What is the Doppler shift equation for light?

In summary, the conversation discusses the calculation of the period of a pulsating star from different frames of reference, specifically from the rest mass frame and from the perspective of an observer traveling at a high speed relative to the star. The correct equation for this calculation is the relativistic Doppler shift equation, which takes into account the effects of time dilation. The final answer is 4.41 seconds, but caution is advised when applying this approach to events that occur at different space and time coordinates.
  • #1
criznet
i've been having a tough time trying to solve the following problem.

A pulsating star has a period of 3 sec as seen from the rest mass frame of the star. What is the period of the star as measured by an observer traveling 2.2e8 m/s with respect to the star?

I assumed that it was simply the doppler shift for light and I found the equation.

f` = f sqrt(1+v^2/c^2) / sqrt(1 - v^2/c^2).

So in changed the given period of 3 sec to frequency by inverting it. plugged in 2.2e8 for v and 3.0e8 for c. I came up with the observed frequency and inverted it for my answer, but it seems that i am incorrect. anyone have insight into this?

dave
 
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  • #2
IIRC Relativistic Doppler Shift is:
sqrt((1+v/c)/(1-v/c)) = λ'/λ

Hoever, you're looking for time dilation instead, it's the frequency of the pulsar, not the light, that you're interested in.
 
  • #3
Both you and Nate have the right equation for the relativistic Doppler equation. Here's a page on the relativistic Doppler equation for reference:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/reldop2.html

What you want is time dilation. When two events occur at the same location in space but at different times, you can very simply relate the time between those events observed by two observers like this:

t2 = gamma t1

I get 4.41 seconds.

Be careful when taking this approach: when the two events take place at different space and time coordinates, the expression is more complicated.

- Warren
 
  • #4
For anyone reading this thread who is unfamiliar with gamma:

gamma = 1 / sqrt(1 - (v/c)^2)

- Warren
 

1. What is the Doppler shift for light?

The Doppler shift for light is a phenomenon in which the wavelength of light changes due to the relative motion between the source of the light and the observer. This shift can either be towards longer wavelengths (redshift) or shorter wavelengths (blueshift).

2. How does the Doppler shift for light occur?

The Doppler shift for light occurs because light is an electromagnetic wave and its wavelength is affected by the motion of its source or observer. When the source of light is moving away from the observer, the wavelength of light appears longer, resulting in a redshift. Conversely, when the source of light is moving towards the observer, the wavelength appears shorter, resulting in a blueshift.

3. What is the equation for calculating the Doppler shift for light?

The equation for calculating the Doppler shift for light is Δλ/λ = v/c, where Δλ is the change in wavelength, λ is the original wavelength, v is the relative velocity between the source of light and observer, and c is the speed of light.

4. How is the Doppler shift for light used in astronomy?

The Doppler shift for light is an important tool in astronomy for measuring the motion of celestial objects. By analyzing the redshift or blueshift of light from distant galaxies, astronomers can determine the velocity at which they are moving away or towards us, providing valuable information about the expansion of the universe.

5. Can the Doppler shift for light be used to measure the rotation of celestial bodies?

Yes, the Doppler shift for light can also be used to measure the rotation of celestial bodies, such as stars or planets. By observing the Doppler shift of different parts of a rotating object, astronomers can determine its rotational speed and axis of rotation.

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