A red shift measurement shows that the speed of a distant...

A red shift measurement shows that the speed of a distant galaxy relative to an astronomer on the Earth is $v=0.25 c,$ where $c$ is the speed of light. a. How far away is the galaxy? b. If a source of electromagnetic radiation in this galaxy emits blue light with $\lambda=450 \mathrm{nm}$ (as viewed by an observer at rest in the galaxy), what is the wavelength observed on the Earth? Hint: Consider the Doppler shift formulas for light in Chapter $23 .$

A red shift measurement shows that the speed of a distant galaxy relative to an astronomer on the Earth is $v=0.25 c,$ where $c$ is the speed of light.
a. How far away is the galaxy?
b. If a source of electromagnetic radiation in this galaxy emits blue light with $\lambda=450 \mathrm{nm}$ (as viewed by an observer at rest in the galaxy), what is the wavelength observed on the Earth? Hint: Consider the Doppler shift formulas for light in Chapter $23 .$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Cosmological Distance Measurement

Cosmological distance measurement involves estimating how far away galaxies or other astronomical objects are based on their redshift and recession velocity. This concept often utilizes Hubble's Law, which relates an object's velocity (inferred from redshift) to its distance, assuming the expansion of the universe.

Redshift

Redshift is the phenomenon where the wavelength of light is increased (shifted toward the red end of the spectrum) when an object such as a galaxy is moving away from the observer. This concept is fundamental in astrophysics for gauging the speed and distance of astronomical objects, and it is an indicator of the expansion of the universe.

Relativistic Doppler Shift

The relativistic Doppler shift extends the classical Doppler effect to account for the effects of special relativity when dealing with speeds comparable to the speed of light. It provides the correct formula to determine how the observed wavelength of light is altered due to the relative motion between the source and the observer, incorporating time dilation effects.

Transcript

Please give Ace some feedback