Relativity: Gravitational Redshifting

In summary, the problem asks at what frequency a signal from Alpha Centauri would be received on Earth, assuming an infinite distance and disregarding cosmological and scattering effects. The equation for gravitational redshifting is not applicable in this situation, but by considering the variables r and rs, one can deduce that the signal would be redshifted at first and then blueshifted at Earth.
  • #1
sawre
2
0

Homework Statement


A signal of frequency 500Ghz leaves the surface of the star Alpha Centauri,
travels through space, and arrives at the surface of the Earth. At what frequency is the signal
received on planet Earth?
(Hint: For this problem, treat Earth and Alpha Centauri as if the separation were infinite. Also,
ignore any cosmological effects, motion of the star or planet, and any interstellar scattering effects)

Homework Equations



Gravitational redshifting: 1/sqrt(rs/r) -1

The Attempt at a Solution



The equation for gravitational redshifting doesn't seem to be useful in this situation since Earth is taken to be infinitely far away. Just be thinking about it one could deduce that the signal is redshifted at first and then blueshifted at earth. But if this is correct I don't know of an equation for shifting from a low gravitational potential to a higher one. Anyone have some hints to get me thinking in the right direction?
 
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  • #2
sawre said:

Homework Statement


A signal of frequency 500Ghz leaves the surface of the star Alpha Centauri,
travels through space, and arrives at the surface of the Earth. At what frequency is the signal
received on planet Earth?
(Hint: For this problem, treat Earth and Alpha Centauri as if the separation were infinite. Also,
ignore any cosmological effects, motion of the star or planet, and any interstellar scattering effects)


Homework Equations



Gravitational redshifting: 1/sqrt(rs/r) -1

The Attempt at a Solution



The equation for gravitational redshifting doesn't seem to be useful in this situation since Earth is taken to be infinitely far away. Just be thinking about it one could deduce that the signal is redshifted at first and then blueshifted at earth. But if this is correct I don't know of an equation for shifting from a low gravitational potential to a higher one. Anyone have some hints to get me thinking in the right direction?

Make sure you know what the variables r and rs represent. You may need to apply this equation more than once.

Cheers -- sylas
 
  • #3
ah..i was labouring under an obviously wrong idea of what the r stood for. thanks
 

Related to Relativity: Gravitational Redshifting

1. What is gravitational redshifting?

Gravitational redshifting is a phenomenon in which the wavelength of light is stretched as it travels through a region of strong gravitational force, resulting in a shift towards the red end of the electromagnetic spectrum.

2. How does gravitational redshifting occur?

Gravitational redshifting occurs due to the gravitational time dilation effect predicted by Einstein's theory of general relativity. As light travels through a strong gravitational field, it must overcome the force of gravity, which causes it to lose energy and thus increase in wavelength.

3. What objects can cause gravitational redshifting?

Any object with a strong gravitational field can cause gravitational redshifting. This includes massive objects such as stars, black holes, and galaxies.

4. How is gravitational redshifting measured?

Gravitational redshifting can be measured using spectroscopy, which involves analyzing the spectrum of light emitted by an object. The amount of redshift can be determined by comparing the observed spectrum to the expected spectrum for the object.

5. What are the implications of gravitational redshifting?

Gravitational redshifting is an important phenomenon in astrophysics and has several implications. It can be used to measure the mass of objects, to study the structure and evolution of the universe, and to test the predictions of general relativity.

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