*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:*

- 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.)

- 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.)

- 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.

- 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.

- 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.

- 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.*

- Drop the ball, and as you do say, "Go." The timer starts the stopwatch
on "Go."

- 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.

- 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.

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.

STEP TWO:

- 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)

- 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.

- Starting at the beginning of the top piece of tape, place a mark
every 20cm. The bottom piece does not need to be marked.

- 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.

- Repeat number four for each of the interval marks you placed on
the wall.

- Find the average time for each of the intervals and record it
on the data table.

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).

STEP THREE: PLOTTING AND GRAPHING THE DATA:

- Graph 1

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

- Graph 2

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

- Graph 3

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

Data Table I

**Drop****Distance ball traveled****Time (seconds)****Velocity (distance/time)****1****2****3****4****5****Average Velocity**________________

PING-PONG ALTIMETER

Data Table II

Interval Trial 1 Trial 2 Trial 3 Average Time (sec) Distance Ball Traveled (cm) 0cm 20cm 40cm 60cm 80cm 100cm 120cm 140cm 160cm 180cm 200cm 220cm 240cm 260cm 280cm 300cm

PING-PONG ALTIMETER

Data Table III

°R Interval

Original Distance Ball Traveled (From Data Table One) {D1}
Distance Ball Traveled (cm) {D2}
Altitude (cm) {D1-D2= Altitude}
0cm
20cm
40cm
60cm
80cm
100cm
120cm
140cm
160cm
180cm
200cm
220cm
240cm
260cm
280cm
300cm

How could we make the topographical profile more accurate?

What does the graph look like in comparison to your model (i.e.. the same, inverted, etc.)?

Which looks more like the model, the graph you generated from the shorter or longer distances between readings (intervals)?

The Laser Rangefinder aboard NEAR sends out a laser beam and “catches”
it as it returns from being reflected by the surface of 433 Eros.
The instrument records how long it takes the beam to reach the
surface and bounce back up. The scientists know how

Why did you not divide in half to find the distance to the object in

Why do we not use the term "Sea level" for Mars and other planets?

You will now calculate the altitude of the points along your model. To do this subtract the distance the ball traveled, at each interval (from Data Table II) from the distance the ball traveled in Step One (column B, Data Table I). The number you come up with will be zero or greater. Use Data Table III to do your calculations. {The number in column B in this table should be the same for every interval. Remember, it was the baseline altitude and does not change.}