BONUS
MATERIALS
The Mystery of Dark Matter: Bonus Materials
The Mystery of Dark Matter resource was originally designed by Perimeter Institute for students in senior
physics courses. These new bonus activities have been developed for students studying astronomy in an
introductory science course. These activities have been used in both senior and intermediate classes and have
been reviewed by hundreds of classroom teachers.
This resource is not just about dark matter—it is about the nature of science. Science is not a fixed body of
facts to be learned but a process of understanding that is still ongoing. The resource starts with an exploration
of orbital motion to introduce one of the biggest mysteries facing physicists today then continues with students
using the tools and techniques developed by astronomers to further explore the evidence for dark matter.
Activity 1: Mass and Orbits (30 minutes)
The students explore the effect of mass on orbits through a variety of methods: spacetime fabric, planetary
data, computer simulations, role playing and a 1-minute animation. After these exercises, the students could
be shown the first half of the Mystery of Dark Matter video (chapters 1 to 4) and discuss the first four concept
questions before doing Activity 2.
Activity 2: Gravitational Lenses (30 minutes)
The students explore gravitational lensing with masking tape, plates, wine glasses, and an astronomical image.
After this exercise the students could watch the rest of the video and discuss the rest of the concept questions.
Video: The Mystery of Dark Matter (30 minutes)
The video contains quite a bit of material from the senior physics course. Students will get more out of viewing
it if they have already done the two worksheets above. The video is available online at PI`s website
(www.perimeterinstitute.ca) so students can watch it again at home.
Concept Questions (30 minutes)
These questions are designed to promote discussions between students to deepen their understanding of
concepts in the video. The students will use a multiple-choice booklet which can be made by printing Appendix
A, cutting the paper into quarters and stapling them together at the top. The technique is most effective when
the students first choose an answer on their own, then show you their chosen letter (which gives you a quick
assessment of the class), and finally find another student with a different answer and discuss which is right and
why. The first four questions deal primarily with mass and orbits and the remaining six deal with gravitational
lensing and the theories and experiments trying to make sense of the mystery of dark matter.
Activity 1: Gravity and Orbital Motion
Name ________________________
You will be using a large sheet of stretchy fabric to model orbital motion. Pull the fabric down in the center by
using a large weight or by a person pulling underneath. Your challenge is to roll a ball on the fabric so that it
orbits as many times as possible. You may not move the fabric to keep it going.
1)
a) Predict and Explain: Which variables might influence the ability of the ball to orbit?
b) Observe and Explain: What combination of variables must be just right for the ball to orbit?
c) Extend and Explain: Why doesn’t the Moon fall down to the Earth?
2)
a) Predict and Explain: How will the radius of an orbit affect the period of the orbit?
b) Observe and Explain: Compare the orbital periods for balls at different radii.
c) Extend and Explain: Does the planetary data below agree with your observations?
Orbital Radius
Orbital Period
Planet
(x1010 m)
(days)
Mercury
5.79
88
Venus
10.8
225
Earth
14.9
365
Mars
22.8
688
3)
a) Predict and Explain: How will the mass of the ball affect the period of the orbit?
b) Observe and Explain: Compare the orbital periods for balls with different masses.
c) Extend and Explain:
How does the data below support your observations?
Natural and Artificial
Satellites of the Earth
ISS
Hubble Space Telescope
GPS Satellite
Moon
Mass
(kg)
4.17x105
1.11x104
2.37x103
7.35x1022
Orbital Radius
(x106 m)
6.73
6.94
26.6
384
Orbital Period
(days)
0.063
0.067
0.5
27.3
Compare the data for objects orbiting around the Earth with data for objects orbiting around Jupiter.
How does the data show that the period of the orbit does depend on the mass of the central object?
Moons of Jupiter
Io
Europa
Ganymede
Callisto
Mass
(x1022 kg)
8.93
4.80
14.8
10.8
Orbital Radius
(x108 m)
4.22
6.71
10.7
18.8
Orbital Period
(days)
1.77
3.55
7.15
16.7
4)
You and a group of students are going to act out how the moons of Jupiter orbit. What variables do you
need to consider for the motion to be accurate? How do the speeds of the moons compare?
5)
The mass of Earth, Jupiter and the Sun are 5.98 x 1024 kg, 1.90 x 1027 kg and 1.99 x 1030 kg respectively.
Your parents wonder how astronomers measure the mass of astronomical objects. Outline how you will
explain it to them.
Answers and extra information for teachers
These activities allow students to explore orbital motion using stretchy
fabric. The fabric that works best is fairly thick, stretchy in all directions; it is
sold at most large fabric stores as swimwear, active wear, or four-way
stretch. Get square pieces that are as large as possible. Trap a small object in
the centre of the fabric with an elastic band to provide a handle. Assorted
small smooth balls like glass marbles, mouse balls, or ball bearings are used
for the planets. Avoid billiard balls (too heavy) and ping pong balls (too light).
Teachers at OAPT 2011 workshop
CREDIT: P. Whippey
Students MUST predict and explain and write their ideas down BEFORE having them explore. This encourages
the building of strong mental models instead of random playing.
1) The students may take a while to be successful. Give them time to work it out as a cooperative group
investigation. Eventually they will realize that the ball needs to be launched sideways and at just the right
speed. To work well the fabric needs to be level and taut with as deep a well as possible. Students can see an
answer to “Why doesn’t the Moon fall down?” at:
http://www.perimeterinstitute.ca/en/Outreach/Alice_and_Bob_in_Wonderland/Alice_and_Bob_in_Wonderland/
2) It should be very clear, that the smaller radii have shorter periods. This can also be seen with the
planetary data (and further down with the satellite data – as long as you stay within one system).
3) They should be able to notice that the mass of the orbiting ball doesn`t matter - much. A glass marble and
a small super ball can have the same orbits even though one has ten times the mass of the others. You can
demonstrate this by launching the two balls at the same time. There are other variables that come into play
here (friction, surface area, etc) so the results may not be exact.
The International Space Station (ISS) is much more massive than the Hubble Space Telescope (HST), but
their radii and periods are about the same. The mass of the orbiting body doesn’t matter. This is similar to how
objects fall at the same rate.
Our moon has an orbital radius similar to Jupiter`s Io, but a much greater period. The difference is due to
the difference in the mass of the central bodies (Jupiter is 320 times more massive than the Earth).
4) The benefit of a role playing exercise is in the discussions between students before the performance
rather than the performance itself. The smaller orbits should have shorter periods. The orbits should be
circular, they are only very slightly elliptical, and in the same direction. The mass of the orbiting object is
irrelevant. You might also want to supplement these activities with a computer simulation of orbital motion.
Two very good ones are provided by Physics Education Technology (PhET).
http://phet.colorado.edu/en/simulation/gravity-and-orbits is of objects orbiting Earth and
http://phet.colorado.edu/en/simulation/my-solar-system is of objects orbiting the Sun.
5) Astronomers measure the radius and period of the orbit of satellites and use a formula to calculate the
mass of the central object. Based on this activity students should be able to deduce that astronomers use the
orbital radius and period to determine the mass. Senior physics students should be able to develop the formula
from Newton’s law of gravity and a formula for circular motion to get:
(in m),
4 r 3 where, M is the mass of the central object (in kg), r is the radius
-11
M
T is the time for one orbit (in s), and G is 6.67 x 10 N m2/kg2.
2
GT
Activity 2: Gravitational Lenses
1.
Name ________________________
Einstein described gravity as the warping of space by mass and predicted that light would be deflected by
large masses. The bending of light by warped space can be modelled with a saucer representing the
warped space near the Sun and some masking tape representing light from a distant star. Take the
masking tape and press half of its length on the table. Place the edge of the saucer in its path as shown
below. Carefully press the rest of the tape so it travels smoothly onto the edge of the saucer, along the
saucer’s surface and off onto the table again.
a) Draw the path of the light on the diagram below. Place the Earth at the end of the path.
b) Place your eye at page level at the end of the path and look back along the path of the light. Where
would you think the star was? Draw this on the diagram.
c) The bending of light was first observed during a solar eclipse in 1919. Why did this observation have
to take place during an eclipse?
Sun
(saucer)
Masking Tape
(starlight)
Figure 1: Top view
2.
Gravity distorts images in way that is similar to the base of a wineglass. Place the wineglass over one of
the circles below, but slightly off centre. Move the glass around slightly. Move your head to change your
point of view. Sketch the images you see.
3. The image below shows a massive white galaxy. The blue ring around it is the warped image of a tiny
galaxy that is much farther away. Suppose that the central galaxy was made entirely of invisible matter. What
would be different in the image? What would be the same?
Massive galaxy
acting as a lens
The distorted image of a
distant galaxy located
behind the lensing galaxy
CREDIT: NASA, ESA, and P. Marshall and T. Treu
(University of California, Santa Barbara)
Answers and further information for teachers
1. The starlight bends as it passes by the Sun. However, we think of light travelling in straight lines so we
extrapolate the light back to a “virtual” position that would be visible. The observations had to take place
during an eclipse because if you want to look at star light passing near the sun, you have to look toward the sun
and this means it is daytime and the sun’s light is so bright, you won’t be able to see any stars unless the moon
blocks most of the light.
Earth
Sun
2. The wine glass should have a smooth curve from base to stem (see below). You can get a variety of shapes
depending on the wine glass and how it is centred. You should be able to get a single arc, a double arc and a
thin ring. Try looking from the side and from above.
3. If the central galaxy was made of invisible matter, then you would only see the arcs of the distant galaxy.
However, you would still know that the central galaxy was there by its lensing effects. Astronomers use
gravitational lensing to map out the distribution of dark matter in the galaxy.
(see: http://www.nasa.gov/centers/goddard/news/topstory/2006/clumpy_darkmatter.html)
There are many simulations and animations for gravitational lensing on the internet.
This is one that shows what the Earth would look like if it orbited a black hole:
http://jila.colorado.edu/~ajsh/insidebh/lensearth_640x480.gif
This is one that shows what the distant galaxy would look like if the lensing galaxy were removed:
http://www.ifa.hawaii.edu/info/press-releases/Bolton7-08/lensing_animation.html
Students may get black holes and dark matter confused. Both of them do not emit light but for different
reasons. Black holes are extremely dense objects that do not emit light because light cannot escape from their
immense gravitational fields. Black holes can be made of either ordinary matter or dark matter. Dark matter is
dark because it doesn’t emit, absorb or interact with light in any way except gravitationally. We do not know
what dark matter is but we do know that it is diffuse and accounts for at least 21% of the universe. Contrast
this with the normal matter that we do know about which accounts for roughly 4% of the universe!
Worksheet 3: Dark Matter Concept Questions
For each of the following questions, select the best answer and provide a brief explanation.
1.
Physicists can calculate the mass of the Sun using their measurements of the radius of
a) the Sun and the Sun’s speed
b) the Sun’s orbit and the Sun’s speed
c) a planet and the planet’s speed
d) a planet’s orbit and the planet’s speed
2.
The light from a star can tell physicists about its speed. The light from a really fast star will be
a) brighter
b) fainter
c) redder
d) redder or bluer
3.
The mass of galaxies can be determined by the orbital method and the brightness method. When both
methods are used physicists found that the measurements disagreed
a) slightly and the orbital method gave a higher mass
b) slightly and the brightness method gave a higher mass
c) enormously and the orbital method gave a higher mass
d) enormously and the brightness method gave a higher mass
4.
In which galaxy has dark matter has been detected?
a) Triangulum
b) Andromeda
c)
UGC 11748
d)
all galaxies tested
5.
Dark matter can also be detected by the way it bends light. The mass calculated using this gravitational
lensing method has discovered lots of dark matter in
a) our solar system
b) our galaxy
c) clusters of galaxies d) all three places
6.
The mass found by gravitational lensing agrees with the amount of mass found by
a) orbital method
b) brightness method c) both methods
d) neither method
7.
Dark matter could be made of astronomical objects that we know about but which are hard to see.
However, the missing matter can`t be made of
a) planets, because each solar system would have to have thousands of huge planets
b) black holes and brown dwarfs because we should be able to detect them by gravitational lensing
c) black holes because we should be able to detect the materials they spray out when forming
d) all of the above
8.
Physicists are trying to detect dark matter directly. They think it is made of
a) protons, neutrons and electrons
b) WIMPS
c) WIMPS and/or axions
d) protons, neutrons, electrons, WIMPS and axions
9.
Most of the experiments to detect dark matter directly take place underground in order to block out
a) cosmic rays
b) radioactivity
c)
sunlight
d) noise
10. At present physicists
a) know what dark matter is except for a few small details
b) have some ideas of what dark matter might be and are testing these in debates
c) have some ideas of what dark matter might be and are testing these with experiments
Answers and notes for teachers
These questions are designed to provide an opportunity for students to deepen what they have learned from
the video through discussions. Booklets of large font letters can help this process. Ask them to show you their
choice - so you can assess their understanding - and then have them turn and find someone with a different
letter and explain their reasoning to each other.
1. d) radius of a planet’s orbit and the planet’s speed
You might want to have them draw labeled diagrams to explain their answers.
2.
d) redder (if moving away) or bluer (if moving toward)
Many students may choose just redder because almost all galaxies are red-shifted because of the
expansion of the universe. However, this light will be shifted on one side to be more red and on the other
side to be less red because of the orbital motion.
3.
c) enormously and the orbital method gave a higher mass
The two techniques are very well established and they give very different answers.
4.
d) all galaxies tested
The video talks specifically about two galaxies, but also mentions that many more have been tested and
all of these show this missing mass.
5.
c) clusters of galaxies
Lensing has been used within our galaxy to look for smaller concentrated masses like brown dwarfs and
black holes. The dark matter in our galaxy is too diffuse to be detected by this technique.
6.
a) orbital method
Two very different lines of evidence – lensing and orbital motion – are telling us that there is a lot of
missing matter. They say that there is six times more dark matter than ordinary matter.
7.
d) all of the above
Physicists first checked to see if the missing matter was just ordinary matter that is hard to see. These
possibilities have been ruled out.
8.
c) WIMPS and/or axions
Physicists have evidence that dark matter cannot be ordinary matter like protons, neutrons and electrons.
9.
a) cosmic rays
Cosmic rays are very high energy particles bombarding the Earth whose origins are not well understood.
They can trigger the dark matter detectors so a couple of kilometres of rock is needed to block them.
Radioactivity from the surrounding rock can also affect the detectors and other shielding is needed for
that and the rooms must be kept extremely clean to keep radioactive dust out.
10. c) have some ideas of what dark matter might be and are testing these with experiments.
Appendix A: Multiple Choice Booklet
AB
CD
Credits
Lead Author
Associate Author
Roberta Tevlin
Danforth Collegiate and Technical Institute
Toronto, Ontario
Dave Fish
Sir John A Macdonald Secondary School
Waterloo, Ontario
Special Thanks to the Teachers at
EinsteinPlus 2011
Waterloo, Ontario
OAPT 2011
Hamilton, Ontario
STAO 2010
Toronto, Ontario
TDSB Eureka 2011
Toronto, Ontario
OTF Physics Camp 2011
Sudbury, Ontario
About Perimeter Institute
Perimeter Institute for Theoretical Physics (PI) is an independent, non-profit, scientific research organization
working to advance our understanding of physical laws and develop new ideas about the very essence of
space, time, matter and information. Located in Waterloo, Ontario, Canada, PI also provides a wide array of
research training and educational outreach activities to nurture scientific talent and share the importance of
discovery and innovation among students, teachers and the general public. In partnership with the
Governments of Ontario and Canada, PI is a successful example of public-private collaboration in scientific
research, training and outreach.
http://www.perimeterinstitute.ca/