By completing this activity, the learner will:

• understand that the sizes of the polar ice caps on Earth and Mars

depend on the lengths of the seasons.  The fact the planet has a season depends on the tilt of the axis of rotation.  The length of the season on each planet depends on the time it takes the planet to make one orbit around the sun. 
• measure the sizes of the polar ice caps on Earth and Mars using image processing techniques.
• compare the changing sizes of ice caps on Earth and Mars using the tilt of the axis of rotation, the time to complete an orbit (one year), and the time for one rotation about the axis (one day). 

National Mathematics Education Standards

Materials and Technology Required

Scientific Background Information

Teacher Lesson Plans

Activity 1: Observe polar caps on Earth and Mars as they change over time. Sketch the ice coverage of Mars' polar caps at different times of the Martian year.

Activity 2: Measure Mars' polar ice cap using image processing software.

Activity 3: Measure Earth's polar ice cap using image processing software.

Debriefing:Make comparisons between Mars' and Earth's changing polar ice caps.

Activity 1:

Observe the diagram of Earth.  Earth and Mars have similiar tilts of their axes of rotation.

View the on-line movie, Earth Changing Polar Ice Caps Animation several times.

View the on-line movie, Mars Changing Polar Ice Caps Movie (mpg, QT, or anim_GIF) several times.  In the space provided, carefully sketch: (i) the maximum extent of ice coverage; (ii) the minimum extent of ice coverage; and (iii) the average or middle extent of ice coverage.
 

Maximum extent  of ice coverage	Average extent  of ice coverage	Minimum extent  of ice coverage
Mars rotates 667 times each orbit around the Sun.  How many days do you think there are between maximum and minimum ice coverage?  Why? 667/2= 333 Martian days, which are about as long as Earth days.

Go back to Activities.

Activity 2:

One procedure frequently used to conduct scientific investigations is called IMAGE PROCESSING.  In this activity, students use technology to download and analyze images and movies of the dynamic Earth and Martian polar ice caps.  Specifically, students will measure the areas of these polar caps and how they change over time. 

Be sure you have the following items on your computer before you begin:

• image processing software (Mac or PC)
• image format converters (Mac or PC)
• saved TIF images of Mars 1 and 2 on your computer's hard drive.
• saved TIF images of Earth 1 and 2 on your computer's hard drive.
• Movie, Mars Changing Polar Ice Caps Movie (mpg, QT, or anim_GIF), saved on your computer's hard drive.

2. Open the image: Open the winter image of Mars in TIF format by moving the pointer to the File pull-down menu at the top of the screen, depress the mouse button, drag down to Open, and let go.  Select the HST image oct96_mars.tif. You must use TIF format images with this image processing software, but if you would like to see the image using a WWW-browser, it is oct96_mars.gif.  
Note: GIF and JPG images can be converted into TIF images using image format converters, such as Gif Converter (Mac) or Paint Shop Pro (PC).

3. Set the Image Scale: Move the pointer to the Analyze pull-down menu at the top of the screen, depress the mouse button, drag down to Set Scale, and let go.  A new window will open. In the center of the window is a box labeled Units.  You must set the units first.  Click on the down arrow in the box and select kilometers as your unit of measurement.  At the top of the window enter 292 in the Measured Distance box and 4362 in the Known Distance box (this corresponds to a scale of 292 pixels = 4362 km).  Click OK and start measuring!

4. Draw a Diameter: Using the Segment Tool (Tools window, 5th icon from the top in the right hand column, labeled "select lines"), draw the longest segment you can across the diameter of the white ice cap.  Once the segment is drawn, return to the Analyze pull-down menu, drag down to Measure, and release the mouse button.  Again, click on Analyze, drag down to Show Results, and release the mouse button.  A Results window will appear with your answer in the column marked length.  You may need to make the window larger.

5. Freehand Tool to Measure Perimeter and Area: This image processing program has 4 tools for selecting regions for study.  The first tool in the right hand column of the tool window is used to drag out rectangular areas.  The second tool in the right hand column of the tool window is used to define oval or circular areas.  Using the third tool in the right hand column of the tool window, you can connect a sequence of points with line segments, to create a polygon of your own design.  To close the polygon (connect your last point to your first point), just click the mouse twice in rapid succession.  The fourth selection in the right hand column of the tool window allows you to freehand any curve you want (this is called the Freehand Tool and looks like a heart).  Determine the area of the polar ice cap using the freehand tool to trace the outside.  Select Analyze and Show Results to view the measured value for perimeter and area.  Record your results below.

6. How big is the winter Martian Polar Ice cap compared to the state or country in which you live? 

7. Now that you know how to measure various aspects of Mars, let's get data for both the maximum and minimum extent of the Martian northern polar ice cap. The minimum extent image is mar97_mars.tif and available for viewing through your WWW-browser as mar97_mars.gif.

Record your data here:

 

MARS	maximum extent	minimum extent	difference between
diameter	km	km	km
perimeter	km	km	km
area	km2	km2	km2

9. Does anything on Earth compare to these sizes? 
What? 

Go back to Activities

Activity 3: 
 

Click for Animated GIF

In the previous section you learned about the changing polar ice cap on Mars. Now, lets apply what you have learned to the study of Earth's northern polar ice cap.  Determine the maximum, minimum, and average extent of snow and ice coverage for Earth's north pole.  Use the following images 02.tif and 08.tif. (These can be viewed through your WWW-browser as 02.gif and 0.8.gif.)  Set the scale to be 248 pixels = 12756 km using the same procedure you used for Mars in the previous section. 

Record your data below:
 

Earth experiences a "thermal lag" because the 75% of Earth that is covered with water is very resistant to changing its temperature when the amount of solar radiation is changed.  Thus Earth's average temperature lags behind the dates of the seasons, as determined by the position of the Earth in its orbit.

Click on the image to see the full size chart

• Which planet has a larger ice cap during the winter?
• Which planet has the smaller ice cap during the summer?
• Which planet has the largest change in the size of its polar ice cap?
• Why does a "thermal lag" exist on Earth but not on Mars?

• How can a telescope in near-Earth orbit make pictures of Mars that seem to be from above, looking down? See scientific background for information.
• If you know the scale, you can make similar measurements for any planet or moon. However, most images on the WWW are in GIF or JPG format.  What do you need to do in order to use these image processing programs?