Introduction to GPS 2 - The Three Dimensional Case

Published on
04/07/2009

Activity Overview

In this Derive™ activity, students write the analytic expressions for the four spheres and find the exact point of intersection. They also study the GPS system used to accurately determine your position on the Earth.

Before the Activity

See the attached DFW file for detailed instructions for this activity

Print pages from the attached DFW file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity Procedures:

Set up a 3D plot window and graph a 3D sphere

Study the standard equation of a sphere, and examine the conversion equations between rectangular coordinates to spherical coordinates

Enter the expression for a sphere, plot its graph, and translate it to another point

Plot the translated sphere and the 3 given equations

Estimate the point of intersection

Write the analytic expressions for the four spheres, solve the system, find the exact point of intersection, and verify the estimation

Study the facts about a GPS system

Record the spherical coordinates of satellites which transmit signals to GPS

Note down the time differences recorded by the GPS

Convert the positions of satellites from spherical to rectangular coordinates

Enter the expressions for the distances between the GPS and the satellites

Solve the system and determine the position of the GPS

Rotate the plot and find the point of intersection

After the Activity

Students answer questions listed on the activity sheet.

Review student results:

As a class, discuss questions that appeared to be more challenging