BONUS MATERIALS
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The Mystery of Dark Matter
Introduction
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 over a hundred
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 means: 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
(chapters 5 to 7) and discuss the rest of the concept questions.
Video: The Mystery of Dark Matter (30 minutes)
The video contains significant 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
to 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.
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Name:
Student Activities
Activity 1
Gravity and Orbital Motion
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?
Planet
Orbital Radius
(x1010 m)
Orbital Period
(days)
Mercury
5.79
88
Venus
10.8
225
Earth
14.9
365
Mars
22.8
688
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Name:
Student Activities
Activity 1 - Continued
Gravity and Orbital Motion
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
Mass
(kg)
Orbital Radius
(x106 m)
Orbital Period
(days)
ISS
4.17x105
6.73
0.063
Hubble Space Telescope
1.11x104
6.94
0.067
GPS Satellite
2.37x103
26.6
0.5
Moon
7.35x1022
384
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
Mass
(x1022 kg)
Orbital Radius
(x108 m)
Orbital Period
(days)
Io
8.93
4.22
1.77
Europa
4.80
6.71
3.55
Ganymede
14.8
10.7
7.15
Callisto
10.8
18.8
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.
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Teacher’s Notes
Activity 1: Gravity and Orbital Motion
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 give you something to grip. 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).
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.
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:
where, M is the mass of the central object (in kg),
r is the radius (in m),
T is the time for one orbit (in s), and
G is the universal gravitational constant 6.67 x 10-11 N m2/kg2.
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 has
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).
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Name:
Student Activities
Activity 2
Gravitational Lenses
1.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 modeled 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)
Starlight
(masking tape)
2.Gravity distorts images in way that is similar to the base of a wine glass. Place the wine glass 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 smaller 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
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Teacher’s Notes
Activity 2: Gravitational Lenses
Answers and Extra 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. These observations have to take place during an eclipse because if you want to look at starlight
passing near the Sun, you have to look toward the Sun; 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 23% of the universe.
Contrast this with the normal matter that we do know about which accounts for roughly 4.6% of the universe!
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Student Activities
Name:
Concept Questions
The Mystery of Dark Matter Video
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
EXPLAIN:
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
EXPLAIN:
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
EXPLAIN:
4.In which galaxy has dark matter has been detected?
a) Triangulum b) Andromeda c) UGC 11748
d) all galaxies tested
EXPLAIN:
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
EXPLAIN:
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
EXPLAIN:
7.There are ordinary astronomical objects that are difficult to see
and could produce some of the same effects as Dark Matter.
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
EXPLAIN:
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
EXPLAIN:
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
EXPLAIN:
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
d) have no idea what dark matter might be and aren’t very
interested in it
EXPLAIN:
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Teacher’s Notes
Concept Questions: The Mystery of Dark Matter Video
Answers and Extra Information 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.
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.
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.
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.
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. Individual stars in these galaxies can be blue-shifted if
they are moving towards us when they are observed. There are
also a few galaxies, such as Andromeda, that are blue-shifted
due to local interactions.
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.
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. They can trigger the dark matter detectors so a couple
of kilometres of rock acts like a filter to reduce their signal.
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.
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.
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Appendix
#
Appendix A
Multiple Choice Booklet
AB
CD
Appendix
The Mystery of Dark Matter
Bonus Materials Credits
Lead Author
Associate Author
Roberta Tevlin
Dave Fish
Danforth Collegiate and Technical Institute
Toronto, Ontario
Sir John A Macdonald Secondary School
Waterloo, Ontario
Executive Producer
Image Credit
Greg Dick
MACSJ0717, covers
Director of Educational Outreach
Perimeter Institute for Theoretical Physics
X-ray (NASA/CXC/IfA/C. Ma et al.); Optical (NASA/STScI/IfA/C. Ma et al.)
Special Thanks to the Teachers at
EinsteinPlus 2011
Waterloo, Ontario
OTF Physics Camp 2011
Sudbury, Ontario
OAPT 2011
Hamilton, Ontario
Photo of Teachers at OAPT, p. 4
P. Whippey
SLACSJ0737+3216, p. 6
NASA, ESA, and P. Marshall and T. Treu (University of California, Santa Barbara)
STAO 2010
Toronto, Ontario
TDSB Eureka 2011
Toronto, 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. www.perimeterinstitute.ca
Made in Canada
© 2011. Perimeter Institute for Theoretical Physics
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