# How can I identify the appropriate spectral line for Doppler calculation?

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In summary, the blog post states that the spectrum of Alpha Centauri (A. Cen.) is obtained through a spectroscope. The spectrum of the sky/sun is used as a reference for calculations since A. Cen. and Sun are G2V type stars. When the A. Cen.'s spectrum is superimposed on the Sun's spectrum, A. Cen's lines have shifted to the left (blue). Using the two iron (Fe) lines identified at 5371.5 Å and 5424.1 Å, the shift between A. Cen. and Sun is calculated to be 4 pixels. Radial velocity is then calculated using the formula V = C * (Δλ / λ).
Hi,

I was looking into Doppler shift calculations, and I came across this blog post. It gives a very simple and straight forward account of calculating the velocity of a star.

Following is the summary the blog post:

Spectrum of Alpha Centauri (A. Cen.) is obtained through Lhires III spectroscope. Spectrum of the sky/sun is used as a reference for calculations since A. Cen. and Sun are G2V type stars.

When the A. Cen.'s spectrum is superimposed on the Sun's spectrum, A. Cen's lines have shifted to the left (blue). Shift is 4 pixels.

From the spectrum, two Iron (Fe) lines are identified at 5371.5 Å and 5424.1 Å. They are 52.58 Å apart, and number of pixels between them is 258 pixels. Therefore 1 pixel = 0.2 Å.

Shift between A. Cen. and Sun is is 4 pixels. Therefore, shift in terms of wavelength is 0.8 Å (-0.8 Å, because of blue shift).

Radial Velocity is calculated using the formula: V = C * (Δλ / λ). Where: C ( speed of light) is 3*10^5 km/s, Δλ is 0.8 Å and λ is 5424.1 Å. The equation gives velocity as -44.25 km/s. Taking into account Earth's heliocentricity of 20 km/s, the final velocity of A. Cen. is -44.25 + 20 = -24.25 km/s. This is very close to the astronomical database value of -22.3 km/s.

Here is what I'm confused about: If we use the other Fe line (at 5371.5 Å) as the rest wavelength, the velocity will be -44.68 + 20 = 24.68 km/s (0.4 km/s increase). If we consider spectral lines towards the left (blue region) of the spectrum, the velocity will be higher.

For example, consider an object that emits lines at 4000 Å, 5500 Å and 7000 Å. The shift in wavelength due to Doppler is 1 Å. The Doppler calculations will indicate velocity of 75 km/s at 4000 Å; 54.54 km/s at 5500 Å and 42.85 km/s at 7000 Å.

Therefore, how to identify the appropriate spectral line for Doppler calculation?

Last edited:
Hello there,

Do I understand correctly that you conclude a velocity of 24.25 km/s from a shift of 4 pixels ? What is your estimate for the accuracy of this calculated velocity ?

Re your last paragraph: what is the formula for doppler shift as a function of velocity ?

BvU said:
Hello there,

Do I understand correctly that you conclude a velocity of 24.25 km/s from a shift of 4 pixels ? What is your estimate for the accuracy of this calculated velocity ?

Re your last paragraph: what is the formula for doppler shift as a function of velocity ?
BvU said:
Hello there,

Do I understand correctly that you conclude a velocity of 24.25 km/s from a shift of 4 pixels ? What is your estimate for the accuracy of this calculated velocity ?

Re your last paragraph: what is the formula for doppler shift as a function of velocity ?

24.25 km/s from a shift of 4 pixels in that particular spectral image. 1 pixel is 0.2 Å, shift is 4 pixels or 0.8 Å.

3*10^5*(-0.8/5424.1) = -44.25 km/s+ 20 km/s = -24.25 km/s

Formula of Doppler shift as function of velocity: Δλ / λ = V/ C (Calculations)

24.25 km/s from a shift of 4 pixels in that particular spectral image. 1 pixel is 0.2 Å, shift is 4 pixels or 0.8 Å.

3*10^5*(-0.8/5424.1) = -44.25 km/s+ 20 km/s = -24.25 km/s
So what if the actual shift is 4.43 pixels ? Or 3.85 ?
Formula of Doppler shift as function of velocity: Δλ / λ = V/ C (Calculations)
So not all frequencies will shift the same 1 Angstrom

DrClaude
Formula of Doppler shift as function of velocity: Δλ / λ = V/ C (Calculations)
To make it clearer:
$$\Delta \lambda = \frac{v \lambda}{c}$$
i.e., the shift is not the same for all wavelengths, since it depends on ##\lambda##.

BvU said:
So what if the actual shift is 4.43 pixels ? Or 3.85 ?
My point is that from the given 4 pixels (which can mean anything between 3.5 and 4.5 pixels, I must assume), you can not calculate a velocity in 4 digits accuracy. You get ##44\pm 5## km/s. And the same absolute error in the final ##24\pm 5## km/s (provided the 20 km/s correction has a considerably smaller error)

BvU said:
So what if the actual shift is 4.43 pixels ? Or 3.85 ?

So not all frequencies will shift the same 1 Angstrom

DrClaude said:
To make it clearer:
$$\Delta \lambda = \frac{v \lambda}{c}$$
i.e., the shift is not the same for all wavelengths, since it depends on ##\lambda##.

Ah. Based on the image in the blog, I had assumed that the shift will be uniform across the entire spectrum.

Thank you.

## What is Doppler Shift?

Doppler Shift is the change in frequency of a wave as it moves towards or away from an observer. It is commonly observed in sound and light waves, and is caused by the relative motion between the source and the observer.

## How is Doppler Shift calculated?

The formula for calculating Doppler Shift is Δf/f = v/c, where Δf is the change in frequency, f is the original frequency, v is the relative velocity between the source and observer, and c is the speed of the wave. This formula applies to both sound and light waves.

## What factors affect Doppler Shift?

The main factor that affects Doppler Shift is the relative velocity between the source and the observer. Other factors include the speed of the wave, the direction of motion, and the angle of approach between the source and observer.

## What is the difference between positive and negative Doppler Shift?

Positive Doppler Shift occurs when the source and observer are moving towards each other, causing an increase in frequency. Negative Doppler Shift occurs when the source and observer are moving away from each other, causing a decrease in frequency. This is true for both sound and light waves.

## What are some real-life applications of Doppler Shift calculations?

Doppler Shift calculations are used in various fields, including astronomy, meteorology, and medical imaging. In astronomy, it is used to measure the speed and direction of celestial objects. In meteorology, it is used to track the movement of weather systems. In medical imaging, it is used to create images of internal structures and monitor blood flow in the body.

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