Comets, Asteroids and Meteors • E4
Vegetable Light Curves
Activity E4
Grade Level: 9–12
Source: This activity comes from the web site for NASA’s Dawn Mission, at the Jet Propulsion Laboratory. The
activity was contributed by Dr. B. J. McCormick (McREL). It is in the public domain.
What’s This Activity About?
Tips and Suggestions
Most asteroids are small chunks of rock, orbiting in a
belt between Mars and Jupiter. We see them through
large telescopes because they reflect the light of the Sun.
Occasionally, it is possible to see variations in the reflected sunlight and use these to determine the shape
and surface features of the asteroid. (Astronomers have
joked over the years that the irregularly shaped asteroids
resemble nothing as much as potatoes.)
•A
s suggested in the write up, it may be useful to review
Moon phases with students before doing this activity.
See section B of The Universe at Your Fingertips for a
range of moon-phase activities.
•N
ote that building a potato rotating device is required
before your students can do this lab. Instructions and
a list of parts needed is given in the write up, but this
means that this is an activity for which you need to
prepare significantly in advance.
What Will Students Do?
Students will observe the surface of rotating potatoes to
help them understand how astronomers can sometimes
determine the shape of asteroids from variations in reflective brightness.
What Will Students Learn?
Concepts
Inquiry Skills
Big Ideas
• Asteroids
• Rotation
• Light curves
• Experimenting
• Inferring
• Predicting
• Graphing
• Recording
• Comparing
• Observing
• Explaining
• Reasoning
• Patterns of change
• Models and simulations
• Interactions
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Vegetable Light Curves TEACHER GUIDE BACKGROUND
In the Activity, “Vegetable Light Curves,” students will observe the surface of rotating potatoes
to help them understand how astronomers can sometimes determine the shape of asteroids
from variations in reflective brightness. When astronomers graph data relating to reflective
brightness as a function of time, the resulting graph is called a “light curve.” A good animation
that illustrates and presents additional information about light curves can be found at:
http://spaceguard.rm.iasf.cnr.it/tumblingstone/issues/special-palermo/lightcurve.htm.
MATERIALS



Activity Sheet, “Vegetable Light Curves”
Several sheets of graph paper
A watch with a second hand
Materials for each team of three:
 Two potatoes—one spherical and one elongated; a cucumber and carrot are optional
 An illumination system—a 40-watt lamp and a dark background or a darkened room
 An assembled potato-rotating system
 Sharpened dowel sticks to mount the vegetables. (There An alternative method would
are several ways in which you can prepare the equipment be to have two or more sets
for this activity. See “Vegetable Light Curve Assembly of equipment assembled and
Instructions” for equipment sources, complete assembly have teams rotate from
instructions, and safety precautions. You will need to select station to station until they
the method most appropriate for your classroom setting have completed their
and your students’ experience in the laboratory. observations.
― You may assemble all the equipment yourself.
― You may assemble part of the rotating system yourself and have your students mount the vegetables themselves. ― You may have students assemble all the equipment.
Optional
 Copies of the assembly instructions and safety precautions from “Vegetable Light Curve
Assembly Instructions” if you decide that students should set up their own equipment.
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PROCEDURE
Part 1: Light Curves
Section One
1. Divide students into teams of at least three members and distribute copies of the Activity
Sheet, “Vegetable Light Curves,” to each team.
2. For Section One, Question 1, ask team members to engage in a general discussion of the
various factors that might affect the apparent brightness of an asteroid. Tell students that
they can assume observations are being made from a space platform and that clouds and
dust are not factors to be considered. Then have them address the remaining questions.
Circulate among the groups and ask appropriate, leading questions to stimulate their
discussion.
3. After allowing sufficient time for teams to complete their answers, call the class together for
a share-out session. Have each team share one factor from their list of answers to
Question 1. Students probably will quickly identify size and distance from Earth as factors
that affect brightness. They may also conclude that reflectivity or albedo of the asteroid will
have an effect on its brightness, especially if they have completed the Activity, “Seeing
Circles—Studying Albedo.” Less obvious will be the effect that phase or degree of
illumination has on asteroid brightness.
Make sure the students’ answers to
If your students do not understand moon phases, you may
Question 2 include a clear
wish to have them access
understanding that asteroids are
http://www.usno.navy.mil/USNO/astronomicalnot like stars—they do not emit
applications/astronomical-information-center/phaseslight. Instead, like the moon, we see percent-moon for an explanation.
them only because they reflect light
from the sun. Hold up a potato and
Click on this (see obtain a moon phases activity guide:
http://lhsgems.org/GEM250.html
ask students if they could see the
potato in a totally dark room. They
should recognize that you could not
see the potato at all since reflected light provided by a source such as a lamp or the sun is
what enables you to see the potato. This point should be emphasized here because “seeing
things” is often taken for granted without thinking about what makes it possible for us to see
them. Ask them what fraction of the total surface of the potato they can see. The fraction (or
percentage) of the surface we can see, which at most is 50%, is directly related to the
amount of light reflected from the surface back toward you.
Students’ answers to Question 3 should indicate an understanding that asteroids pass
through phases, just as the moon does. You may wish to engage them in a discussion or
review of moon phases.
To help students answer Question 4, ask how the motion of an asteroid might affect its
brightness. Make sure student answers include the fact that asteroids revolve in an elliptical
orbit as well as about internal axes.
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To stimulate students’ reflection on Question 3, ask what factors other than surface area
might affect the observed amount of light. Student answers might include the difference in
reflectivity (albedo), which might be due to differences in color or texture due to cratering.
4. Pose the question, “How might Earth-bound astronomers obtain an estimate of the shape of
an asteroid?” Emphasize that “shape” implies three-dimensional characterization. After
students have exhausted their possible answers, tell them that they will be modeling a
technique that astronomers have used for many years to obtain information about the shape
of asteroids.
Section Two
Your explicit student instructions for Section Two will depend upon how much of the equipment
assembly you have decided to have your students complete and how many complete set-ups
you have for your class. See your options in “Vegetable Light Curve Assembly Instructions.”
1. Divide the class into teams of at least three members. (These groups may be the same as
the ones in Section One or they may be different.) Each team should determine the time that
is necessary for an elongated potato to make 10 complete revolutions.
2. Instruct the students to follow the directions in Section Two of the activity sheet as they
make observations. All team members should make individual observations of the rotating
potatoes, except as noted above. As you move about the room, make sure that the
observing student’s line of sight is level with the potato.
Sections Three and Four
1. Sections Three and Four of the activity should be completed as a team.
2. When all teams have finished, collect the reporting sheets and graphs and post them around
the room.
3. Engage students in a discussion of the conclusions that were reached in Section Four.
Below are some important concepts that you should bring out as students discuss the
answers to their conclusions.
Question 2. Pay particular attention to the rotational aspects of asteroid brightness. Make
sure students understand that asteroids are expected to rotate about internal axes. As a
consequence, the image of an asteroid at a particular time will depend on its rotational
position with respect to the observer unless the asteroid is spherical, in which case there will
be no rotational dependence of the brightness.
Question 3. It might be concluded that the area of the larger side is twice that of the smaller
side. However, if there is a difference in the albedo of different areas of the asteroid, then
that conclusion may not be valid. For example, in the Vignette, “More Discoveries…Better
Descriptions,” there is a sentence that describes Vesta:
“In 1987 speckle interferometry showed that 4 Vesta is dimmest when its
maximum cross section faces Earth and that its surface features have more
influence on its light curve than does its shape.”
Question 4. If the observed end of the asteroid is uniform in albedo and not distorted by
craters, the light curve would be much like that provided by a sphere. In other words, a
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graph of light reflected versus time would be a straight line if the end of the asteroid were
perfectly circular.
Question 5. At any one observational time, one measures the light curve of a rotating
asteroid at a particular point in its orbit. This means that it is impossible to see all of an
asteroid’s reflective properties from a single observational point of view, i.e., the backside or
the ends of the asteroid will remain obscure. However, as an asteroid moves around the sun
in an elliptical orbit, its position (think “tilt” or “inclination”) with respect to the Earth changes.
This positional change coupled with its rotational properties provides a different view over
time. Therefore, a sequence of light curves measured over a long time frame may provide
sufficient information to determine an asteroid’s entire shape.
Question 6. You might want to have a potato mounted at a 45-degree angle for students to
observe as they discuss their answers to this question.
Questions 7 and 8. Students’ answers to these questions will depend upon their original
measurements in Section Two. The main emphasis here is to help students see the
relationship between rotational rate and the angle through which a potato rotates during a
given period of time. If you have the students pursue the “Quantitative Extensions” (below),
they will use the rotational rate determined in the activity.
Question 9. You should be able to read the answers to these questions from the light curve.
 Eros was brightest at about the three-hour mark.
 It was dimmest shortly after the four-hour mark.
 One Eros “day” is about 5.25 hours. (The day ends before the light curve does. The
last peak you see is the beginning of another day.)
Question 10. The two brightest peaks were different in amplitude because light was
reflecting from two different surfaces. The same is true for the two lowest reflecting surfaces.
Question 11. The light curve of a regularly shaped asteroid would be very close to a straight
line because its surface would reflect the same amount of light regardless of what part of its
surface we were viewing. The greater the differences in light reflected during the period of
rotation, the greater the irregularities of the asteroid surface reflecting the light.
4. Ask students how much more difficult this activity would be if the observer were sitting:
a) Across the room from the rotating potato.
b) The length of a basketball court away from the rotating potato.
c) The length of a football field away from the rotating potato.
o How does the distance between the rotating vegetable and the observer
affect the accuracy and reliability of the observations?
o How does the length of a football field compare with the distance between an
Earth-bound telescope and an asteroid? Between a space telescope and an
asteroid?
o Would the observer’s eyesight affect the reliability of the observations? How
do the differences among the observer’s visual abilities model the differences
in technology used by early astronomers (small, Earth-bound telescopes) and
that used today (Hubble Space Telescope)?
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5. Distribute copies of the Vignette, “I Can See You More Clearly Now.” Allow students time to
read the vignette and then ask:
a) Do you think that these images of Vesta and Ceres taken from the Hubble Telescope
are clear enough for scientists to make accurate observations? Why or why not?
b) How might better images of Ceres and Vesta be made? (One possible student
answer might be for a spacecraft—manned or unmanned—to travel to the asteroids
for a “close-up” look.)
Quantitative Extensions
The procedures provided in this activity provide dynamic—but only qualitative—information
about light curves. Should you wish to do so, you can place the activity on a more quantitative
footing by having the students pursue one or both of the procedures outlined below.
 This more quantitative exercise is made possible by the fact that in the activity the
students have determined the rotational rate for their potato in degrees per second.
Ask the students to use a protractor and prepare a sheet of paper with lines drawn on it
from a center point of the paper out to the edges so that the lines are separated by 30degree intervals. They should complete a 360-degree pattern of repeating lines. Have
the students label these index lines by placing 0, 1, 2, 3, etc. at the ends of the lines.
Now have them orient the paper so that index line 0 extends to their right. Index line 3
should point toward them. Next, have them place their long potato on the paper such
that its long axis is aligned with index line 0, with the potato center at the origin of the
lines. Have them place a mark with a pen on the end of the potato near and in line with
index line 0. Now ask them to visually estimate the fraction (or percentage) of surface
they can see, and record their estimate along with the index number (0 in this case).
Now instruct the students to rotate the potato by hand until the mark on the potato lines
up with index line 1. Again, they should estimate the fraction of visible surface area and
record the result along with the index number. This procedure should be repeated until
the potato is rotated through 360 degrees (or more). Now the students can use their
previously determined value of rotational rate in degrees per second to evaluate the
time it took for the potato to reach the position corresponding to a given index line when
the potato was on the rotation apparatus! In effect, the students are setting up a
snapshot of what the potato would have looked like when it passed through 30, 60, and
so on degrees. To have them complete the activity, instruct them to determine the
number of degrees of rotation for each index mark and divide the degrees by their
previously determined rotational rate to provide the time required for the potato to reach
that snapshot point when it was on the rotation apparatus. They can then plot a graph of
percentage (or fraction) of surface area visible vs. time and produce a reasonably
accurate “potato light curve.” To aid them in making estimates of surface area it may be
helpful to draw lines around the circumference of the potato at roughly 1 cm intervals. It
also might be instructive to pursue with them the interpretation of the number they obtain
when they divide 0 (the degrees corresponding to index line 0) by the rotation rate.

The above activity can be made even more accurate by setting up a camera (digital
preferred) and photographing the potato at each index mark. For best results, zoom in
so that the potato fills the frame. The resulting set of photographs can now be printed on
plain paper with a standard printer and appropriate software. The image of the potato
can be cut out from each photograph and weighed on a good balance. The weight of
each piece can then be expressed as a fraction of the weight measured in the photo with
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the potato exposed to the maximum extent. This procedure provides a reasonably
quantitative measure of visible surface area, which can then be graphed against time as
determined above.

Light meter on Calculator Based Lab (CBL) with light probe. Illuminate the potato in a
darkened room. Measure the reflectivity. Then compare with measurements above.
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ADDITIONAL TEACHER RESOURCES WEB SITES
http://nssdc.gsfc.nasa.gov/planetary/factsheet/asteroidfact.html
Asteroid Fact Sheet
http://solarsystem.nasa.gov/educ/educators/index.cfm
Solar Systems Exploration
http://solarsystem.nasa.gov/missions/profile.cfm?Sort=Alpha&Letter=D&Alias=Dawn
Missions to Asteroids: Dawn
http://solarsystem.nasa.gov/missions/profile.cfm?Sort=Alpha&Letter=D&Alias=Deep%20Space
%201
Missions to Asteroids: Deep Space 1
http://solarsystem.nasa.gov/missions/profile.cfm?Sort=Alpha&Letter=G&Alias=Galileo
Missions to Asteroids and Planets: Galileo
http://neo.jpl.nasa.gov/missions/hayabusa.html
Missions to Asteroids: Hayabusa (MUSES-C)
http://solarsystem.nasa.gov/missions/profile.cfm?Sort=Alpha&Letter=N&Alias=NEAR%20Shoe
maker
http://neo.jpl.nasa.gov/missions/near.html
Missions to Asteroids: NEAR
http://solarsystem.nasa.gov/missions/profile.cfm?Sort=Alpha&Letter=S&Alias=Stardust
Missions to Comets: Stardust
http://stardustnext.jpl.nasa.gov/
Missions to Comets: Stardust-NExT
http://solarsystem.nasa.gov/missions/profile.cfm?Sort=Target&Target=Comets&MCode=Rosett
a
Missions to Comets: Rosetta
http://www.astro.uu.se/planet/asteroid/shapes/
Interactive showing examples of irregular-shaped asteriods in 3-D.
http://neo.jpl.nasa.gov/images/vesta.html.
Hubble Space Telescope and Keck images of Vesta
http://dawn.jpl.nasa.gov/multimedia/video/vesta.mov
Animation of Vesta rotation
http://www.figurethis.org/challenges/c61/challenge.htm
This activity asks students to determine if the Statue of Liberty's nose is out of proportion to her
body size. The activity, from the Figure This! list of 80 math challenges, illustrates how to use
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similarity and scaling to design HO gauge model train layouts and analyze the size of characters
in Gulliver's Travels.
http://dawn.jpl.nasa.gov/
Missions to Asteroids: Dawn
PRINT RESOURCES
McSween, H.Y. (1999). Meteorites and their parent planets. Cambridge; NY: Cambridge
University Press.
Peebles, C. (2000). Asteroids: A history. Washington, DC: Smithsonian Institution Press.
Roth, G.D., (1962). The system of minor planet. Princeton, NJ: Company Inc.
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APPENDIX C—STANDARDS ADDRESSED National Science Education Standards addressed:
Science as Inquiry
Understandings about Scientific Inquiry
 Different kinds of questions suggest different kinds of investigations. Some involve
observing and describing objects; some involve making models.
 Current scientific knowledge and understanding guides scientific investigations.
 Mathematics is important in all aspects of scientific inquiry.
 Technology used to gather data enhances accuracy and allows scientists to analyze
and quantify results of investigations.
 Scientific explanation emphasizes evidence.
 Science advances through legitimate skepticism.
 Scientific investigations sometimes result in new ideas for study.
Physical Science
Motions and Forces
 The motion of an object can be described by its position, direction of motion and
speed. That motion can be measured and represented on a graph.
Transfer of Energy
 Light interacts with matter by reflection. To see an object, light from that object must
enter the eye.
Earth and Space Science
Earth in the Solar System
 The Earth is the third planet from the sun in a system that includes the moon, the
sun, eight other planets and their moons, and smaller objects such as asteroids and
comets.
 Most objects in the solar system are in regular and predictable motion.
Science and Technology
Understandings about science and technology
 Scientific inquiry and technological design have similarities and differences.
 Many different people in different cultures have made and continue to make
contributions to science and technology.
 Science and technology are reciprocal.
 Perfectly designed solutions do not exist.
 Technological designs have constraints.
 Technological solutions have intended benefits and unintended consequences.
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Comets, Asteroids and Meteors
History and Discovery of Asteroids
More Discoveries…
Better Descriptions
VIGNETTE
From the 1890s through the 1930s, asteroid research was buzzing with excitement; a total of
1140 asteroid discoveries occurred during this time. With such a surge in activity, it became
necessary to record and communicate the latest findings. Beginning in 1890s, this responsibility
was fulfilled by the Rechen-Institut in Berlin. They kept track of asteroids, published predictions
of asteroid positions and the RI Circulars, which contained updated information about asteroids.
During the early 1930s, the rate of asteroid discovery averaged about 38 per year. At the same
time, new photographic (see “Silver to the Rescue”) and spectroscopic (see “Dawn
Dictionary”) technologies merged with telescopes to determine asteroids’ shapes and the
elements in their atmospheres. By 1929, Nicholas Bobrovnikov had used these newlydeveloped technologies to determine the spectra of twelve asteroids. He found that Ceres was
bluer than Vesta, indicating that Ceres was reflecting more high-energy radiation than Vesta.
Spectroscopes break up visible light into a spectrum of different wavelengths so that the light energy can be
analyzed... Notice in the illustration above, visible light accounts for a small part of the electromagnetic spectrum.
Consider this in the historical context of asteroid research: imagine how much more is out there than meets the eye!
By 1939, asteroid discoveries and studies came to a screeching halt. Why? Think about world
history. What was going on in Europe during the late 1930s through the 1940s? With the
beginning of World War II in 1939, asteroid research virtually ended for almost three decades
because the world’s attention and resources were directed to the war effort. However, as you
will see, some of the technologies developed for the war effort ultimately advanced future
asteroid studies.
Asteroid Research in the Post-World War II Era
After World War II, the activities of the Rechen-Institut were scattered. Parts of the material
were moved to Heidelberg, but at least half of it remained in Soviet-controlled Berlin. The
German observatories that had undertaken asteroid work before the war lacked essentials like
photographic plates to continue their work. When the International Astronomical Union (IAU)
met in Copenhagen, Denmark in 1946, it assigned most of the activities that had been centered
in Germany to Soviet astronomers and observatories.
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The Minor Planet Center at Cincinnati, Ohio was established as the IAU center for asteroid
research in 1947. Since asteroid programs had become so disorganized
during the war, the primary efforts of the center were focused on keeping
Data collection,
track of the almost 1,600 known asteroids. Other activities of the center,
organization, and
under the direction of Paul Herget, included publishing Minor Planet
publication.
Circulars, collecting and maintaining asteroid observations and
calculating asteroid orbits and their positions. Eventually the Center was transferred to
Cambridge, Massachusetts.
Another astronomer studying asteroids during the post-war period was Netherlands-born
Gerard Kuiper, who worked in the McDonald Observatory in Texas.
New technology
From 1950 to 1952, he conducted an asteroid survey using a 10-inch
makes it possible to
telescope that recorded asteroids down to a magnitude of 16.5 and
find smaller, dimmer
photographed the entire ecliptic twice. This technique produced a
asteroids and to
clearer picture of asteroid distribution in space and provided statistical
study asteroid
data on asteroid population. In 1960, Tom Gehrels was involved with
characteristics.
the Palomar-Leiden Survey, observing smaller areas of the sky and
making brightness and distance measurements of some 1,800 asteroids. In 1971, Gehrels
edited the first text on asteroids and organized the first asteroid conference in Tucson, Arizona.
More accurate brightness measurements
Whereas 19th-century astronomers could measure an
asteroid’s brightness to an accuracy of 0.1 of a
magnitude, new photographic technologies (see “Silver to
the Rescue”) improved the accuracy of measurements to
about 0.05 of a magnitude. The advent of the RCA
photomultiplier tube during World War II was first used in
astronomy in the early 1950’s in a process known as
differential photometry. Three measurements, using
ultraviolet (U), blue (B), and visual (V) filters, were
integrated in minutes with an accuracy of 0.001 magnitude.
This UBV system became the standard method for
measuring brightness.
A photomultiplier tube detects very weak
light, converts it to electricity and
amplifies the signal. It is used in
photometry which measures the relative
amounts of light in different wavelengths
(visible colors), thereby making asteroid
research more quantitative.
Rotation rates from light curves
The introduction of computers that corrected for air mass and subtracted background sky
brightness, decreased the time necessary to process the data from the UBV observations, and
made it possible to measure asteroid rotation rates from their light curves (see “Vegetable
Light Curves”). Astronomers had attempted to detect asteroid light variations as early as 1810,
but small variations (some as small as a few hundredths of a magnitude), erratic curves
resulting from irregular shapes, and varying numbers of brightness peaks during each rotation
made meaningful measurements difficult until the late 1960s.
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Asteroid shapes based on light curves
Starting in 1971, astronomers tried a number
of methods for modeling asteroid shapes
based on their light curves. Modeling
techniques included rotating Styrofoam
bodies covered with substances such as
powdered rock and graphite powder. Another
procedure known as the convex-profile
inversion produced a two-dimensional
convex profile, which was then used to
produce a three-dimensional shape.
The camera system aboard the Galileo spacecraft
captured a series of high resolution images of asteroid
Ida’s rotation. This sequence enabled scientists to
create a 3-D model of the asteroid.
A new technology, speckle interferometry,
was developed in the mid-1970s. SU uses ground-based telescopes and computer technology
to make highly detailed or high-resolution images of asteroids by clustering together loads of
tiny “specks” to form a clearer picture. These large telescopes capture a series of rapid
exposures lasting only a few thousandths of a second. If you had a camera with a shutter speed
that fast, you would never have to worry about somebody blinking or developing a blurry picture
simply because somebody moved. This super-fast freeze frame also makes it possible to
eliminate the blurry effects of a constantly moving atmosphere. Therefore, when a series of
frames, taken over several minutes, are combined into a single image by a computer, the result
is a clearer picture of an asteroid’s shape. Based on such observational data and theoretical
calculations, the shapes of 1 Ceres and 2 Pallas were determined to be nearly spherical, and 3
Juno and 4 Vesta were found to be elliptical.
The rest of the story
In 1987, speckle interferometry revealed some surprising information. It showed that 4 Vesta is
dimmest when its maximum cross section faces Earth, and that its surface features have more
influence on its light curve than does its shape. If you have done the Vegetable Light Curve
activity, you learned that the surface area directly affected the light curve. The larger the
exposed surface area, the more light was reflected, so
the brighter the object appeared. This 1987 finding about
Vesta may appear to contradict the Vegetable Light
Curve activity. Instead it shows that variations of
brightness in an asteroid’s light curve involve not only the
amount of surface area being observed, but also the
albedo – the degree to which light is reflected - of
irregularities and craters on an asteroid’s surface.
In the 1980s, new electronic techniques employing
CCDs are electronic detectors placed in
charge-coupled devices (CCDs) had an enormous
telescopes. The CCD shown here is
packed with 100s of tiny light sensing
impact on asteroid research. CCDs combined with
diodes, each of which records the
computer data processing provide astronomers with
brightness of light and transmits this
greatly enhanced observational capabilities. For example,
data to a computer.
the Spacewatch Program used CCDs in the discovery of
a near-earth asteroid in 1989. This Arizona-based program, which has as a general goal of
discovering small objects in the solar system, has identified numerous new asteroids smaller
than 100 meters in diameter using CCD technology. CCD equipment is now available to
amateur astronomers who have been finding comets and asteroids for years. Other successful
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professional electronic discovery programs are now located in New Mexico, Hawaii, and in other
parts of the world.
The Hubble Space Telescope in orbit.
Observations by the ground-based Keck II
Telescope in Hawaii, the Hubble Space
Telescope, and unmanned spacecraft (see “I Can
See You More Clearly Now” and “Modern Era of
Asteroid Study”) are now contributing new
knowledge about asteroids’ shapes, rotation rates,
and surface features. The Dawn mission’s
technology will allow us to “travel back in time”
about 4.6 billion years. By focusing on the internal
structure, density, magnetization, elemental and
mineral composition of Vesta and Ceres, scientists
will gather evidence to shed some light on the
mysteries of our solar system’s origins.
VIGNETTE: More Discoveries…Better Descriptions
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Additional Resources
http://fuse.pha.jhu.edu/~wpb/spectroscopy/spec_home.html
This “Learning from Light” educational Web site offers activities and informative texts about
concepts of light and astronomical spectroscopy suitable for middle and high school students.
http://www.exploratorium.edu/snacks/spectra.html
Provides instructions for a hands-on activity to build your own spectroscope out of a shoebox.
http://imagine.gsfc.nasa.gov/docs/introduction/emspectrum.html
This NASA Web site offers helpful, student-friendly texts about the electromagnetic spectrum.
Featured topics include: Measuring the Electromagnetic Spectrum, Why Do We Have to Go to
Space to See All of the Electromagnetic Spectrum? Space Observatories in Different Regions of
the EM Spectrum and more.
http://cfao.ucolick.org/
The Center for Adaptive Optics includes information and images about the latest technology for
improving visual images obtained from various optical instruments including astronomical
telescopes.
http://cobalt.golden.net/~kwastro/Stellar%20Magnitude%20System.htm
This article “The Stellar Magnitude System” originally published in Sky & Telescope magazine
explains how magnitude has been measured throughout history, and shows how the
measurement system changed in response to new technologies.
http://seds.lpl.arizona.edu/nineplanets/nineplanets/asteroids.html
Historical information on asteroid discovery, data and images of specific asteroids.
http://nssdc.gsfc.nasa.gov/planetary/factsheet/asteroidfact.html
Asteroid Fact Sheet
http://neo.jpl.nasa.gov/images/vesta.html.
Hubble Space Telescope and Keck images of Vesta
http://www.ast.cam.ac.uk/HST/press/oposite.stsci.edu/pubinfo/PR/97/27/vesta.mov
Animation of Vesta rotation
http://www-ssc.igpp.ucla.edu/dawn/index.html
Dawn
VIGNETTE: More Discoveries…Better Descriptions
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Comets, Asteroids and Meteors
History and Discovery of Asteroids
Vegetable Light Curves
ASSEMBLY INSTRUCTIONS
1. The following materials and equipment are needed for each team:
• Two potatoes. One potato should be spherical and the other should be elongated. If you use
potatoes that are very elongated—you’ll get better results. A long sweet potato of nearly uniform
diameter would work well. A cucumber might be substituted for the second potato if it is more
convenient to do so. A long carrot of more or less uniform diameter may also be used for
making additional observations.
•
An illumination system. Ideally this will consist of a dark background against which the
potatoes can be viewed, and a 40-watt lamp and shield that directs light primarily in one
direction. \Alternatively, the activity may be carried out in a dark room.
•
Parts for potato rotation system. Obtain the
following items for each system, as shown in the
To order a motor, contact Scientifics.
photograph below: 1) a small electric motor with a
Web address: www.scientificsonline.com
Phone orders: 1-800-728-6999
¼-inch drive shaft to provide a means of rotating
Address: 60 Pearce Ave.
the potatoes at a constant, slow rate. A heavyTonawanda, NY 14150-6711
duty motor that revolves at a steady 3 rpm is sold
Item
number:
F30607-44
by Scientifics at a nominal price that works
Cost: $15.95
exceedingly well for this activity. The directions
that follow utilize this motor. The motor has a hole
in the shaft and a flange that permits it to be attached to plywood or another base with screws if
it is so desired; 2) a 2- to 3-inch piece of electrical or other tape that is about ¾-inches wide;
3) a small hose clamp; 4) a ¾-inch long paper clip that has been cut with wire cutters to provide
a loop 3¼ inches long; and 5) a small screwdriver.
The Universe at Your Fingertips • Astronomical Society of the Pacific
ASSEMB L Y INSTRUCTIONS: Veg et ab l e L i g h t Cu r v es
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2. Assemble the potato rotation system as follows: Insert the loop of the cut paper clip into the
hole in the motor’s shaft so that the cut ends are pointing upward. Hold it in place while you tightly
wrap it with the tape. Next, place the hose clamp over the tape and tighten it securely with a
screwdriver. The potatoes can be pushed down on the upward-pointing ends of the cut paper clip to
mount them securely to the motor and shaft. In the photograph below, you can see a picture of a
potato mounted in this fashion. In the following sections, these upward-pointing paper clip segments
will be referred to as “mounting pins.”
3. Procedures: First, choose the spherical potato. Gently push it down on the mounting pins so it will
be securely held in place while the motor rotates the potato in front of the observer. The mounting
pins should be inserted into the approximate center of gravity of the potato so it does not wobble
during rotation. You may want to determine the center of gravity ahead of time and mark it with a
pen. With the motor running, make the required observations.
A similar procedure is followed with the elongated potato mounted in a horizontal orientation. This
potato should be mounted in such a way that the mounting pins are stuck into the potato half-way
between the two ends very near the center of gravity. You may want to find the approximate center
of gravity by determining the point where the potato can be more or less balanced on the eraser of
a pencil or other blunt object. Once again, you do not want the potato to wobble. With the motor
running, make the required observations.
Similar procedures are followed for mounting the long potato in a vertical position and making the
required observations. Once again, do this with care, since you do not want the potato to wobble.
If you extend the activity to include a carrot, be very careful so that you do not bend the mounting
pins. It may be advantageous to “drill” small holes in the carrot with an opened paper clip to match
the mounting pins before the carrot is placed on the apparatus. This should be done carefully to
avoid getting injured should the paper clip slip.
ASSEMB L Y INSTRUCTIONS: Veg et ab l e L i g h t Cu r v es
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Alternative Rotation Devices
Other rotation devices might be designed. For example you might use a faster motor
and couple it with a gearbox (also available from Scientifics) to provide an acceptable
lower rotational speed. Rotation speeds faster than approximately 3 rpm are not
desirable. A motor/gear box combination for reducing the rotation speed of a faster
motor might be used in conjunction with a discussion of machines such as levers and
gears. A motor that does not have a hole in the shaft will require a different mounting
system. If motors are not available, you might use a woodworker’s hand drill to hold a
sharpened dowel stick (hazardous, be careful) upon which the potato is mounted and
then ask a team member or other individual to turn the drill at as close to a constant,
but low, speed as possible. Finally, if none of the above is feasible, have a team
member or other individual rotate the dowel stick by hand at a slow and constant rate.
The potato should be rotated at a speed such that observers are able to see clearly
how the surface area changes as the potato rotates. If these latter two methods are
used the quantitative extensions will not be feasible.
ASSEMB L Y INSTRUCTIONS: Veg et ab l e L i g h t Cu r v es
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Comets, Asteroids and Meteors
History and Discovery of Asteroids
Vegetable Light Curves
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?
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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.”
Observation of round potato
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.
Other observations of elongated potato in horizontal position
Observations of elongated potato in vertical position
ACTIVITY REPORTING SHEET: Vegetable Light Curves
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Comets, Asteroids and Meteors
Observations of additional vegetables
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.)
Fraction of Surface Seen vs. Time
Decimal Fraction
of Surface Seen
Time
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.
ACTIVITY REPORTING SHEET: Vegetable Light Curves
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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.
ACTIVITY REPORTING SHEET: Vegetable Light Curves
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Comets, Asteroids and Meteors
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.
The Johns Hopkins University Applied
Physics Laboratory
9. This is the light curve of the asteroid Eros taken from
the NEAR spacecraft.
 At what time (in hours) was Eros the brightest?
 When was it the dimmest?
 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?]
Light curve of Eros
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.
ACTIVITY REPORTING SHEET: Vegetable Light Curves
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