A galaxy is moving away from Earth. The "blue" hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 458 nm .
Part A
How fast is the galaxy moving?
Answer--> v=____ c
Part B
How far is it from Earth based on Hubble's law?
Answer--> d=____ ly
[Please help. I'm stuck on this]
did you google Hubble's Law?
To determine the answers to Part A and Part B, we need to use Hubble's law and apply the Doppler effect. Here are the necessary steps to solve this problem:
Step 1: Understand Hubble's Law
Hubble's law states that the recessional velocity of a galaxy is directly proportional to its distance from Earth. Mathematically, it can be expressed as v = H0 * d, where v is the recessional velocity, H0 is Hubble's constant, and d is the distance from Earth.
Step 2: Convert the wavelengths to frequencies
Since we're dealing with light waves, we need to convert the given wavelengths to frequencies using the equation c = λ * f, where c is the speed of light (approximately 3 * 10^8 m/s), λ is the wavelength, and f is the frequency. Rearranging the equation, we get f = c / λ.
Given:
λ1 = 434 nm (blue hydrogen line emitted)
λ2 = 458 nm (measured on Earth)
Step 3: Find the frequencies
Using the formula f = c / λ, we can find the frequencies of the emitted and measured wavelengths.
f1 = c / λ1
f2 = c / λ2
Step 4: Apply the Doppler effect equation
The Doppler effect describes the change in frequency or wavelength of a wave observed by an observer moving relative to the source of the wave. The equation can be written as:
f2 = (c + v) /λ1
Here, v represents the recessional velocity of the galaxy.
Step 5: Solve for v
Solving the Doppler effect equation for v, we get:
v = (f2 * λ1 - c) / λ1
Substituting the known values, we can determine the recessional velocity (v) in terms of the speed of light (c).
Step 6: Solve for d
Using Hubble's law, we know that v = H0 * d. Rearranging the equation, we get:
d = v / H0
Substituting the calculated value of v and the given value of Hubble's constant (H0), we can determine the distance (d) in the desired units.
So, by following these steps, you can find the answers to Part A and Part B of the problem.