Ping-pong Altimetry Lab

Objective:

The learner will understand, through a hands-on experience, the basic concepts behind the use and working of a laser altimeter for the study of solar system topography.

Outcomes:

• Students will plot and graph data they have collected using a hands-on version of laser altimetry.
  
• Students will gain an understanding of the use of laser altimetry in the study of planetary topography.

Introduction:

January 10, 1999, the satellite NEAR begins an orbit of 433 Eros, which makes it the first spacecraft to orbit, and study, an asteroid. One of the instruments aboard the satellite is a laser altimeter. The laser will be used to take topographical measurements of the surface of 433 Eros. With this data, topographical maps and 3 dimensional models will be created. This activity will introduce you to the concept of laser altimetry and how the data is used in order to create maps and model solar system bodies.

Materials:

Ping-pong ball
wooden blocks of various sizes
masking tape - 2 pieces @ 10 cm each (optional)
meter stick
stop watch
graph paper (enough for 3 graphs per group)
pen/pencil

Procedure:

This activity requires at least two people per group. Three people per group would be the optimum. The jobs can be rotated if group members so desire. Read through the whole activity before beginning.

STEP ONE:

1. Choose a spot on a wall 2.2 m or higher from the floor, and place one 10 cm length of tape on the wall, at that height, parallel to the floor. (You may need a chair.)
   
2. Holding the ball next to the tape on the wall, between your first finger and thumb, drop it and watch to see how high it bounces back up. Mark that spot on the wall with your finger. It is best to do this step two or three times to determine the highest point of return. (Using the mortar lines on cinder block walls will work well, too. Be sure to use the same two lines throughout this whole activity.)
   
3. Measure 45 cm toward the floor and mark this spot with the second piece of tape. This will be the constant for measuring the time for the ping-pong ball's period.
   
4. Measure the distance from the first piece of tape (or mortar line) to the floor and back up to the second tape line. Record this on your data sheet. This distance will be used to create a baseline for all other measurements, so be as precise as you can.
   
5. As in number two, one partner should hold the ping-pong ball next to the higher piece of tape, between the first finger and thumb, and approximately one inch from the wall.
   
6. One partner should have a stopwatch and have his/her eyes level with the second piece of tape. A third partner, if available should be recording the results of each ball drop using the attached data sheet or one that your group makes up for itself. * Note: A spreadsheet would work well for recording and calculating this data.
   
7. Drop the ball, and as you do say, "Go." The timer starts the stopwatch on "Go."
   
8. The timer will stop the watch when the ball rebounds and reaches the lower line. (His/her eyes should be level with the lower piece of tape. The time should be stopped as soon as any part of the ball touches any part of the line.) Record the time on the data sheet. Repeat this step four more times.
   
9. Calculate the velocities (V=D/T). After finding the velocity for each of the trials, find the average velocity of the ping-pong ball. This average will be used later in this lab. It will be your baseline for comparing data.

STEP TWO:

Now that you have found the velocity of the ping-pong ball, you will use this information to plot the topography along a line of latitude of an asteroid. You will be creating your own asteroid terrain on the floor against the wall where you just did Step One.

1. Create the topography model of your asteroid, along the wall where you did Step One. In order to do this you need to place the wooden blocks against the wall in a line about 6-8 feet long. Be sure that you build in some hills, mountains, valleys, etc. (See Figure A)
   
2. If you used tape in Step One instead of the mortar lines, you will probably want to add new lengths of tape to the originals that extend over the entire length of your topographical model. Be sure that the new lines remain parallel to the floor so that the heights don't change along the length of the model.
   
3. Starting at the beginning of the top piece of tape, place a mark every 20cm. The bottom piece does not need to be marked.
   
4. Again, starting at first interval mark you made at the beginning of the tape, you will drop the ping-pong ball as you did in Step One, and record the time in Data Table II. Drop the ball and record the results two more times. Be sure to be as accurate as you can with the timing.
   
5. Repeat number four for each of the interval marks you placed on the wall.
   
6. Find the average time for each of the intervals and record it on the data table.
   

STEP THREE: PLOTTING AND GRAPHING THE DATA:

You will now plot the data for the average times and create graphs of the altimetry readings for your topographic model. The graphs will use different intervals between readings, so that you can compare the preciseness of different levels of accuracy (called spatial resolution).

Graph 1

1. Plot the average time for every 60cm interval. (0cm, 60cm, 120cm, etc.)
2. Connect the points with a smooth line.
3. Label the graph appropriately.
   

Graph 2

1. Plot the average time for every 40cm interval.
2. Connect the points with a smooth line.
3. Label the graph appropriately.
   

Graph 3

1. Plot the average time for every 20cm interval.
2. Connect the points with a smooth line.
3. Label the graph appropriately.