Download Lesson 18 - Dark Matter

Comprehension Check

Set Newton’s Law of Universal Gravitation
equal to the centripetal force and determine
the orbital speed of the following planets
(mean orbital radius given) if the mass of the
sun is 1.991x1030kg):
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

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Mecury (5.79x1010m)
Venus (1.08x1011m)
Mars (2.28x1011m)
Neptune (4.50x1012m)
Comprehension Check
Mercury – 4.79x104m/s
 Venus – 3.51x104m/s
 Mars – 2.41x104m/s
 Neptune – 5.43x103m/s

Orbital Speed vs Orbital Radius
Orbital Speed (m/s)
60000
50000
40000
30000
20000
10000
0
0.00E+0 1.00E+1 2.00E+1 3.00E+1 4.00E+1 5.00E+1
0
2
2
2
2
2
Orbital Radius (m)
Dark Matter
Physics 12
Video Questions
1.
2.
3.
How would you describe the graph that best shows the
v against r relationship for planets orbiting the Sun?
How would you describe the graph that best shows the
v against r relationship observed for stars orbiting the
centre of a galaxy?
When astronomers measure the mass of the galaxy
Triangulum using the Brightness Method the result they
get is much less than when they measure the mass
using the Orbital Method. This fact can best be
explained by the fact that:
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the stars in Triangulum are made of lighter elements than those
in the Sun.
the Orbital Method underestimates the mass of Triangulum.
Triangulum contains a large amount of unseen mass.
Triangulum contains only mass that emits visible light.
4.
Observations that indicate the presence of dark matter have been
made in:
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5.
Evidence for dark matter comes from observations of:
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6.
the orbit of the Moon around Earth and gravitational lensing.
the orbits of stars and gravitational lensing.
the orbit of the Moon around Earth and the orbits of stars.
the orbits of stars, the orbit of the Moon around Earth, and gravitational
lensing.
Dark matter is called “dark” because it:
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7.
only the Andromeda and Triangulum galaxies.
only the Andromeda, Triangulum, and Milky Way galaxies.
every galaxy that has been examined for dark matter.
many, but not all, galaxies that have been examined for dark matter.
only emits high-energy radiation such as X-rays and gamma rays.
only emits low-energy radiation such as microwaves and radio waves.
reflects light but does not emit other radiation like stars do.
does not emit or reflect any type of radiation or light.
Most physicists think that most dark matter is made of:
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WIMPs or axions.
brown dwarf stars.
black holes or planets.
stars like the Sun.

Astronomers have studied galaxy UGC
128 for many years. They have measured
its brightness and calculated that the
mass of stars within a radius of 1.30 x
1021 m is 3.34 x 1040 kg. Stars orbiting at
this radius has been measured travelling
at a speed of 1.30 x 105 m/s. What
percentage of the mass within this radius
is dark matter?
Orbital radius of star
(x 1020m)
Measured
speed
(x 105 m/s)
Calculated
speed
(x 105 m/s)
Gravitational
Mass
(x1041 kg)
Missing
Mass
(%)
1.85
2.47
2.36
1.69
8.99
2.75
2.40
3.18
2.37
4.26
2.25
6.48
2.47
1. Use the values from the table above to plot measured
speed against orbital radius on the graph provided.
Label this line “measured”.
2. For each orbital radius, calculate the speed expected
if the only mass is the luminous mass of 1.54 x 1041
kg. Record your answers in the “Calculated speed”
column.
3. Plot calculated speed against orbital radius on the
graph provided. Label the line “calculated”.