Use doppler shift to find star velocity

In summary, the conversation discusses a problem involving the speed of a star in order to make violet light appear as blue light. Two attempts are made using equations, but neither are correct. The problem is the last one in a set of homework, causing confusion and a request for assistance. The answer is expected to be in terms of "c" and the variables used in the equations are not clearly defined.
  • #1
Covenant32
15
0

Homework Statement



How fast would a star have to travel to make violet light (λ = 400 nm) appear to be blue (λ = 450 nm)? Assume the star is moving along the line that connects the star to the Earth.

Homework Equations



λr = λc / (c-Vr)

f= fo (c +- Vr / c +- Vs)

The Attempt at a Solution



Well, to be honest I am completely confused with this problem. It is the last problem in a homework set, so it is most likely the most difficult.

First attempt:
400-450 = -5e-8.
Now solve for v:
Δf = fs*((1+v)/c)
v = Δf*c/fs-1 = -5e-8*3e8/(4e-7) - 1 = -3.75E7 m/s, so the star would have to be moving away from you at 37,500,000 m/s.

Second attempt:

Vr = 450 * 3e8 / 400 * 3e8 = 1.125.


Neither are correct. Any assistance or guidance is truly appreciated. Thank you.

 
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  • #2
I have no idea why the template is copied multiple times. Sorry about that.
 
  • #3
The answer is in terms of "c". So, I thought that perhaps I could just find the ratio of 3.75e7 to 3e8, which is .125, but that is incorrect.

I'm really lost on this blasted problem. It is the last one of close to 40 I've done.
 
  • #4
I don't see how you're using the equations. Define the variables in the first equation and give the units of measure please.
 
  • #5




To find the velocity of the star using Doppler shift, we can use the equation λr = λc / (c-Vr), where λr is the observed wavelength, λc is the rest wavelength, and Vr is the radial velocity of the star. In this case, we are looking for the velocity that would make a violet light (λ = 400 nm) appear as blue (λ = 450 nm).

Using the given values, we can plug them into the equation as follows:

450 nm = 400 nm / (3.0 x 10^8 m/s - Vr)

Solving for Vr, we get Vr = 1.2 x 10^7 m/s. This means that the star would have to be moving away from Earth at a velocity of 12,000,000 m/s for the violet light to appear as blue.

It is important to note that this calculation assumes the star is moving directly away from the observer (along the line connecting the star to Earth). If the star is moving at an angle, the velocity calculated using this method may be slightly different. Additionally, this calculation assumes the star's velocity remains constant, which may not be the case in reality.

Overall, using Doppler shift to find the velocity of a star can provide valuable information about its motion and can help us better understand the universe.
 

1. How does the Doppler shift method work?

The Doppler shift method works by measuring the change in frequency of light emitted from a star. As the star moves towards or away from the observer, the frequency of light shifts either towards the blue end (blueshift) or the red end (redshift) of the spectrum. This shift in frequency can be used to calculate the velocity of the star.

2. What is the formula for using Doppler shift to find star velocity?

The formula for using Doppler shift to find star velocity is v = c * (Δλ / λ), where v is the velocity of the star, c is the speed of light, Δλ is the change in wavelength between the emitted and observed light, and λ is the wavelength of the emitted light.

3. What equipment is needed to measure the Doppler shift of a star?

To measure the Doppler shift of a star, you will need a spectrometer, which can break down light into its component wavelengths, and a high-resolution telescope to observe the star. Additionally, a computer or software is needed to analyze the data and calculate the velocity of the star.

4. Can the Doppler shift method be used to find the velocity of any star?

Yes, the Doppler shift method can be used to find the velocity of any star, as long as it is emitting light and is visible from Earth. However, it is most commonly used for stars that are relatively close to Earth and have a large enough velocity to produce a measurable Doppler shift.

5. What other factors can affect the accuracy of using Doppler shift to find star velocity?

Other factors that can affect the accuracy of using Doppler shift to find star velocity include the rotation of the star, the presence of multiple stars in a system, and the inclination of the star's orbit. These factors must be taken into account and corrected for in order to obtain an accurate measurement of the star's velocity.

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