Teacher Feature

Lesson Title:
Crater Depth IIIB

Student Objectives:
Using images the students will measure diameter and shadow length, convert to kilometer, calculate crater depth and graph results

Background Information:
Crater depths are indicative of both the strength of the surface material, and the impactor size and speed. A variety of crater depth exercised are available, such as "Long Distance Detective" in Craters! The depth of a crater can be determined from the length of the shadow cast by the crater rim and the angle of the incoming light source. If the angle of incoming light and image scale are provided along with each image, students can measure shadow lengths and calculate crater depths from the relations below.

As shown in the diagram above, using the geometry of triangles, if we know Ø , the angle of the incoming light, and can measure L, the length of the shadow, we can calculate d, the crater depth. The tangent function relates d, L, and Ø as follows: tan Ø = d / L (or L * tan Ø = d ). Crater depths provide clues to surface composition. A crater formed in a firm material such as rock can last much longer than a crater formed in a softer material, such as ice. This distinction is especially important in the outer solar system, when examining craters on such bodies as Europa, Ganymede, and Callisto. These bodies are part-rock, part-ice. While ice behaves almost like rock at the very cold temperatures near Jupiter, its properties are still different enough to let large craters flow slowly over time, eventually resulting in large flat circular areas with no topography at all, called palimpsests [have students brainstorm other modifications here] Crater depths are also important in understanding what events might have modified the crater since its formation. For example, a broad shallow crater on a rocky planet could have been filled in with lava at some point after its formation, either immediately afterwards if the impact was energetic enough to melt the surrounding material, or long afterwards if the planet underwent a period of volcanic activity. If part of a crater floor is higher than another part, it's possible that some sort of fault or other tectonic activity took place nearby, thus disrupting the crater. The simple technique of shadow measurement discussed above also has other applications. On Earth, it can even be used to measure the height of far-off mountains or trees.

Lesson Format:
lecture, individual work, class discussion

Have students go outside and measure heights and shadow lengths for group. Complete the sheet and answer questions, then apply formula to crater measurements.

Class Activity:
"The Shadow Knows"

lab, math application

Materials Needed:
meter stick
crater images
trig table
graph paper (optional)

Work introductory part of activity, then present background information in form of lecture.
Work through formula with class, possibly even using data collected to demonstrate formula and calculation.
Hand out crater images and continue with activity.
Demonstrate conversion to kilometers (scale of photos) as necessary.

Discussion Points:
Review the types of activities that modify craters.
Answers to questions:
1. Illumination angle
2. yes, light strikes all objects at same angle
3. yes
4. height of object and angle of light source, i.e. time of day
data chart completed, problems solved

Other Activities, Misc. Information, etc.:
If available, play the intro. to the classic radio show "the Shadow".
With younger children, just use the intro. activity (provide a structured data table for collecting and recording measurements) and relate to other items [flagpole, building, teacher]. Then discuss the craters.

This module was written by Cynthia Phillips, Dept. of Planetary Sciences, University of Arizona, Tucson AZ, and funded in part by the NASA Spacegrant program.

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Last updated: September 17, 1999, by Matthew Fishburn

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