Posted: February 8th, 2022

By understanding the Doppler Effect, you will verify the observed fact that all galaxies are moving away from us, and you will use the Doppler shift formula to calculate how fast they are receding. You will prove for yourself that the nature of their motion means that the Universe is expanding and you will then use your data on the expansion to be able to calculate the age of the Universe itself.

**Prerequisites: **Read Chapter 20 of textbook.

- Computer and internet access
- Calculator
- Pen/pencil
- Digital camera or scanner
- Download and print the Hubble Diagram Sheet (as an additional option, you can create your graph with the Excel program or create your own graph by hand)

**Total Time Required:** Approximately 2-3 Hours

**Note:** For your lab report, only include your clearly labeled answers to the below questions in all parts. Copy/paste in your photos or diagrams when needed.

Among the great achievements of Einstein was his understanding of the speed of light. The speed of light, in a vacuum, is a constant at ~ 300,000 kilometers/second (the actual velocity is 299,792.458 km/s). The speed of light is essential to the viability of both Einstein’s theories of Special and General Relativity (since the speed of light is a constant it has been given its own mathematical symbol, c). If the speed of light is not constant then neither of Einstein’s theories are credible and would not be accurate in describing physics at the larger-scales of the Universe and objects moving at high velocities close to the speed of light.

Therefore, since the speed of light is a constant any motion by an object emitting light has no effect on the velocity of the light nor does an object seeing light from a source moving towards it measure any change in the speed of the light coming towards it. For example, a car is driving at night with its headlights on at a speed of 75 miles per hour. What is the speed of the light coming from the headlights? Common sense would give its speed as the speed of light plus 75 miles per hour (c + 75) but the measured speed is still the speed of light ( c ). Something had to change in this situation however and in this part of the lab, you will be investigating the change that is occurring here which is known as the Doppler Effect.

For this activity, you will be watching this video and answer questions related to what you see.

For questions 1 – 3, you are going to note what happens when the source and observer are some distance apart with an emission occurring. And then the observer is going to approach the source and then move away.

- When the emitting source and the observer are on opposite sides of the screen, record your observations of the wave and its wavelength as seen by
**both**the emitting source and the observer (be as detailed as possible). - For the portion where the observer is moving to the left, towards the emitting source, record your observations of the wave and its wavelength as seen by
**both**the emitting source and the observer. - For the portion where the observer is moving to the right or away from the emitting source, record your observations of the wave and its wavelength as seen by
**both**the emitting source and the observer.

For the next set of questions the source will be moving, simulating the emitting source (i.e. a star, a galaxy, a quasar) and the observer stationary (i.e. the Earth).

- For the portion where the emitting source is moving towards the observer, record your observations of the wavefronts as they 1) move in the same direction of the moving source, and 2) move in the opposite direction of the moving source. Also, describe the wavelength as seen by the observer.
- This effect on wavelength, as seen by the observer, is known as
**blueshift.**Consult your textbook or other source and explain in your own words using 1 to 2 sentences what is blueshift? (cite all sources in proper APA citation) - For the portion where the emitting source is moving away from the observer, record your observations of the wavefronts as they 1) move in the same direction of the moving source, and 2) move in the opposite direction of the moving source. Also, describe the wavelength as seen by the observer.
- This effect on wavelength, as seen by the observer, is known as
**redshift.**Consult your textbook or other source and explain in your own words using 1 to 2 sentences what is redshift? (cite all sources in proper APA citation) - One observation astronomers make is only a few nearby galaxies within our own local group of galaxies show blueshift while all far away galaxies are redshifted. This is seen as evidence for the Big Bang. In your own words, explain why these observations do or don’t support the theory of the Big Bang.
- Cite all sources in proper APA citation.

The Big Bang Theory says that the Universe began from a singularity and has expanded over time. Evidence indicates that this is an accelerated expansion meaning that objects are moving faster in the expansion at greater distances. This is what astronomers term as **Cosmological Redshift** where the redshifts of objects are greater for increasing distances. In this part, we will be using the redshift measurements of **galaxy clusters** (since galaxy clusters are large and very bright they can be seen at very large distances).

The galaxy cluster closest to our own Local Group can be seen (with a telescope) in the direction of the constellation Virgo. We call this cluster the Virgo cluster; it is approximately 50 million light-years (15 million parsecs) away. Many even more distant clusters have been found in other directions. They all contain some very large elliptical galaxies and many smaller galaxies.

On the following page are pictures showing what an elliptical galaxy would look like if it were located in different galaxy clusters. The farther away from the cluster, the smaller the galaxy looks. There is an inverse relationship between apparent size and distance. Next to each galaxy, there is a spectrum of a bright star in the galaxy. The dark lines are “Balmer” hydrogen absorption lines. These lines are not always found at the same wavelength; they are “shifted.” However, the general pattern that the hydrogen lines form in each spectrum always stays the same. That is how we can tell if a certain line is a hydrogen line, even though it is not always found at the same wavelength. The “shift” of the pattern is the Doppler Effect, and it is caused by the motion (relative to us, the observers) of the star that is emitting the light as seen in Part 1 of this lab.

Copy and paste the below 4 objects (Virgo Cluster, etc.) with their corresponding spectra into your lab report. When the wavelengths of hydrogen lines are measured in a laboratory, using a stationary hydrogen lamp, each line is always found at the same wavelength. We call this wavelength the “rest wavelength” and denote it by rest. For your reference: The rest wavelengths of the hydrogen lines (from right to left) are:

Hα (H−alpha) λrest = 656 nm [1 nm =10−9 meter]{“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><mi>H</mi><mi>α</mi><mo> </mo><mo>(</mo><mi>H</mi><mo>-</mo><mi>a</mi><mi>l</mi><mi>p</mi><mi>h</mi><mi>a</mi><mo>)</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi>λ</mi><mi>r</mi><mi>e</mi><mi>s</mi><mi>t</mi><mo> </mo><mo>=</mo><mo> </mo><mn>656</mn><mo> </mo><mi>n</mi><mi>m</mi><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced open=”[” close=”]”><mrow><mn>1</mn><mo> </mo><mi>n</mi><mi>m</mi><mo> </mo><mo>=</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>9</mn></mrow></msup><mo> </mo><mi>m</mi><mi>e</mi><mi>t</mi><mi>e</mi><mi>r</mi></mrow></mfenced><mspace linebreak=”newline”></mspace></math>”}

Hβ (H−beta) λrest=486 nmHγ (H−gamma) λrest =434 nmHδ (H−delta) λrest=410 nm{“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><mi>H</mi><mi>β</mi><mo> </mo><mo>(</mo><mi>H</mi><mo>-</mo><mi>b</mi><mi>e</mi><mi>t</mi><mi>a</mi><mo>)</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi>λ</mi><mi>r</mi><mi>e</mi><mi>s</mi><mi>t</mi><mo>=</mo><mn>486</mn><mo> </mo><mi>n</mi><mi>m</mi><mspace linebreak=”newline”></mspace><mi>H</mi><mi>γ</mi><mo> </mo><mo>(</mo><mi>H</mi><mo>-</mo><mi>g</mi><mi>a</mi><mi>m</mi><mi>m</mi><mi>a</mi><mo>)</mo><mo> </mo><mo> </mo><mo> </mo><mi>λ</mi><mi>r</mi><mi>e</mi><mi>s</mi><mi>t</mi><mo> </mo><mo>=</mo><mn>434</mn><mo> </mo><mi>n</mi><mi>m</mi><mspace linebreak=”newline”></mspace><mi>H</mi><mi>δ</mi><mo> </mo><mo>(</mo><mi>H</mi><mo>-</mo><mi>d</mi><mi>e</mi><mi>l</mi><mi>t</mi><mi>a</mi><mo>)</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi>λ</mi><mi>r</mi><mi>e</mi><mi>s</mi><mi>t</mi><mo>=</mo><mn>410</mn><mo> </mo><mi>n</mi><mi>m</mi></math>”}

1.In your lab report under the copied image of the 4 objects, for each corresponding object (label a heading in your report Virgo Cluster through the Bootes Cluster and under each heading you’ll have information for questions #1 – #4, also labeled.) For #1, type out the numbers you estimate for each Balmer hydrogen line (H-alpha, H-beta, etc.) in each galaxy spectra given (match the line pattern as it is labeled on the spectrum of the Virgo cluster galaxy). For example, the Virgo Cluster # 1: H-alpha = 660nm, H-beta = xxx, etc. doing the same for each line and for each object.

The Doppler Effect does not only affect light but occurs with waves of all kinds. A familiar example is the change in pitch of the sound from a car as it moves towards you, passes you, and moves away from you. As the car moves towards you, the sound waves that move past you are more closely spaced than normal, their wavelength is shortened. As the car moves away, the sound waves move past you with longer spacing than normal, their wavelength is increased. Since a high-pitched sound has a short wavelength, and a low-pitched sound has a long wavelength, we can actually hear the Doppler effect.

This is analogous to what happens to light from a moving source. If a star is moving towards us, its light will have a shorter wavelength, the light is blue-shifted. If the star is moving away from us, the wavelength of the light is longer, the light is red-shifted. It is easiest to detect the change in wavelength of the light from the shift of the spectral lines. (The shift of the line is the difference between the observed wavelength and the rest wavelength.

2. For each of the 4 objects in your #1 question, now compare the rest wavelength and the observed wavelength of the hydrogen lines. For example: for the Virgo Cluster we found H-alpha = 660nm. The rest wavelength is 656nm. Therefore, the wavelength is different by ____?(you would show this calculation and for the others). Which wavelength is longer? Are the galaxies moving towards us or away from us? (State this for each one.)

The shift of the line gets larger as the speed of the light source (relative to us) increases. There is a formula that makes it possible to determine how fast a source is moving by measuring the change in wavelength.

Doppler Formula:(λobs−λrest)λrest=vc{“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><mi>D</mi><mi>o</mi><mi>p</mi><mi>p</mi><mi>l</mi><mi>e</mi><mi>r</mi><mo> </mo><mi>F</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>u</mi><mi>l</mi><mi>a</mi><mo>:</mo><mspace linebreak=”newline”></mspace><mfrac><mfenced><mrow><msub><mi>λ</mi><mrow><mi>o</mi><mi>b</mi><mi>s</mi></mrow></msub><mo>-</mo><msub><mi>λ</mi><mrow><mi>r</mi><mi>e</mi><mi>s</mi><mi>t</mi></mrow></msub></mrow></mfenced><msub><mi>λ</mi><mrow><mi>r</mi><mi>e</mi><mi>s</mi><mi>t</mi></mrow></msub></mfrac><mo>=</mo><mfrac><mi>v</mi><mi>c</mi></mfrac></math>”}

where:

λobs{“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><msub><mi>λ</mi><mrow><mi>o</mi><mi>b</mi><mi>s</mi></mrow></msub></math>”} is the wavelength we observe,

λrest{“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><msub><mi>λ</mi><mrow><mi>r</mi><mi>e</mi><mi>s</mi><mi>t</mi></mrow></msub></math>”} is the wavelength from an object which is at rest,

v{“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><mi mathvariant=”script”>v</mi></math>”} is the speed of the object relative to us,

c{“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><mi mathvariant=”script”>c</mi></math>”} is the speed that the wave travels at.

A light wave travels at the speed of light, which is 3000,00 km/sec.

3.Use the Doppler formula to determine the speeds of the galaxies. (perform your calculations for just one of the four Balmer lines, show your work for all calculations

4.Compare the distances to the galaxies and the speeds with which the galaxies are moving away from us, and describe their relationship to Earth.

Use the __‘Hubble Diagram’ sheet__ linked at the start of the lab, __or__ create a graph using Excel, __or__ by hand to go into your report (if using the last two options the Hubble Diagram can be viewed as help in scaling your graph) plot your calculated data.

For each galaxy, plot the recession velocity (y-axis) versus the given distance (x-axis). Draw one straight line which best fits the four data points you have plotted. (line of best fit must go through the (0,0) point on your graph) On your graph calculate and label the __slope__ of this “best-fit” line? (slope = rise / run)

You have just done the same calculations that the astronomer Edwin Hubble did in the late 1920s. The relation you described between the distances and speeds of galaxies is called **Hubble’s Law**, and the slope of the line is known as the **Hubble Constant, HO.**

What does Hubble’s Law tell us about the Universe? At first, it may seem as if we (in the Milky Way) are in a “privileged position” in the Universe since all other galaxies are moving away from us. Are we at the center of the Universe?? We will perform a “thought experiment” to find the answer.

Imagine that A, B, C, D, and E are galaxies. The arrows represent the speeds of the galaxies as seen from A (longer arrow = higher speed). This diagram represents what Hubble’s Law states.

1. Change your perspective again and do the same for an observer sitting in Galaxy E.

2.Describe what would an observer sitting in galaxy C would see when they looked at the other galaxies? Also, draw arrows for each of the other galaxies to represent the speeds that this observer would measure. (this can be done in Word by inserting an arrow, or by hand)

- Look at the diagrams in questions 1. and 2. What relation will observers in galaxies C and E find between speeds and distances of galaxies? Is the Hubble law the same for observers in all galaxies?

What you have seen in this thought experiment is precisely the explanation of why the proportionality between galaxy distances and speeds leads to the deduction that the Universe is expanding. All galaxies are getting farther and farther apart all the time!

It is also possible to make an estimation of how long the expansion has been going on; this is the time which astronomers take as the “Age of the Universe,” or the time since the Universe began to expand. The Hubble constant you calculated is the expansion rate of the universe going forward in time while the **inverse** of the Hubble constant, 1/HO, will take you backward in time to the origin of the Big Bang.

(show your work for all calculations)

- First, find the inverse of your value of HO.

HO = ____________________ 1/HO = ____________________

- Multiply 1/HO by 3.09 x 1019 km/Mpc to cancel the distance units.
- Since you now have the age of the Universe in seconds, divide this number by the number of seconds in a year, 3.16 x 107 sec/yr. (The latest Measurements of the age of the universe, as determined by the Planck satellite, is 13.82 billion years (or 1.382 x 1010). Let’s calculate how close your measurements came to this Planck age!)
- Calculate the percentage difference with this formula:

(Age (planck) – Age (measured) / Age (planck)) x 100 = - In a paragraph (50 word minimum) describe, in your own words, the relationship you have seen in this lab between the expansion of the Universe and the determination of the age of the universe.

**NOTE**: You must provide a reference list showing the source(s) that you used, including our own textbook, in proper APA citation format.

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