Q3.2 COLLAPSE TIMESCALE (5 points possible)
Imagine that you live in a distant galaxy far far away. This galaxy is in a different universe, and so may have different cosmology.
It seems that in this distant universe, all galaxies have the same luminosity, which you have worked out is 7.0×1030W.
You are studying a particular galaxy which you have just discovered. You take a spectrum and find that it has a strong hydrogen line at a wavelength of 659.2 nm. In the laboratory, this line occurs at a wavelength of 656.3 nm.
What is the redshift of this galaxy?
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You measure the flux from this galaxy and get a value of 3.6×10−18W m−2.
How far away (in Mega-parsecs) is this galaxy?
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If you assume that this universe is expanding at a constant rate, how old is this universe? Type your answer in billions of years.
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To find the redshift of the galaxy, we can use the formula for redshift:
z = (observed wavelength - laboratory wavelength) / laboratory wavelength
Given that the observed wavelength is 659.2 nm and the laboratory wavelength is 656.3 nm, we can calculate the redshift by plugging these values into the formula:
z = (659.2 nm - 656.3 nm) / 656.3 nm
z ≈ 0.0044
Therefore, the redshift of this galaxy is approximately 0.0044.
To find the distance of the galaxy, we can use Hubble's law, which states that the recessional velocity of a galaxy is proportional to its distance from us. The equation for Hubble's law is:
v = H0 * d
Where:
v is the recessional velocity of the galaxy,
H0 is the Hubble constant,
d is the distance to the galaxy.
In this case, the recessional velocity can be calculated using the redshift and the speed of light:
v = z * c
Where:
z is the redshift,
c is the speed of light (approximately 3 × 10^8 m/s).
Given that the flux from the galaxy is 3.6 × 10^-18 W m^-2, we can calculate the recessional velocity:
3.6 × 10^-18 W m^-2 = z * c
z = (3.6 × 10^-18 W m^-2) / c
Now we can use the redshift to calculate the distance to the galaxy:
v = z * c = [(3.6 × 10^-18 W m^-2) / c] * c
d = v / H0
The value of the Hubble constant, H0, is approximately 70 km/s/Mpc.
Therefore, the distance to the galaxy in Mega-parsecs (Mpc) can be calculated as:
d = v / H0
Finally, to calculate the age of the universe, we need to use the concept of the "Hubble time." The Hubble time is the inverse of the Hubble constant, given by:
Hubble time = 1 / H0
The age of the universe is then:
Age of the universe = Hubble time / 1 billion years
So, to find the age of this universe, we can calculate:
Age of the universe = 1 / H0 / 1 billion years
Given that the Hubble constant, H0, is approximately 70 km/s/Mpc, we can calculate the age of the universe.