University of Michigan - Department of Astronomy

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Version: discussion


Craters

Watch out! The sky is falling, the sky is falling!

-- Chicken Little

Overview


Introduction

One look at the surface of the Moon should convince you that "empty space" is not so empty after all. There is actually a wide range of objects floating between the planets, from tiny particles to asteroids that can be a hundred miles across, debris left behind when the planets were formed. These objects can be perturbed from their orbits (by a close passage by a planet, a passing star, any number of things) and onto paths that cross ours -- or any other planet or moon. When that happens, a collision occurs and an impact crater is formed.

Impacts should occur roughly equally on all solar system bodies. However, on geologically active bodies like Earth, craters are regularly erased by the geologic activity. On bodies with an atmosphere (again like Earth), erosion can also slowly wear away the craters. This can help us determine the relative age of the surface, since the craters are erased whenever the surface is re-made. See the Geologic Age activity for more on relative dating methods.

The size and shape of the crater depend on the impactor: its size, shape, speed, and the angle is hits the ground with. Specifically, the size of the crater depends on the energy of the impactor. However, the relationship is not linear, but rather is a power law:

eqn. 1diameter=k times E to the nth power

where D is the diameter, E is the energy of the impactor when it hits the ground, n is the power, and k is a constant. In part one of this lab, you will use a model to determine what k and n are.

The energy when the impactor strikes the ground is all kinetic,

eqn. 2kinetic energy =1/2 m v-squared

where m is the mass of the impactor, and v is the speed it's going when it hits the sand.


Part 1: Make Some Craters

Your GSI will give you a box of sand, a jar of sand with a contrasting color, a ball bearing, and at least one other object. Try making a few craters before getting into the activity to get a feel for what you need to do to get a few nice and different craters without spraying sand all over your neighbors or hitting anyone with the ball bearing. ALso make sure you can get the ball bearing back without completely destroying your crater. You may want to try placing the box on the floor so you can get different heights easily, and try throwing the ball bearing at an angle to get oblong craters. Please note that you will need to clean up any spilled sand when you are done, so you'll want to consider that . Once you think you have a good handle on it, retrieve the ball bearing and place the box where you want it (floor or table.)

  1. Smooth the sand and sprinkle a thin layer of colored sand on top. Do not knock the boxes on the floor to smooth the sand!
  2. Drop the ball bearing into the box and observe the shape of the crater and the pattern of ejecta (material excavated by the impact and tossed out of the crater.)
  3. Drop an object that isn't round and observe the shape of the crater and the pattern of ejecta.
  4. Throw the ball bearing in and an angle and observe the shape of the crater and the pattern of ejecta.
  5. Does the shape of the crater depend more on the shape of the impactor, or the angle it hits the ground at? What about the pattern of ejecta? How do you know?








  6. Add up to 4 more craters so you have a total of 3 - 7 craters. Note what happened to the earlier craters.
  7. Sketch the craters in another group's box, or a box provided by your instructor. Number the craters from oldest to youngest (i.e. if there are 5 craters, the oldest should be numbered 1 and the youngest 5). All craters should have a unique number. Explain how you arrived at the numbers, especially noting if you couldn't detremine the relative age of any craters (e.g.. if you can't actually tell whether the crater you labeled 2 is older or younger than 3, but both are younger than 1 and older than 4.)






 


Part 2: The Power Law

Since the relationship between D and E is a power law, a graph of D vs. E would be curvy, and it would be very hard to figure out what n and k are. However, the rules of logarithms let us re-write the equation aseqn. 3logD = n log E + log k

If you compare this the the equation of a line, you can see n is the slope of a log-log graph, and log(k) is the y - intercept.

Below is a log-log graph made up of data from several lab classes. The students dropped the ball bearings from fixed heights into the boxes of sand, then measured the crater diameter in meters and determined the impact energy.

graph of log D vs log E

A full size version of the graph is available at https://dept.astro.lsa.umich.edu/ugactivities/Labs/craters/graph.gif

  1. Add a best fit line to the graph.
  2. Determine the slope of the line. Show your work. Indicate the points you used on the graph.




  3. Determine the y - intercept (note where the 0 is on the x axis!): __________
  4. Find k from the y - intercept. Show your work.




  5. Write equation 1 with your values of n and k:

  6. Retrieve the objects from you box and clean up any spilled sand.

Questions:

  1. A quick glance at the Moon through a telescope shows you a surface covered with craters. What does this tell you about the age of the Moon's surface compared to the age of the Earth's surface? Explain in 2 - 3 sentences.




  2. The diameter of the crater from the asteroid that probably killed the dinosaurs is about 180 km. According to this set of data, how much kinetic energy did that asteroid have when it hit the Earth? Show your work, and be sure to check the units used to find n and k.




  3. A good estimate for the velocity (based on observations of other impacts) of this asteroid when it hit the Earth would be about 20 km/s. What was the mass of the asteroid? Show your work.





Updated: 2/21/14 by SAM based on input from LH, JMM, JEB, AK

Copyright Regents of the University of Michigan.