# Galaxies and the Expanding Universe Learning Objective By understanding the Doppler Effect

Hα (H–alpha)          λrest = 656 nm           1 nm =10–9 meter
‘} Hβ (H−beta)         λrest=486 nmHγ (H−gamma)   λrest =434 nmHδ (H−delta)       λrest=410 nm{‘version’:’1.1′,’math’:’
Hβ (H–beta)         λrest=486 nmHγ (H–gamma)   λrest =434 nmHδ (H–delta)       λrest=410 nm
‘} 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’:’
Doppler Formula:λobs–λrestλrest=vc
‘} where: λobs{‘version’:’1.1′,’math’:’
λobs
‘} is the wavelength we observe, λrest{‘version’:’1.1′,’math’:’
λrest
‘} is the wavelength from an object which is at rest, v{‘version’:’1.1′,’math’:’
v
‘}      is the speed of the object relative to us, c{‘version’:’1.1′,’math’:’
c

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