Lab 3

Landing on Mars

Introduction

In 2003, NASA will be launching two rovers to Mars, MER-A (Mars Exploration Rover) and MER-B. Each rover will traverse the surface of Mars collecting samples and sending the analysis back to Earth. There are many goals for the rovers including on-site verification of hypothesized geology, searching for water, and searching for evidence of past life. To select the landing sites for each rover, scientists need to consider several different parameters, each of which has corresponding constraints. Since it is impossible to pinpoint the actual landing site due to the many variables involved, the site is defined as an error ellipse. The rover has a very high probability of landing inside this ellipse, provided that all the constraints on the parameters are met. Utilizing information on parameters and constraints such as that used by scientists, your task will be to select an appropriate landing site for the MER-A.

This lab activity involves the use of Geographic Information Systems (GIS). GIS is a computer system capable of assembling, storing, manipulating, and displaying geographically referenced information. Maps have traditionally been used to explore the Earth and its resources. GIS technology, as an expansion of cartographic science, has enhanced the efficiency and analytic power of traditional mapping. As the scientific community recognizes the environmental consequences of human activity, GIS technology is becoming an essential tool in the effort to understand the process of global change. Various map and satellite information sources can be combined in modes that simulate the interactions of complex natural systems. In fact, many disciplines already benefit from GIS techniques. Some common applications include transportation planning, site selection, emergency response planning, and simulating environmental effects.

Application of GIS in the geosciences has grown tremendously over the past few years as scientists and land-use specialists have become able to prepare thematic maps and determine spatial relations among multiple data sets. Many of the data sets produced are available on the web, including those that involve data on topography; oil, gas, coal, and mineral deposits; biodiversity; and geologic hazards (earthquakes, volcanoes, and landslides). In many cases, the data is obtained by remote sensing devices.

Technology Problem

Your job is to select an appropriate landing site for the MER-A. The landing site will be described as an error ellipse, so you will need to determine the ellipse's mathematical equation and include a sketch of the landing site ellipse. Since there is more than one location on Mars that might be considered as an appropriate landing site, you will need to justify your selection to an audience of your peers.

You will be using the scientific method to solve your technology problem. There are five steps to the scientific method – problem, question, hypothesis, test, and decision. The first two steps of the scientific method (problem, question) involve exploring your technology problem to develop a better understanding of the situation. You will probably begin by gathering information through bibliotechnology research.

Bibliotechnology Research

Bibliotechnology research is the main investigative avenue to gain information and answer questions as you employ the scientific method. Some questions that you might want to consider include, what does the surface of Mars look like? What are the parameters involved with landing the rover on Mars? What are the constraints for each parameter? Which parameters should you use to locate the best landing site? How are locations and distances measured on Mars? What are the mathematical characteristics of your error ellipse? What is its mathematical equation? What does a sketch of the ellipse look like? How do you project a figure drawn on a spherical surface onto a two dimensional plane? As you research the technology problem, you will probably come across terminology that is specific to that problem. It will be helpful to generate a glossary of these terms and update it as you progress through the lab.

Many parameters must be considered to choose an appropriate landing site for an exploration rover on Mars. Each parameter must meet specific guidelines called constraints. The parameters that the United States Geological Survey (USGS) uses to determine an appropriate landing site are latitude, elevation, wind speed, surface slopes, surface images, total rock coverage, size of rocks, radar reflectivity or albedo, and thermal inertia. The constraints on these parameters can be found on the first two web sites given below. These web sites, which are maintained by USGS and NASA, also contain surface maps of Mars, satellite data, and other useful and interesting information. You also should find that the second two web sites in the following list are useful. However, this list is not meant to be complete. You are encouraged to search the web for other relevant sites.

• This is the site for MER produced by the USGS.
  http://webgis.wr.usgs.gov/mer_ab/mer_ab.html
• This is the site for MER produced by NASA.
  http://marsoweb.nas.nasa.gov/landingsites/mer2003/mer2003_NS.html
• This site will help you to calculate the coefficients for the general equation of the ellipse.
  http://www.flipcode.com/documents/circle.html
• This is a site with general information about an ellipse.
  http://www.ping.be/~ping1339/reduc.htm

Mathematics Tools

In the investigation of your problem, you will need to select mathematics tools that help explain the problem, that best fit the problem, and that provide a solution to the problem. You may wish to review linear modeling, trigonometry, graphing, map interpretation, interpreting data, and concepts regarding an ellipse such as its characteristics, equation, and area.

Model Portfolio

As part of the solution to the technology problem, you will need to create a model portfolio. The model portfolio should contain a thorough description of the technology problem and its identifying characteristics. You need to explain the mathematics, technology, and science you use to solve the problem. In addition, you need to include the mathematical and/or physical models you create. It is important that you keep a careful record of all of your work. It should be complete enough so that someone else could follow your work step by step. The model portfolio will be very helpful when you present your thesis defense. Remember that there may be several appropriate landing sites on Mars. The model portfolio will be helpful when explaining to other scientists the rationale for your selection of a landing site.

Model Development

The third step of the scientific method is to develop a hypothesis about the technology problem. You can think of the model(s) you create as a hypothesis. Your model constitutes a proposed explanation of the technology problem.

Now that you have familiarized yourself with the technology problem, you are ready to determine an appropriate landing site – an error ellipse for the MER-A. You may want to explore suggested landing sites that are described on the web sites in the previous section. You will need to research all of the parameters, select those that you think are most important, and identify the corresponding constraints. Your error ellipse will need to satisfy the constraints on your parameters. In order to simplify the process, choose latitude as one parameter, and then select at least two other parameters listed on the web sites developed by the USGS or NASA.

From your bibliotechnology research, find the web site that provides map details of Mars. You can check out the characteristics of potential landing sites by turning on and off the different map layers. This will allow you to see the values of each parameter. There is a legend for each layer so that you know if the constraints you chose are being met. After you have selected a landing site, you need to define the error ellipse.

To write the mathematical equation for the error ellipse, you need to take into account the fact that the surface of Mars is spherical. You will need to translate surface information to the x-y plane by using a map projection. A map projection is a method for transforming a map on a spherical surface to a map on a 2-dimensional plane. The map projection used for these web sites is called Simple Cylindrical Projection. You will use this projection to convert the latitude and longitude to the corresponding x and y values. (You will need to do more research to find the formulas that "project" these maps onto the x-y plane.)

From your research, you have a web site that will help you approximate the length of the major axis and the appropriate angle. Remember that the length of the major axis and the rotation (azimuth) measured from due north of the ellipse depend on the latitude you chose. The length of the minor axis of the error ellipse will always be 30 km. You may want to use the linear modeling feature of your graphing calculator to get a better approximation for the length of the major axis or for the measure of the azimuth. To create a linear equation for major axis length with respect to the latitude, choose at least five ordered pairs from the graph at the web site. Write the equation for the ellipse using the x-y plane. Identify the foci and the azimuth, and then calculate the area of the error ellipse.

As part of your model portfolio, make sure that you provide a written conclusion regarding your choice of landing site, summarize your research on the parameters and constraints, justify the location and equation of the error ellipse, provide the error ellipse equation, and include a sketch of the error ellipse as it would appear on the x-y plane.

Test the Model

Now that you have created a model to identify appropriate landing sites, you need to test the model. On the web site, http://webgis.wr.usgs.gov/mer_ab/mer_ab.html, is a button that looks like the Greek letter Phi (j). If you click this button, you will be asked for the latitude and longitude that you have chosen. After typing in your latitude and longitude, click the compute button to plot your ellipse and produce a summary page. Review this information to see if your location satisfies the constraints of the parameters that you have chosen. This web site also contains the locations of landing sites already chosen by scientists. The web site is linked to information that provides justification for the selected landing site. This will allow you to see how close you are to a real landing site

Decide to Retain, Reject, or Modify the Model

After you have tested the model, you can make a decision regarding the model. This action depends on how well your model satisfies the constraints of the parameters you chose. If it does not match the parameters and constraints, then you will want to revise the model appropriately.

Thesis Defense

You will be asked to give an oral presentation of your model portfolio. This presentation is called the thesis defense. Imagine that you are giving your presentation to an audience of scientists with similar knowledge regarding the technology problem. Provide a written conclusion for your landing site choice, summarizing your research. Include in this presentation the parameters you chose, the latitude and longitude of your location along with the corresponding x and y coordinates, the length of the major and minor axes of the ellipse, the azimuth of the ellipse, and the area of the ellipse. State the linear equations that were used to calculate the length of the major axis and the azimuth. Provide the error ellipse equation, and include a sketch of the error ellipse as it would appear on the x-y plane. As justification, discuss the process you used to determine the latitude and longitude based on the constraints for your parameters.