Using the Doppler formula to find radial speed of a star

In summary, High resolution spectroscopy has revealed that the H line of a star is located at a wavelength of 656.250 nm, while the lab measurement shows a wavelength of 656.280 nm. Using the Doppler formula, we can calculate the line-of-sight velocity of the star to be 13.7 km/s. The units of Δλ and λ0 cancel out, leaving the answer to have the same units as the speed of light, which is 3*105 km/s.
  • #1
owengmcdonnel
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Homework Statement



High resolution spectroscopy reveals that the H line is located at a wavelength
of 656.250 nm for this star. The wavelength of H measured in the lab is 656.280 nm.
Calculate the line-of-sight velocity of the star.



Homework Equations



Here's the Doppler formula:

Vr = (Δλ/λ0)c

where Vr is the radial speed of the star, Δλ is the Doppler shift, λ0 is the rest wavelength or the wavelength measured in the lab, and c is the speed of light.



The Attempt at a Solution



I'm just having trouble with units. I need the answer (the radial speed of the star) in km/s, but i don't know what units to put the other variables (Δλ, λ0, c) in.
 
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  • #2
λ= 656.28 nm
Δλ=656.28-656.25=.03 nm
c=3*108 m/s=3*105 km/s

so finally ,
v=13.7 km/s

The units of Δλ and λ cancel, so v has basically same units as c
 

1. What is the Doppler formula and how does it work?

The Doppler formula is a mathematical equation used to calculate the radial speed of a star based on the shift in its spectral lines. It takes into account the wavelength of the spectral lines and the relative motion of the star towards or away from Earth. The formula uses the concept of the Doppler effect, which states that the observed wavelength of a wave changes when the source of the wave is in motion.

2. How do scientists use the Doppler formula to find the radial speed of a star?

Scientists use spectroscopy to analyze the light emitted by a star and determine its radial velocity. By comparing the observed wavelength of the spectral lines to their expected wavelength, scientists can calculate the amount of shift and use the Doppler formula to find the radial speed of the star.

3. Can the Doppler formula be used for all types of stars?

Yes, the Doppler formula can be used for all types of stars as long as they are emitting light with spectral lines that can be analyzed. This includes stars of different sizes, temperatures, and distances from Earth.

4. How accurate is the Doppler formula in determining the radial speed of a star?

The accuracy of the Doppler formula depends on various factors such as the precision of the spectroscopic measurements, the stability of the star's spectral lines, and the distance of the star from Earth. With advanced technology and techniques, scientists can achieve high levels of accuracy in determining the radial speed of a star using the Doppler formula.

5. Are there any limitations to using the Doppler formula to find the radial speed of a star?

While the Doppler formula is a powerful tool for calculating the radial speed of a star, it does have some limitations. For example, it can only measure the radial velocity of a star towards or away from Earth, and it cannot determine the transverse velocity (movement across the sky). Also, the formula assumes that the star's motion is linear, which is not always the case. Overall, the Doppler formula is a useful tool, but it should be used in conjunction with other methods to get a more complete understanding of a star's motion.

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