ACTIVITY REPORTING SHEET
In this activity, you will investigate a technique astronomers have used for many years to obtain information about the shape of asteroids. You may wish to review the information in the Vignettes, "What Can You See With a Telescope?" and "Seeing Circles -- Studying Albedo," before you begin this activity.
Section One
Based on your previous experience and reading, answer the following questions.
1. List some factors that might affect an asteroid's brightness.
2. Is light emitted by or reflected from an asteroid?
3. How would the brightness of light from an asteroid depend on its orbital position in space? Explain your answer.
4. How does the position of the Earth, relative to that of an asteroid, affect the asteroid's apparent brightness?
5. In addition to moving in its orbit, what other motions might an asteroid undergo that would affect its apparent brightness?
Section Two
In this activity, you will observe a potato's surface as it rotates in front of you. The potato may already be mounted and ready for observation or "some assembly may be required." Your instructor will give you explicit instructions.
With one exception (see below), in Section Two each team member should make his/her individual observations. When you are the observer, sit in front of the rotation apparatus provided. Make sure that your eyes are level with the potato as it rotates on the apparatus. You should try to "stare" at the potato without moving your head during the observational period. When you are ready to start, have a teammate turn on the rotation device.
Carefully observe the potato rotating for several complete rotations and then decide whether or not you can see a change in the amount of visible surface area as the potato rotates. Then answer for yourself the question, "Does the amount of visible surface area change as the potato rotates?" In the space below, write a simple statement about how the observable surface area changes with rotation during several complete rotations. For example, your answer might be similar to one of the following statements: "It does not change much at all," or "It gets bigger then smaller," or "It gets bigger and stays that way."
You will observe at least one additional potato mounted in two different orientations. Your teacher may instruct you to make additional observations.
Using a watch, your team should determine the time, in seconds, required for a horizontally mounted elongated potato to make 10 complete revolutions. A team member should record this time in the space below.
Section Three
As a team, discuss your observations of the round potato and your individual answers to the question, "Does the amount of visible surface area change as the potato rotates?" Reach a team consensus about the best answer to the question. As a team, decide what a graphical sketch of fraction (or percentage) of visible surface area (y-axis) vs. time (x-axis) would look like for the round potato. Keep in mind that the maximum percentage of surface area that you can observe while seated in front of the potato is approximately 50%, i.e. you cannot see the back of it. (See illustration below of the axis system and of a sketched graph. This sketch may or may not be similar to the ones you deduce from your observations.)
Make three graphical sketches-for the round potato and for the elongated potato in each of its two mounted positions. Make sure you label your sketches.
Section Four
Select a recorder. As a team, answer the following questions after you have created your graphs.
1. Did any of your sketches show periodic or repeating features, i.e. peaks and valleys that repeat over and over? If so, explain why. If not, explain why.
2. The sketches you have created are very similar to the light curves graphed by astronomers. In this case light reflected from an asteroid is measured electronically and the amount of light reflected (called the amplitude of the reflected light) is graphed against time. Explain how you think such measurements can give astronomers an estimate of the shape of an asteroid.
3. If an asteroid is observed throughout one complete rotation and its maximum brightness is twice as great as its minimum brightness, what can be inferred about the area of the largest side compared to the smallest side?
4. If astronomers happened to observe a carrot-shaped asteroid that is rotating around its long axis while its "north" pole (the stem end) is facing Earth, what would the light curve for this asteroid look like?
5. In order to obtain a good estimate of the shape of an asteroid, it is necessary to observe light curves at different parts of the asteroid's orbit. Explain why this is necessary. (Hint: think about your answer to Question 3 and about the two sketches for the long potato.)
6. If the potato were mounted at an angle, say 45 degrees, to the axis of rotation, what do you think your sketch would look like?
7. The period of rotation of an asteroid is the time required for one complete rotation. Based on the measurements you made of the 10 revolutions of the long potato in Section Two, calculate its period of rotation in seconds.
8. Again, based on the measurements you made on the long potato, calculate the time in seconds required for it to rotate through one degree.
9. This is the light curve of the asteroid Eros taken from the NEAR spacecraft.
- At what time (in hours) was Eros the brightest?
- What is the period of rotation for Eros?
- How long does it take Eros to rotate through one degree?
- If you were a few kilometers from Eros and could observe it with your naked eye, how long do you think you would have to watch it to discern its rotational motion? [Hint: Would it depend on Eros's shape and surface features?]
10. You can see two peaks and two troughs (valleys) in Eros's light curve. There is a difference in the reflectivity amplitude of the two peaks, and the bottoms of the two troughs are also different in reflectivity. How do you explain these differences in amplitude? (Hint: Think about how the surface might change as the asteroid rotates).
11. The amplitude or the height of the peak in the curve gives astronomers an indication of the irregularity of an asteroid's shape. High amplitudes imply very irregular shapes. Explain why this would be the case. (Hint: Think about your answer to Question 4.)
12. In light of your answers to the questions above, explain why it is necessary to send Dawn-like missions to asteroids to determine with certainty their physical characteristics.
