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Mars Craters Common Problem

The most common problem encountered when working with students on this assignment is that they initially derive the depth-diameter equation by inputing data (depth, diameter) in kilometers. Because they are then measuring small craters in the Xanthe Terra images, however, many students then use the depth-diameter equation incorrectly by inputting diameter in meters. When students encounter this difficulty, after I evaluate their homework I have them go back to the part of the assignment where they derived the depth-diameter equation, have them alter all values in Excel to meters instead of kilometers, and re-derive the equation. Voila! Not the same equation.

In some instances when I teach the class, if they submit a short write-up explaining the two equations they derived and why they're different, then re-perform their depth analysis for the Xanthe Terra craters, I amend their grade on the assignment.

This is often the first time that students realize that an equation's derivation is sensitive to the units employed when the equation is constructed, and it's a highly useful lesson to have them learn for themselves.