Doppler shift of object in expanding universe

In summary, the doppler shift (Δf) of the object moving away from us, with a measured wavelength of light λ=1.55μm and at a distance of 10 megaparsecs, is 4.78x10^11 s^-1. The object is redshifted.
  • #1
leroyjenkens
616
49

Homework Statement


What's the doppler shift (Δf) of the object moving away from us if we measure a wavelength of light λ=1.55μm emitted from it and it's at a distance of 10 megaparsecs? And is the object red or blue shifted?
Added information to the problem is for each megaparsec the object is away from us, it's moving 74 km/s faster.


Homework Equations


[tex]f=\frac{c}{λ}[/tex]

[tex]f=\frac{\sqrt{1-β}}{\sqrt{1+β}}f_0[/tex]
For source and receiver receding from each other.

[tex]f=\frac{\sqrt{1+β}}{\sqrt{1-β}}f_0[/tex]
For source and receiver approaching each other. (shouldn't need this one)

β = [itex]\frac{v}{c}[/itex]


The Attempt at a Solution



I find frequency first, by using equation #1, and converting the micrometers of the wavelength to meters. I find it to be 5.1666667x10-15.
Then I plug that into the second equation to find f0, which is 5.1794269x10-15

f0 is larger than f. Does f0 stand for initial frequency? Well, the difference in frequencies is f0-f, which is 1.276x10-17

So I assume that means the frequency was stretched? Which means it was redshifted?
I guess if it was compressed, I would have received a negative number, and that would have meant it was blueshifted?

Thanks.
 
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  • #2
leroyjenkens said:
I find frequency first, by using equation #1, and converting the micrometers of the wavelength to meters. I find it to be 5.1666667x10-15.
That number has missing units, but as a frequency it is certainly wrong. Is it the inverse value, if you add units?

f0 is larger than f. Does f0 stand for initial frequency?
Right.

So I assume that means the frequency was stretched? Which means it was redshifted?
I guess if it was compressed, I would have received a negative number, and that would have meant it was blueshifted?
Right.


By the way: 10 MPc is too close to ignore the local motion of objects. But that is an issue of the problem statement, you can ignore it here.
 
  • #3
That number has missing units, but as a frequency it is certainly wrong. Is it the inverse value, if you add units?
From the first equation, f ends up with 1/s. Hertz is the unit of frequency, and hertz is 1/s, right? And I just figured out one of the things I did wrong. How the heck I ended up with such a small number from equation 1, I have no idea.

So f is actually 1.935x10^14 and f0 = 1.94x10^14

Which means delta f = 4.78x10^11 s^-1

Since since it's a positive number, that means it's redshifted? Did I fix my mistakes?

Thanks.
 
  • #4
leroyjenkens said:
So f is actually 1.935x10^14 and f0 = 1.94x10^14

Which means delta f = 4.78x10^11 s^-1
That looks more realistic (and those are the inverse values of the numbers in post 1)

Since since it's a positive number, that means it's redshifted? Did I fix my mistakes?
Right. You don't need the sign to know it is redshifted - it is moving away, so it is redshifted, done.
 
  • #5
mfb said:
That looks more realistic (and those are the inverse values of the numbers in post 1)

Right. You don't need the sign to know it is redshifted - it is moving away, so it is redshifted, done.

Thanks. Yeah, I knew it was redshifted by the fact that it was moving away, but the way the question is worded, it makes it sound like I need to use the value I obtained to determine whether it was redshifted or blueshifted. Thanks again.
 

What is the Doppler shift of an object in an expanding universe?

The Doppler shift of an object in an expanding universe refers to the change in the wavelength of light emitted by the object as it moves away from or towards an observer due to the expansion of the universe. This shift is caused by the stretching of space between the observer and the object, resulting in a longer wavelength (redshift) or shorter wavelength (blueshift) of light.

How does the Doppler shift of objects in an expanding universe provide evidence for the Big Bang theory?

The Doppler shift of objects in an expanding universe, specifically the observed redshift of light from distant galaxies, is one of the key pieces of evidence for the Big Bang theory. This redshift indicates that the galaxies are moving away from us and from each other, supporting the idea that the universe is expanding from a single point of origin, as predicted by the Big Bang theory.

What is the difference between the Doppler shift in an expanding universe and the Doppler effect in a stationary system?

The Doppler shift in an expanding universe is similar to the Doppler effect in a stationary system in that both involve a change in the wavelength of light due to the relative motion between the source and observer. However, the key difference is that the Doppler shift in an expanding universe is a result of the expansion of space itself, whereas the Doppler effect in a stationary system is caused by the relative motion of the source and observer in a fixed, non-expanding space.

How does the Doppler shift of objects in an expanding universe affect our measurements of their distances and velocities?

The Doppler shift of objects in an expanding universe can significantly affect our measurements of their distances and velocities. This is because the observed redshift of light from these objects must be corrected for the expansion of the universe in order to accurately determine their distances and velocities. Failure to account for this effect can lead to significant errors in our measurements and understanding of the universe.

Can the Doppler shift of objects in an expanding universe be used to determine the age of the universe?

While the Doppler shift of objects in an expanding universe is a key piece of evidence for the Big Bang theory, it cannot be used on its own to determine the age of the universe. Other factors, such as the cosmic microwave background radiation and the observation of distant supernovae, are also used in conjunction with the Doppler shift to estimate the age of the universe. However, the Doppler shift is an important tool in our understanding of the expansion and evolution of the universe.

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