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Worksheet 3 - Dark Matter within a Galaxy |
Useful formulas
Astronomers have analysed
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, or 77.4 billion
times the mass of the Sun.
It is expected that the stars that
lie outside this radius will orbit
in the same way that planets
orbit the Sun. In this activity you
will analyse the motion of stars
located in the outer regions of
UGC 11748.
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| 1. |
Use the values from the table above to plot measured speed against
orbital radius on the graph provided below.
Label this
line "measured".
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| 2. |
a) 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.
b) Show a sample calculation.
c) Plot calculated speed against orbital radius on the graph
provided. Label the line "calculated".
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| 3. |
Compare the "measured" and "calculated" plots.
Discuss a possible explanation for any differences.
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| 4. |
a) Use the measured speeds to calculate the mass of the galaxy
contained within each orbital radius.
Record your answers in the
"Gravitational mass" column.
b) Show a sample calculation.
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| 5. |
For each orbital radius, calculate the difference between the
gravitational mass within this radius and the total
mass of the stars
(1.54 x 1041 kg). Represent this difference as a percentage of the
gravitational mass within the
orbital radius. Record your answers in
the "Missing Mass" column.
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| 6. |
Do your results support the following statement? "It is reasonable to expect that stars orbit around the gravitational
mass contained within the radius of their orbit in the same way that
planets orbit around the Sun." Discuss.
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| 7. |
Explain the shape of your plot for measured speed against
orbital radius.
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