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Day 8.13
Dark Matter
(6.2)
1) Astronomers have analyzed the stars in the galaxy UGC 11748. They found that most of the stars lie
within a radius r = 1.64 x 1020 m and that the total mass within this radius is 1.54 x 1041 kg.
a) At what speed are the stars at the outer radius moving?
GMm/r2 = mv2/r
v = sqrt(GM/r) = 2.58 x 105 m/s
b) There are a few stars that lie further out. They should be moving
A) faster
B) slower
C) about the same speed
D) not enough information
v = sqrt(GM/r) means that a greater orbital radius will result in a slower speed.
c) What speed would you expect for a star at a radius of 6.48 x 1020 m?
The simplest way is to take 2.58 x 105 m/s and multiply by sqrt (1.54/6.48) = 1.26 x 105 m/s
d) The speed turns out to be 2.47 x 105 m/s. This means that either the equations are wrong or that there
is a lot of mass that was not seen. How much mass was missed? What percentage is ‘invisible’?
GMm/ r2 = mv2/r
M = v2r/G = 5.93 x 1041 kg.
(5.93-1.54)100 /5.93 = 74%
Watch the video: The Mystery of Dark Matter. http://www.youtube.com/watch?v=OHihXCVUNUY
3) Which of the above graphs shows the v against r relationship for planets orbiting the Sun?
A)
B)
C)
D)
B
v = sqrt(GM/r)
4) Which of the above graphs shows the v against r relationship for stars orbiting the centre of a galaxy?
A)
B)
C)
D)
A
This constant velocity was seen in the example above, where the radius was quadrupled and the
speed should have been halved, but was almost the same - 2.58 x 105 m/s vs. 2.47 x 105 m/s. This is the case
in every galaxy that has been studied and was completely unexpected by astronomers. There is unseen
matter extending way beyond the visible part of the galaxy.
Note: The first part of the graph has been left blank. Stars within the central bulge of the galaxy follow
pattern D. It forms this pattern because the larger radii will contain more stars. This is similar to the
gravitational field strength within the Earth.
5) What could this unseen matter be?
Small cold objects like planets, asteroids, brown dwarfs. Tiny particles like dust or gas. Black holes.
Neutrinos. All of these possibilities were tested and couldn’t account for more than a tiny fraction.
6) The unseen matter is called “dark matter” and is invisible because it
A) only emits high-energy radiation such as X-rays and gamma rays.
B) only emits low-energy radiation such as microwaves and radio waves.
C) absorbs and reflects light but does not emit other radiation like stars do.
D) does not absorb, emit or reflect any type of radiation or light.
Astronomers checked all wavelengths and found that 80% of the mass is invisible. Absorption and
reflection would make the matter visible.
7) If you can’t see the dark matter how do you know it is there?
A) orbits of stars, orbits of galaxies, gravitational lensing
B) orbits of planets, orbits of galaxies, gravitational lensing
C) orbits of planets, orbits of stars, orbits of galaxies, gravitational lensing
D) orbits of planets, orbits of stars, gravitational lensing
There is not enough dark matter in the solar system to affect the motions of the planets. Orbital motion and
lensing can show the presence of dark matter just as they can help detect black holes.
8) Do the scrambled science activity to explain why physicists think that 80% of the matter in our universe
is dark matter – a new form of matter that has never been detected directly.
9) Black holes are different from dark matter because black holes
A) interact with light, have more total mass, are made from ordinary matter
B) are denser, have more total mass, are made from ordinary matter
C) are denser, interact with light, are made from ordinary matter
D) are denser, interact with light, have more total mass,
Black holes are concentrations of mass, whereas dark matter seems to be spread out. Black holes will
interact with light; they just won’t emit the light once it has captured it. The dark matter may be diffuse
but it is responsible for much more mass than all the black holes. It’s like a rock compared to the entire
atmosphere. Black holes are formed from ordinary matter, though what it is like at the singularity is
unknown.
p. 279 #1 – 4, p. 284 #4-6, p. 309 #36, 46