### IIIB. CRATER DEPTH

Concepts:

• Geometry: Triangles, angles
• Measurement
• Conversions (scales)
• Graphing data
• Drawing conclusions from graphs and data

Crater depths are indicative of both the strength of the surface material, and the impactor size and speed. A variety of crater depth exercises 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 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

• Given d and Ø, multiply both sides of the equation above by L to get:

L * tan Ø = d

Activity: Given a Galileo image, its scale (either in km/pixel, or the size of a feature), and the angle of incoming light, determine the depths pf the craters in the image. Here is one possible image.

• For each crater, measure:

• its diameter (in pixels or centimeters, then convert to km)

• the length of shadow it casts

• Calculate the depth of the crater, given the angle of incoming light, Ø, and the shadow length, L, using

L * tan Ø = d

• Graph crater depth vs. diameter.

Interpretation:

• Are there any relationships between crater diameter and depth?

• Crater diameter is related to the mass and speed of the impactor, as discussed in section IIIA. What other factors might influence crater depth?

• later tectonic or volcanic activity (crater could be filled with lava)

• relaxation of the crater (surface composition)

Scientific context: Scientists often have to do considerable amounts of detective work when analyzing images taken of other worlds. The exercises above demonstrate how scientists start from a single picture and extract valuable information not only about the appearance of the surface, but also the approximate sizes of impacting bodies and the depths of craters on the surface. 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 almost no topography at all, called palimpsests. (Example image)

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!

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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.

Galileo Solid State Imaging Team Leader: Dr. Michael J. S. Belton

The SSI Education and Public Outreach webpages were originally created and managed by Matthew Fishburn and Elizabeth Alvarez with significant assistance from Kelly Bender, Ross Beyer, Detrick Branston, Stephanie Lyons, Eileen Ryan, and Nalin Samarasinha.

Last updated: September 17, 1999, by Matthew Fishburn