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Computing the heights of the crater walls

Computing the heights of the crater walls

The geometry of a crater shadow is shown in the figure below:

Crater Shadow Geometry

Fig. 1: Moon crater shadow geometry

The height of the crater is h, the apparent length of the shadow is s, and the altitude of the sun as seen from the end of the shadow is the angle a. They are related simply by:

From spherical geometry (you can derive it if you wish), the altitude of the sun as seen from a crater with selenographic latitude bc and longitude lc is given by:

where bo and co are the selenographic latitude and co-longitude of the Sun, respectively.

Using these formulae, your measurements, and the selenographic coordinates of the Sun and craters interpolated from the tables, estimate the heights of the crater walls, and their uncertainties.


Part 5: Write it up!

Whew! That was involved, huh?

The research you had to do to hunt down everything was relatively simple (i.e., because I told you where to look), and is similar to what you encounter in any scientific project. Making the actual measurements is only one part of the problem. Making sense of the measurements, like using them to estimate something interesting (like the heights of lunar crater walls), is quite another.

For your writeup, try to organize all these various steps into a coherent narrative. However, also keep it brief: be concise and to the point. I won’t be impressed by lots of extraneous information or off-topic speculation. I will, however, wonder why you haven’t stuck to the topic.

A typical outline would be:Introduction:Briefly state the problem and what you intend to measure.Observations:Briefly describe the observations and the experimental data set that resulted from it (show the raw data, for example).Data Reduction & Analysis:Briefly describe how the measurements made from the data and how any measurement uncertainties were estimated. This is where you should give a table summarizing your measurements.Results:Summarize the additional data that were collected in a table and give the sources. Describe how you will go from measurements to derived quantities (in this case, describe the shadow projection geometry and how you go from observables to estimated crater heights, crater diameters, etc.). Present the results, and give “the answers”, with uncertainties.Discussion:Summarize your final results, and interpret them. In this case, you might, for example, compare the heights you estimate for the one or two easily measured craters on your image to the heights of terrestrial impact features (e.g., Barringer Crater in Arizona). Are the different? Why?Conclusions:Wrap it up. Give a one or most two paragraph summary of the project, what you learned, what could be done better, etc.

This is not all that different than how one would organize observations, data analysis and interpretations into a scientific paper.