## EXERCISE 4 "WHERE IS MR. TOAD?"

The purpose of this exercise is show that it is possible to locate and measure rocks and other features on the surface of Mars. Mr. Toad can be viewed in 3-D.

### EQUIPMENT

This is an exercise that young students might be able to do because part of it only requires images, a map base, a protractor, and a straight edge (or triangle with straight edges).

### BACKGROUND

Two Viking spacecraft landed on Mars when Mars was about 363 million kilometers from Earth (at closest approach, Mars is about 56 million kilometers from Earth).

Each lander had two cameras separated by 0.822 meters. The directions or azimuths of the pictures are known with respect to reference directions for each camera on the lander.

The map that has been furnished (see note, link, and warning below) shows a plan view of Viking Lander 2. If you look carefully at the map, you can see two pairs of concentric circles with "plus" signs in their centers. They are labled Camera 1 (left one) and Camera 2 (right one).

The dashed lines extending from the "pluses" are the reference directions for each camera. The reference direction for Camera 1 extends to the right of the Camera 1 "plus" and the reference direction for Camera 2 extends to the left of the Camera 2 "plus."

### EXERCISE

In the two images below, the sun was toward the left. This causes the shadows to extend from rocks toward your right.

Picture 21H034/595 was taken with Camera 1. It has a starting azimuth of 288.5 degrees and an ending azimuth of 298.5 degrees. Picture 22H033/595 was taken with Camera 2. It has a starting azimuth of 97.5 degrees and an ending azimuth of 107.5 degrees.

See EXERCISE 3 for procedures for 3-D or stereo-viewing.

Your viewing screen should be 600 or more pixels wide to show these pictures side by side. If the pictures don't appear side by side, try increasing the size of your viewing window.

#### EASY PART

Most explorers have great imaginations. They often name mountains and peaks for animals, fictitious characters, or familiar objects. On Mars, they named a rock for Mr. Toad -- a character in Kenneth Grahame's book "The Wind in the Willows."

Can you find Mr. Toad in the pictures above? Once you think you have found Mr. Toad you may use the remaining clues to confirm your guess.

1. The rock is shaped like a toad.
2. The rock appears to have warts (like a toad). The "warts" are shallow pits in the rock.
3. Mr. Toad's two bulging eyes are on the left side of the toad (rock).
4. Mr. Toad is in the upper half of both pictures.
5. Mr. Toad is in the center of the right picture.
6. Mr. Toad is in the left-hand side of the left picture.
7. Mr. Toad has a mouth. Is he smiling?
9. What do you think about locating a small rock on a planet that is tens to hundreds of million kilometers away from you?
Mr. Toad is a big toad by Earth standards. He is about 25 centimeters long. This part of finding Mr. Toad involved making a guess (a theorem) and with more information confirming or revising the theorem.

#### DIFFICULT PART

Now that you have found Mr. Toad, you can locate him on the map.

1. Measure the starting and ending azimuths from the reference direction in a clockwise direction for each camera and plot a point for each. Remember: Picture 21H034/595 was taken with Camera 1. It has a starting azimuth of 288.5 degrees and an ending azimuth of 298.5 degrees. Picture 22H033/595 was taken with Camera 2. It has a starting azimuth of 97.5 degrees and an ending azimuth of 107.5 degrees.
2. Draw lines from the "pluses" through the plotted points for each camera.
3. You will get two wedges that extend from the "pluses." These two wedges include parts of the fields of view of each camera on the map and are 10 degrees wide.
4. The area common to both cameras is where the wedges overlap. Does the map show a rock labeled Toad in the area overlap?
5. Select several points on Mr. Toad which can be identified in each picture.
6. Compute the azimuths of these points. (Interpolate between the starting and ending azimuths of the camera.)
7. For each pair of azimuths, extend the azimuths from the location (+) of the corresponding camera. These azimuths should cross each other.
8. Plot the point of intersection.
Can you find other things this way?

If you had enough time and more pictures, could you make a map of the rocks on Mars?

(Note. I have included "boltdown angles" in the azimuths given)

Note. The working map that you have on your WEB site, which is linked below, is a suitable base map. The extended mission map in the back of Professional Paper 1389 is also suitable. If the map is hard to read and you don't have Professional Paper 1389, you can request copies of the map from James E. Tillman or Henry J. Moore.

## WARNING:

This section includes a link to the map for this exercise. Do not click on the link below unless you have a very fast link, a large memory and a capable system. The biggest, fastest workstations take about 30 seconds to process and display them.

Lander 2, end extended mission. [Bit Map: 3.48 MBytes]

#### VERY DIFFICULT PART

Here are some sketches of a Viking lander. Figure A is a perspective view. Figure B is a plan view (from the top). Figure C is view from the left side.

You can make your own map of the Viking Lander 2 region shown in the pictures above using the following information:

1. The Lander Science Coordinate System is used for the map.
2. The origin is at center of the upper planar surface of the prismatic lander body. The three axes are perpendicular.
3. X is perpendicular to the planar surface and positive downward.
4. Y and Z are in the plane of the upper planar surface of the lander body.
5. Z is positive in the forward direction. It passes half-way between the two cameras.
6. Y is positive to the left, as viewed from the lander.
7. The coordinates of Camera 1 are:
X = -0.487, Z = +0.472, Y = +0.411
8. The coordinates of Camera 2 are:
X = -0.487, Z = +0.472, Y = -0.411
In addition, there are Camera Coordinate Systems.
1. For both cameras, elevation angles are measured from a plane passing through the camera mirrors and perpendicular to the azimuth axes of the cameras. Down is (+) and up is (-).
2. Azimuths are measured clockwise from a reference direction.
3. The reference directions for Lander 2 with "boltdown" corrections are:
Camera 1 171.37 degrees counterclockwise of +Y
Camera 2 5.45 degrees clockwise of +Y
4. Diode displacement corrections are needed for precise work.
If you have questions or problems with the VERY DIFICULT PART contact:
George LeCompte (lecompte@atmos.washington.edu)