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LESSON:
ROVERS ON MARS Subjects: physical science and mathematics Time: Two or more 60-minute periods (one for Internet reading; one for activity) for each lesson; parts may be assigned as outside class work. Lesson Objectives: Students will:
Materials
Correlation
to National Standards Students will study the latest Missions to Mars, which have been such a success since this past January 2004. To begin, students use this Self Assessment Guide for reading the transcript, viewing the VideoStream, or listening to the RealAudio of "Rovers on Mars" from the Online NewsHour, January 26, 2004. A teacher key with answers is provided in the materials section of the lesson. Students complete while reviewing the story:
LESSON ONE - Long Distance Post Cards Many images are taken by the camera of Opportunity for a 360-degree panoramic view. Specifically, 25 pictures wide by 3 pictures high for a total of 75 pictures. If each of these pictures is a 3x5 postcard size picture taking up 600 kilobytes of memory, then how fast can the entire panoramic mosaic be sent to Earth once the pictures are all taken? Second, if the scientists send a 600-megabyte software patch to correct or to direct the probe functions, then how long does it take those instructions to get to Mars? Moreover, how long does it take the probes to send a message back that all is well or that something else needs to be tried? In order for students to answer these larger questions, they must first answer the following Online Investigation Questions. Pass out the Online Investigation handout provided in the materials section of this lesson. The Web sites below offer a great deal of information, the answers to these questions, and more. A teacher key with answers to the questions is also provided in the materials section. http://marsrovers.jpl.nasa.gov/home/index.html
NOW FOR THE SOLUTIONS TO THE LARGER QUESTIONS: Earlier it was said that many images are taken by the camera of Opportunity for a 360-degree panoramic view. Specifically, 25 pictures wide by 3 pictures high for a total of 75 pictures. If each of these pictures is a 3x5 postcard size picture taking up 600 kilobytes of memory, then how fast can the entire panoramic mosaic be sent to Earth once the pictures are all taken? For a 360 degree panoramic mosaic made with 25 pictures wide by 3 pictures high for a total of 75 pictures at 600 kilobytes each, there would be a total of 75 x 600 = 45000Kb or 45Mb of data in all. First consider sending the data directly to Earth. Since the rover can send 60 Mb in 3 hours, make and solve the proportion 45 Mb : 60 Mb :: H : 3 Hours. H = 3 x 45/60 = 2.25 Hours, well within the time available to the rovers to send directly to Earth. Finally, once the data is sent, it must travel 60000000 Km between Mars and Earth at light speed. At 299792 Km/s this travel time is calculated by using 60000000 Km / 299792 Km/s to yield approximately 200 seconds. Adding this 3.33 minutes to the 3.25 hours of sending time, the picture postcards will arrive directly from the Rover in just under 3 hours 20 minutes. However, sending the same data to the orbiter would take much less time. Solve the proportion 45Mb : 60 Mb :: M : 8 Minutes. M = 8 x 45/60 = 6 minutes to send the data to the Orbiter. Now, the Orbiter can transmit at 128000 bites per second, so that the time to relay the 45 Mb packet back to Earth is found by solving the proportion 128000 Kb : 1 second :: 45000000Kb : S. Solving gives S = 351.5625 or about 352 seconds or about 6 minutes. Plenty of time to spare with a total Rover to Orbiter to Earth transmission time of 12 minutes. Finally, once the data is sent, it must travel 60000000 Km between Mars and Earth at light speed. At 299792 Km/s this travel time is calculated by using 60000000 Km / 299792 Km/s to yield approximately 200 seconds. Adding this 3 minutes 20 seconds to the 12 minutes of sending time, the picture postcards will arrive from Mars in just over 15 minutes. Second, if the scientists send a 600-megabyte software patch to correct or to direct the probe functions, then how long does it take those instructions to get to Mars? Moreover, how long does it take the probes to send a message back that all is well or that something else needs to be tried? The Deep Space Network of radio transmitters on Earth could send the 600 Megabyte patch almost instantaneously, but neither the Orbiter nor the Rover could receive the data that fast. The time to shoot for would be at the same rate that the Orbiter and Rover could send, and that is the same set of times just solved for sending the Panoramic Postcards to Earth! The best method of sending the patch would be to send first to the Orbiter in 6 minutes when the orbiter was in a best position to avoid static or interference from solar wind or planetary presence. Then as the Rover came into position below the Orbiter, have the Orbiter download the patch taking only 6 more minutes. The earliest that the return message from the Rover that all is well or that the patch did not work would not be able to be sent back to Earth until the Rover came back into position 24 hours later!! Extension Activity: Using graph paper or calculator:
LESSON TWO - Coming up with a Better Long Distance Plan Students go online and use the given links above as starting points for researching facts, proposals, and possibilities for future Mars Missions. Students research and design a communications network with Mars Probes to overcome these problems:
Students work in small groups and present their findings and conclusions to the class as a whole. After discussion arguing support and difficulties with the plans, students grade each other's group effort as Good, Better, or Best. Correlation to National Science Standards: Correlation
to Science Content Standards: 9-12
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