GPS THE GLOBAL POSITIONING SYSTEM Central High School Champaign, IL Summer Math 2002 Kathleen Smith Anne Munroe

GPS It’s in cars, boats, planes, tractors, golf carts, cell phones, and …soon… could be implanted in your body! What is GPS? – PowerPoint Overview – Brief Video Longitude and Latitude Contest! Geocaching Web Site GPS Scavenger Hunt in the Park!

GPS technology has matured into a resource that goes far beyond its original design goals. These days scientists, sportsmen, farmers, soldiers, pilots, surveyors, hikers, delivery drivers, sailors, dispatchers, lumberjacks, fire- fighters, and people from many other walks of life are using GPS in ways that make their work more productive, safer, and sometimes easier. These applications fall into five broad categories: Location - determining a basic position Navigation - getting from one location to another Tracking - monitoring the movement of people and things Mapping - creating maps of the world Timing - bringing precise timing to the world Location Navigation Tracking Mapping Timing

What is GPS? GPS is a satellite-based radio navigation system that allows anyone anywhere on the planet to determine their 3D position with great accuracy and precision.

–DOD - NAVSTAR –Russia -GLONASS –EEC - Under development Who maintains GPS?

The system is composed of three segments –Space - The orbiting satellites

The system is composed of three segments –Space - The orbiting satellites – Control - The monitoring stations on earth

The system is composed of three segments –Space - The orbiting satellites –Control - The monitoring stations on earth – User - The GPS units such as you will use today.

The GPS pre-test: When was GPS first used? –Sputnik…1957 –TRANSIT…1960’s –NAVSTAR…1970’s

– 27 at the current time – 24 to maintain a system How many satellites make up a GPS? Your GPS receiver must track at least 3 satellites to give you an accurate position location. *The word “tracking” must appear in the screen’s lower right corner!

From Circles to Waves These two graphs both represent The NAVSTAR constellation of satellites. How would you describe the path of a single satellite in each graph? How would you explain the transition from one graph to the other?

–Government Military Agencies - Conservation, Weather, Rescue –Industry Transportation Fishing Agriculture –General Public Recreation Emergency / Security Reasons Health Related Reasons Who uses GPS?

–Each GPS satellite transmits an accurate position and time signal. –The user’s receiver measures the time delay for the signal to reach the receiver. –Measurements collected from 4 satellites are processed to solve for the 3D position, velocity and time. How does GPS Work?

Where on Earth are we?

Your Task Outside 1) Get a locked reading on your unit. 2) Chose a direction either east-west, or north-south. 3) Walk along the direction vector until the reading on your unit changes. 4) Design a method for finding the circumference of the earth based on your observations.

What you discovered outside. 1) Did you all get the exact same reading? 2) How did you know your direction? 3) How many paces until the reading on your unit changed? 4) What was your method for finding the circumference of the earth? 5) Would the circumference be the same for N/S as E/W?

A Sample Lesson From: Mission Mathematics A NASA/NCTM Project

How Does This Fit Into a Math Class?! Pre Algebra: Latitude and Longitude, Integers Algebra I: Linear Systems, Absolute Value Geometry: Degree Measure, Circles, Spherical Geometry Algebra II: Systems of Circles, 3D Graphing

How Does This Fit Into a Math Class?! Trigonometry: Orbits as Sinusoids, Bearing, College Algebra: Conic Sections, 3D Systems Pre Calculus: Accuracy, Precision, Error Calculus: Discrete Math: Circuits, Paths, Triangulation

Available Materials The WEB: Overview of GPS: U.S. Coast Guard: Inst. of Navigation: GLONASS info: GPS sites: "GPS for Fun": SpatialTek: Craig Haggart: Trimble: Science Junction: junction Lesson Plans:

Available Materials In Print: –Mission Mathematics (NCTM) –MICROGRAVITY NEWS, Fall ‘99 (NASA) –Mathematics Teacher, Nov (NCTM) –Longitude, Sobel, (Walker & CO. NY, also a PBS video) –The Librarian Who Measured the Earth

Available Materials On the Web: Overview of GPS: U.S. Coast Guard: Inst. of Navigation: GLONASS info: GPS sites: "GPS for Fun": SpatialTek: Craig Haggart: Trimble: In Print: Mission Mathematics (NCTM) MICROGRAVITY NEWS, Fall ‘99 (NASA) Mathematics Teacher, (NCTM) Longitude, Sobel, (Walker & CO. NY, also a PBS video) The Librarian Who Measured the Earth,