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*10^30 W.

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.

1. What is the redshift of this galaxy?

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2. You measure the flux from this galaxy and get a value of 3.6*10^-18 Wm^-2.
How far away (in Mega-parsecs) is this galaxy?

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3. If you assume that this universe is expanding at a constant rate, how old is this universe? Type your answer in billions of years.

How far away (in Mega-parsecs) is this galaxy?

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To answer these questions, we need to use the concepts of redshift, luminosity, and the Hubble law. Let's break down each question step by step.

1. What is the redshift of this galaxy?
The redshift of a galaxy is a measure of how its light has been stretched as it travels through space, due to the expansion of the universe. It is calculated using the equation:
Redshift (z) = (Observed Wavelength - Rest Wavelength) / Rest Wavelength
In this case, the observed wavelength is 659.2 nm, and the rest wavelength (from laboratory measurements) is 656.3 nm. Plugging these values into the equation, we can find the redshift of the galaxy.

2. How far away (in Mega-parsecs) is this galaxy?
To determine the distance to a galaxy, we can use the Hubble law, which relates the recessional velocity of a galaxy to its distance from us. The Hubble law states that the recessional velocity (v) of a galaxy is proportional to its distance (d), and the constant of proportionality is known as the Hubble constant (H0). Mathematically, it can be written as:
v = H0 * d
In this case, we need to rearrange the equation to solve for distance (d). Once we have the distance, we can convert it to mega-parsecs.

3. If you assume that this universe is expanding at a constant rate, how old is this universe? Type your answer in billions of years.
The age of the universe can be estimated using the inverse of the Hubble constant. The Hubble constant represents the rate at which the universe is expanding. By taking the inverse of H0 and converting it to billions of years, we can estimate the age of the universe.

To answer these questions accurately, we would need the specific form of the Hubble constant and its uncertainty in this distant universe. Additionally, we would need more information about the properties of the galaxy, such as its magnitudes or absolute brightness, to calculate its exact distance.