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Understanding the Global Positioning System
The global positioning system (GPS) is able to determine the location
of anyone or anything which has a receiver. The complete global
positioning system consists of 29 satellites and a GPS receiver which
can decode signals from the satellites. The GPS receiver is what we
can purchase in stores here on Earth. Each GPS satellite transmits
radio signals which contain the current time. The GPS receiver uses
the time stamp to determine how long it takes the signal to travel
between the satellite and the receiver. In this manner the receiver
can determine the distance to each satellite. Once the distance is
known between the receiver and several satellites, the location
of the receiver can be constructed.
In this activity students will reconstruct a two dimensional map of
another student's journey with the same reconstruction methods used by
the Global Positioning System.
Materials
To complete this activity each student (or group) will need the
following materials:
The Journey
In this activity student Travellers will make a journey in several
stages. Travellers will mark their positions along the way, recording
their distance from three different GPS satellites.
In the second part of the activity, student Mappers will use only the
recorded distances from the GPS satellites to reconstruct the
Travellers' journey.
- Students may work individually or in groups. Each student (or
group) should start with a blank copy of the GPS Coordinate Grid
worksheet and a blank copy of the GPS Log Sheet. The students should
write their names on the GPS Coordinate Grid and check the box next to
Traveller. The students should write their names under Travellers'
Names on the GPS Log Sheet.
- Start by marking your starting location (position 1) with a dot
someplace on the grid.
- Measure the distance from your starting location to GPS
satellite \#1 using a ruler. Always use the center of the black
bullseye at the corner of each satellite image as the point you are
measuring to. Record this distance on the GPS Log Sheet next to
position 1, under GPS satellite \#1.
- Next, measure the distance from your starting location to GPS
satellite \#2 using the ruler. Record this distance on the GPS Log
Sheet next to position 1, under GPS satellite \#2.
- Now, measure the distance from your starting location to GPS
satellite \#3 using the ruler. Record this distance on the GPS Log
Sheet next to position 1, under GPS satellite \#3.
- Mark a second point on the GPS Coordinate Grid, this will be
the second position on your journey. Draw a straight line,
with an arrow, from the starting position to the second position to
indicate which direction you traveled.
- Measure the distance from the second position to each GPS
satellite as you did before and record these distances on the GPS Log
Sheet next to position 2, under the appropriate satellite number.
- Repeat this process for as many positions as you would
like to make on your journey (7 is a nice number). Measure carefully
the distance from each position to each of the GPS satellites
and record the information on your GPS Log Sheet.
- Keep the map of your journey hidden from your fellow classmates.
You classmates are going to try and reconstruct your journey next, and
you wouldn't want them to know what it looks like ahead of time.
Which Way Did They Go?
The information on the GPS Log Sheet constructed in Section 2 will be
used to reconstruct a map of the journey taken by the those who made
the log. In this portion of the activity the students will determine
the location of the Travellers with the same reconstruction methods
used by the Global Positioning System.
- Each student (or group) should start with a blank copy of
the GPS Coordinate Grid and a GPS Log Sheet which has already been
completed by another student (or group). The students should
write their names on the GPS Coordinate Grid and check the box
next to Mapper. The students should write their names under
Mappers' Names on the GPS Log Sheet.
- Using a drawing compass and the GPS Coordinate Grid,
construct a faint arc which is centered on GPS satellite \#1 and
has a radius equal to the distance indicated on the GPS Log Sheet
from GPS satellite \#1 to the starting position. You can use a ruler
to measure the opening distance of the compass.
If the compass will not open wide enough, use a string instead. Tie one end of
the string to your pencil and use the ruler to measure a length of string
equal to the distance indicated on the GPS Log Sheet. Use the string to
construct a faint arc which is centered on GPS satellite \#1 and has a radius
equal to the distance indicated on the GPS Log Sheet from GPS satellite \#1
and the starting position.
- Using a compass (or the string), construct a faint arc which is centered
on
GPS satellite \#2 and has a radius equal to the distance indicated
on the GPS Log Sheet from GPS satellite \#2 to the starting
position.
- You may notice that if you were to complete the compass
circles all the way around each of the first two satellites, they would cross
in
two different locations. This would make it difficult to know which
is the position of the traveller. We can solve this problem, just as
the Global Positioning System does, by using a third satellite.
- Using a compass (or string), construct a faint arc which is centered on
GPS satellite \#3 and has a radius equal to the distance indicated
on the GPS Log Sheet from GPS satellite \#3 to the starting
position.
- The point where these three arcs cross is the only point on
the grid which satisfies the distance requirements recorded on the
GPS Log Sheet. Do to reconstruction error, the three arcs may not touch
exactly in one point. You can approximate the starting point by choosing the
point in the center of the area where the three arcs overlap. This is the
starting position of the journey you
are trying to reconstruct. Mark this crossing point on the GPS
Coordinate Grid with a colored pencil. If you have drawn the arcs
lightly you may leave them in place, or you may carefully erase them.
- Repeat the process above to locate the second
position on the GPS Coordinate Grid using the distances indicated
on the GPS Log Sheet.
- Once you have located the second position, use a colored
pencil to draw a straight line with an arrow from the starting
position to the second position to indicate the direction of
travel.
- Repeat this process to locate all positions on the
journey. Make sure to connect each position with a straight line and
an arrow, to indicate the direction traveled.
- When you have completed reconstructing the journey from the
information on the GPS Log Sheet, compare your map with the
original map made by the student (or group) who constructed the
GPS Log Sheet in the first place. How did you do? Were you able
to figure out the path they took on their journey?
Activity Extensions
There is an advanced version of this activity which allows the
students to calculate the average velocity of the Travellers between
different positions on the journey. See the CHICOS website for a
copy of the advanced lesson. Other activity extension ideas are
listed below.
- A journey through town. Copy the GPS Coordinate Grid onto
a
clear piece of acetate (overhead transparency). Lay the grid over
a map of your town, or any town map. Now, as the students
construct their journey they can mark the position at
specific places in town. The next group, which reconstructs the
journey, can indicate where the Traveller stopped (e.g. toy store,
ice cream shop, local park).
- An interdisciplinary extension. Once this activity is
complete have the students write a short story describing their
adventures along the journey. Or, have them draw a map around the
journey path on the GPS Coordinate Grid indicating where they went
and what they saw along the way.
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