A galaxy is receding away from us with a recession velocity of 100,000 km/s. What is the distance to this galaxy? What is the redshift z of this galaxy?
imagine you have obtained spectra from several galaxies and have measured the Red shift of each galaxy to determine the speed away from us. Here are your results:
Galaxy 1: speed away from us is 10,000 Km/sec.
Galaxy 2: speed away from us in 1,500 Km/sec.
Galaxy 3: speed away from us is 30,000 Km/sec.
extimate the distance to each galaxy from hubble's law. assume that H=23Km/s/Mly
To calculate the distance to a galaxy based on its recession velocity, we can use Hubble's Law. Hubble's Law states that the recession velocity of a galaxy is proportional to its distance from us.
The formula for Hubble's Law is:
v = H0 * d
where v is the recession velocity, H0 is the Hubble constant (approximately 70 km/s/Mpc), and d is the distance.
Rearranging the formula, we can solve for d:
d = v / H0
Plugging in the given values, we have:
d = 100,000 km/s / (70 km/s/Mpc)
Now, let's convert the units from kilometers to megaparsecs (Mpc). 1 Mpc = 3.09 x 10^19 km.
d = (100,000 km/s / (70 km/s/Mpc)) * (1 Mpc / 3.09 x 10^19 km)
Simplifying this expression, we get:
d ≈ 1.43 x 10^3 Mpc
So, the distance to the galaxy is approximately 1.43 x 10^3 megaparsecs.
Now, let's calculate the redshift (z) of the galaxy. Redshift is a measure of how much the light from an object has been stretched due to the expansion of the universe.
The formula for redshift (z) is:
z = Δλ / λ
Where Δλ is the shift in the observed wavelength of light and λ is the rest wavelength.
For objects moving away from us, the observed wavelength (λ') is greater than the rest wavelength (λ). Therefore, we can use the following equation to calculate the redshift:
z = (λ' - λ) / λ
Given that the recession velocity (v) is related to the redshift (z) by:
z = v / c
Where c is the speed of light (299,792 km/s).
In this case, since the recession velocity (v) is given as 100,000 km/s, we can calculate the redshift (z) as:
z = 100,000 km/s / 299,792 km/s
Simplifying this expression gives:
z ≈ 0.333
So, the redshift (z) of the galaxy is approximately 0.333.