the whole moon!

Our Craters

Aristoteles

Copernicus

Theophilus

Timocharis

Tycho

Timetable:
The first week of October--the group will be taught how to use the telescope so field
research can begin.
Friday, October 11--Use telescope to view and measure Tycho, Aristoteles, Timocharis,
and Theophilus.
Saturday, October 12--Use telescope to view and measure Tycho, Aristoteles,
Timocharis, and Theophilus because it is one of the few days one can see Theophilus.
Tuesday, October 15-- Use telescope to view and measure Tycho, Aristoteles,
Timocharis, and Copernicus.
Thursday, October 17--Meet at science library to review notes from crater observations and
see if more research is necessary.
Friday, October 25-- Use telescope to view and measure Tycho, Aristoteles, Copernicus,
Timocharis, and Theophilus because it is one of the few days to best view Copernicus.
Saturday, October 26--Kate's birthday, day off!
Sunday, October 27--Group members will perform flour lab.
Tuesday, October 29--Meet to discuss the results of the flour lab and compare and contrast
to moon observations.
Tuesday, November 5 --Meet to plan for class presentation.
Thursday, November 7 --Meet to finalize plans for presentation to class.
Saturday, November 9 --Use telescope to view and measure Tycho, Aristoteles, Timocharis,
and Theophilus.
Wednesday, November 13--Use telescope to view and measure Tycho, Aristoteles,
Timocharis, and Copernicus.
Thursday, November 14--Classroom presentation and interactive flour lab experiment.
Sunday, November 17--Meet to finalize lab report and incorporate data from classroom
involvement in experiment. Write final essay and finish the whole lab!
Friday, November 22--PARTY! The lab is finally over!