AST1120-lab9
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Astronomy
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Apr 3, 2024
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AST 1120: Stellar Astronomy
Name:
Lab 9 (40 points) Hubble’s Law
Learning Goals
•
Describe the relationship between a galaxy's distance from us and that galaxy's observed redshift.
•
Explain why Hubble's law suggests that our universe is expanding.
•
Explain why Hubble's law suggests that our universe started with a Big Bang.
Introduction
Before the 1920s, most astronomers believed in a Static Universe. A Static Universe or Steady State Universe would be infinitely old, infinite in size, uniform in density and composition, and not expanding. Then in the 1920s, astronomers like Edwin Hubble started measuring the redshifts of galaxies. Not only are most galaxies redshifted (moving away from us), but the farther away they are, the faster they are moving away. Hubble had accidentally discovered the
expansion of the universe. The discovery was quite a shock to the astronomical community in the 1920s. Part 1 – Expansion of Universe Figure 1
1.
Which of the examples on the graph in Figure 1 is showing a directly proportional relationship? Explain your response.
2.
Describe what data you need to collect to measure the expansion of the universe.
Visit the Hubble’s Law Simulator
from University of Nebraska Lincoln.
3.
Zoom out on the animation (scroll wheel on a mouse). Take a screenshot of the browser window and insert below. 4.
Now click on a galaxy on the far left of your screen. Take a new screenshot and insert below. 5.
Click and drag the animation over to the left several times. Then click a new galaxy. What happens? 6.
Click and drag the animation upward several times. Then click a new galaxy. What happens? 7.
Where is the center of the universe? Explain your answer. 8.
Does this animation support a Static Universe or an Expanding Universe? Explain your answer.
Part 2 – Redshifts of Galaxies
2
You will measure the redshifts of several real galaxies using the calcium H line, obtained using spectroscopy. The galaxies and redshifts are shown in Figure 2 of this lab. 9.
Measure the redshift of the H line in millimeters for each of the five galaxies by measuring the horizontal white arrow on each right-hand side image from Figure 2. Record the redshift in Table 1. Table 1: Redshifts of Galaxies (round all values to 3 significant figures)
Galaxy in
9 Redshift of H line (in millimeters)
11 Redshift of H line, λ
shift
(in Å)
12 Recession velocity (in km/sec)
Virgo
Ursa Major
Corona Borealis
Bootes
Hydra
The rest wavelength (in Angstroms, Å) of several spectral lines are shown for comparison on page 5. The comparison lines have the following wavelengths:
a 3888.7 Å
c 4026.2 Å
e 4471.5 Å
g 5015.7 Å
b 3964.7 Å
d 4143.8 Å
f 4713.1 Å
10.You will need a conversion factor to convert your redshift in millimeters into redshift in angstroms, Å. Use spectral lines a and g (labeled on the bottom right of Figure 2). Solve the expression below (subtract: g value minus a value). Show your work. Conversion factor
=
(
Difference betweenlines g
∧
a
∈
Å
)
(
Difference betweenlines g
∧
a
∈
mm
)
11.Use your conversion factor and the data in Table 1 to determine the redshift in Angstroms for each galaxy. Insert the redshift in Å for each galaxy into the appropriate column in Table 1. Hint -just multiply the numbers in column 9 by the conversion factor.
3
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Redshift
(
Å
)
=
Redshift
(
mm
)
×Conversionfactor
(
Å
mm
)
12.Determine recession velocity for each of the five galaxies in Figure 2, using the redshift in Å (found already) and the rest wavelength of the calcium H line. Fill in recession velocity in Table 1. Hint – divide c by λ
rest
. Then multiply this number by the column 11 values. V
=
(
c× λ
shift
)
λ
rest
V = Recession velocity in km
sec
C = speed of light = 3
×
10
5
km
sec
λ
rest
= 3968.5 Å
λ
shift
= wavelength shift from Table 1. 4
Figure 2
5
Figure 3
13.Look at the size of the galaxies shown on the left side of Figure 2. Why is the angular size of the galaxies getting smaller as you look down Figure 2 from top to bottom? (Figure 3 is just for reference)
14.Look at the recession velocity data in Table 1. Are these galaxies obeying Hubble’s Law? Explain your response. 6
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Figure 4 - Hubble and Humason (1931). Equivalent to Figure 26.15 (b) in OpenStax Astronomy 2e
15.For point B above, estimate radial velocity___________ and distance __________
16.For point A shown above: radial velocity ______________ and Distance _________
17.Determine the value of Hubble’s constant, H, using the data in Figure 4. Show your work below. Units of H are km/sec/Mpc.
H
=
(
(
Radial velocity of B
−
Radial velocity of A
)
(
Distance
¿
B
−
Distance
¿
A
)
)
=
¿
18.Convert your Hubble constant into a time. Divide your H value above by 3.09 x 10^19. 7
H
o
(
unitsare seconds
−
1
)
=
H
3.09
×
10
19
=
¿
19.Determine the age of the universe, t, in seconds using the Hubble constant found above. 1 divided by your value of H
o
from above.
t
=
1
H
o
=
¿
20.Convert your age for the universe in seconds into an age in years.
1
year
=
3.156
×
10
7
seconds
. The age in years should be smaller than the age in seconds. 21.What is the percent error between your data and the known value for the age of the universe, 13.8 billion years?
%
error
=
|
(
(
data
−
known
)
known
)
|
×
100
8
Figure 5 - Hubble's Law using modern data from Type 1a Supernovae
22.Determine the value of Hubble’s constant, H, using the more modern data in Figure 5. Show your work below. Units of H are km/sec/Mpc.
H
=
(
(
Radialvelocity of D
−
Radial velocity of C
)
(
Distance
¿
D
−
Distance
¿
C
)
)
=
¿
23.Recent data from SH0ES suggests a value of H = 73 km/sec/Mpc. Use this value as known and compare to your data found above. %
error
=
|
(
(
data
−
known
)
known
)
|
×
100
24.Is Hubble’s constant really constant? Explain. 9
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