Imagine that you have obtained spectra for several galaxies
and have measured the observed wavelength of the H� emission line of atomic hydrogen. The rest wavelength of H� is 656.3 nanometers
(nm). Your results are as follows:
• Galaxy 1: Observed H� wavelength is 664.7 nm
• Galaxy 2: Observed H� wavelength is 659.6 nm
• Galaxy 3: Observed H� wavelength is 679.2 nm
Put these three galaxies into a list sorted by distance away from the Earth, with the closest
galaxy first in the list and the farthest galaxy last in the list. Explain your reasoning.
The galaxy that is shifted most to the red (#3) is the one that is moving fastest away from Earth. That is a direct result of the Doppler shift relationship.
Because of the observed "Hubble constant" relationship that results from the "Big Bang" expansion of the universe, galaxies that are moving fastest away from the Earth are also the farthest away. The average velocity of galaxies away fropm us is approximately proportional to their distance.
More recent findings indicate that the "Hubble Constant" is not quite true. The expansion of the universe appears to be accelerating.
To determine the order of the galaxies based on their distance away from Earth, we need to utilize the concept of redshift. Redshift occurs when light from distant objects, such as galaxies, is stretched as the object moves away from us, causing the observed wavelength of light to be longer than the rest wavelength.
The formula to calculate the redshift for a given wavelength is:
z = (observed wavelength - rest wavelength) / rest wavelength
Using this formula, we can calculate the redshift for each galaxy and determine their distances from Earth. Let's calculate the redshift for each galaxy:
Galaxy 1:
Redshift (z) = (664.7 nm - 656.3 nm) / 656.3 nm = 0.0127
Galaxy 2:
Redshift (z) = (659.6 nm - 656.3 nm) / 656.3 nm = 0.0050
Galaxy 3:
Redshift (z) = (679.2 nm - 656.3 nm) / 656.3 nm = 0.0349
Now, let's sort the galaxies based on their redshift values, with the lowest redshift (closest distance) first:
1. Galaxy 2: Redshift = 0.0050
2. Galaxy 1: Redshift = 0.0127
3. Galaxy 3: Redshift = 0.0349
Therefore, the ordered list of galaxies based on their distance away from Earth, with the closest galaxy first and the farthest galaxy last, is:
1. Galaxy 2
2. Galaxy 1
3. Galaxy 3
Galaxy 2 is the closest to us, followed by Galaxy 1, and Galaxy 3 is the farthest.
To determine the order of the galaxies based on their distance from Earth, we can make use of the Doppler effect. The Doppler effect is the change in wavelength (or frequency) of a wave, such as light, depending on the relative motion between the source of the wave and the observer.
In the case of galaxies, their motion can cause a shift in the observed wavelength of light emitted by them. This shift is known as the redshift or blueshift, depending on whether the observed wavelength is longer or shorter than the rest wavelength. Redshift indicates that the galaxy is moving away from us, while blueshift indicates that it is moving towards us.
Since the rest wavelength of the Hα emission line is known to be 656.3 nm, we can compare the observed wavelength of the Hα line in each galaxy to this value. Let's do that:
Galaxy 1: Observed Hα wavelength = 664.7 nm
In this case, the observed wavelength is larger than the rest wavelength, indicating a redshift. Therefore, Galaxy 1 is moving away from us.
Galaxy 2: Observed Hα wavelength = 659.6 nm
Here, the observed wavelength is slightly smaller than the rest wavelength, indicating a blueshift. Galaxy 2 is moving towards us.
Galaxy 3: Observed Hα wavelength = 679.2 nm
The observed wavelength in this case is significantly larger than the rest wavelength, suggesting a larger redshift. Hence, Galaxy 3 is moving away from us at a faster rate.
Based on this analysis, we can now arrange the galaxies in order of their distance away from Earth:
1. Galaxy 2: Observed Hα wavelength of 659.6 nm (blueshifted, closest to Earth)
2. Galaxy 1: Observed Hα wavelength of 664.7 nm (redshifted)
3. Galaxy 3: Observed Hα wavelength of 679.2 nm (stronger redshift, farthest from Earth)
Therefore, Galaxy 2 is the closest to Earth, followed by Galaxy 1, and Galaxy 3 is the farthest.