Lab 3

Faculty Notes

Landing on Mars

Introduction

In 2003, NASA will be launching two rovers to Mars, Mars Exploration Rover (MER) A and B. Scientists have decided where the landing sites for each rover will be by considering several different parameters. The actual landing site is defined as an error ellipse since it is impossible to predict a pinpoint landing due to the many variables involved. Utilizing the same information that the scientists use, students will choose a landing site for the MER-A based on parameters that they have researched. The students must justify their choice and describe the error ellipse for MER-A's landing.

Math Level

This lab is written at a precalculus level, but it can be modified for other mathematics courses. If the ellipse calculations are deleted, then the lab is appropriate for the intermediate algebra level. If the linear modeling calculations are also deleted, then the lab is appropriate for the beginning algebra level.

Math Topics

The math topics covered in this lab are data analysis, graph interpretation, map reading, inequalities, linear modeling, trigonometry, geometry, and ellipses.

Timeline

The lab could take the whole semester if the parameters and constraints are thoroughly researched. It could take less time if the material is covered in less depth.

Materials and Tools

Students will need to have access to the web. An on-line database may also be needed for this lab.

Pedagogy

The USGS and NASA web sites contain descriptions of landing sites already chosen by scientists. These web sites also have links to information that justify the landing sites selected. Have the students review one or two of these justifications and then summarize their finding in a short paper. This may help the students in their selection of a landing site.

To aid your students in researching the parameters, the key search words are "remote sensing". Most of the parameters are remote sensing terms. An online encyclopedia would be helpful too. To research map projections and the parameters, the students may need to visit a local library for books on remote sensing and map projections.

Once the students have selected parameters, have them turn on each parameter one at a time to help narrow the choice of landing sites.

Calculation for Map Project

Your students could find the formulas for converting from latitude and longitude to x and y coordinates in the book, Map Projections – A Working Manual by John P. Snyder. If your students do not have access to this book you may wish to provide them with the map projection information given below. On the other hand, you may want the students to research several map projections so that they have a better understanding of such transformations.

The map projection used for the MER Project is called Equidistant Cylindrical projection. This projection has received limited use by the USGS but it is probably the simplest of all map projections and one of the oldest. The meridians and parallels are all equidistant straight parallel lines, with the two sets crossing at right angles. The following information is used in the cylindrical projection equations.

To find the latitude and longitude from x and y, use the equations:

Keystrokes for finding a linear equation on the TI-82™ or the TI-83™

STAT
EDIT
1: Edit
Input the latitude values in L1, and input the length values in L2.
STAT
CALC
4: LinReg(ax+b)

Now you should have LinReg(ax+b) on your main screen. Type L1,L2 next to the LinReg(ax+b). Now press ENTER, and the calculator will calculate the equation you want. Repeat this process for the azimuth equation. Use your equations to get a better estimate of the length of the major axis and the measure of the azimuth.

Lab Extension

If you wish to extend the lab, increase the number of parameters used by the students to select a landing site.

Helpful Hints

Your students may need to use both the USGS web site and the NASA web site to find all the information they need for the lab. The web sites were developed by scientists who are practicing in the field. As a result, the web sites may not include some information that is considered common knowledge within the scientific community. For example, the measurement units are not listed. Your students will need to use critical thinking to figure out some of the information obtained from the web sites.

To research the parameters, the students may need to go to a library. Some of the information is not readily available on the web. To help your students, a summary of the parameters is provided in Table 1 on the next page. You can determine how much information you want to give them.

Table 1: Summary of Parameters