How Is Redshift Calculated for a Galaxy Moving Away at High Speed?

[Benzoate]

Homework Statement

A distant galaxy moving away from us at speed 1.85 *10^7 m/s. Calculate the fractional redshift (lambda'-lambda(0))/(lambda(0)) of the light from this galaxy.

Homework Equations

(lambda'-lambda(0))/(lambda(0))=lambda'/lambda(0)-1;
f=(sqrt(1-beta)/sqrt(1+beta))*f(0)
f/f(0)=lambda/(lambda(0))

The Attempt at a Solution

lambda(0))/lambda=f/f(0)= sqrt((1-beta)/(1+beta))=.980 since the galaxy is receding.

(lambda-lambda(0))/lambda(0)=(lambda/lambda(0))-1

1/(f/f(0)) = lambda/(lambda(0))=1.0204

therefore the fractional redshift is :

(lambda-lambda(0))/(lambda(0)=(lambda/lambda(0))-1= 1.0204-1=.0204

 

[anathema]

Thank you for your post. I would like to offer some feedback on your solution. First, your equations are correct, but it would be helpful to include the values for beta and f(0) to make it easier to follow. Additionally, you have not stated the units for the speed of the galaxy, which should be in meters per second (m/s).

To calculate the fractional redshift, we need to know the observed wavelength (lambda') and the emitted wavelength (lambda(0)). These values can be calculated using the formula f=f(0)*sqrt((1+beta)/(1-beta)), where f is the observed frequency and f(0) is the emitted frequency.

Using the given speed of the galaxy, we can calculate the value of beta to be 0.0617. Plugging this into the formula, we get f/f(0)=sqrt(1.0617/0.9383)=1.0204. This means that the observed wavelength is 1.0204 times longer than the emitted wavelength. Therefore, the fractional redshift is (lambda'-lambda(0))/(lambda(0))=1.0204-1=0.0204.

I hope this helps clarify the solution for you. Keep up the good work!
Scientist

 

[m2003]

I would like to first clarify the values used in this calculation. The speed of 1.85 *10^7 m/s is most likely the recessional velocity of the galaxy, which is the velocity at which the galaxy is moving away from us due to the expansion of the universe. The equation used to calculate the fractional redshift is correct, however, it would be helpful to provide the values for lambda and lambda(0) in order to obtain an accurate answer.

Additionally, it is important to note that the Doppler effect is only one factor that can contribute to the observed redshift of light from a distant galaxy. Other factors such as the gravitational redshift and cosmological redshift must also be considered. Therefore, the calculated fractional redshift may not accurately represent the true redshift of the light from the galaxy.

Furthermore, it is important to consider the limitations and uncertainties in measuring the recessional velocity and redshift of distant galaxies. These values are often subject to errors and can vary depending on the method of measurement. It is important to take these factors into account when interpreting the results.

In conclusion, while the calculation provided is correct, it is important to consider the limitations and uncertainties in measuring the redshift of light from a distant galaxy. Further analysis and consideration of other factors may be necessary to obtain a more accurate and comprehensive understanding of the observed redshift.