A high-velocity star HVS 1 is moving at 600 km/s, 0.2% speed of light. Assuming the HVS 1 is moving away from us, and that its velocity is oriented entirely along our line of sight, determine the Doppler shift of the Ha spectral line (6562.8 Angstrom) produced by this star. Is the spectral line located to the red or to the blue of its rest wavelength? Any help would be appreciated. Thanks.

If the star moving away from earth, which is the usual case, the shift is towards the red.

You can use the formula
(delta lambda)/lambda = v/c = 0.002

'delta lambda' is the Doppler shift of wavelength, lambda. That is what they are asking for.

There is a more accurate relativistically correct formula that is the same whether the observer or the source is moving, but at this low v/c value, it gives nearly the same result.

To determine the Doppler shift of the Ha spectral line produced by the high-velocity star HVS 1, we need to use the formula:

Δλ / λ = v / c

Where:
Δλ is the difference in wavelength (Doppler shift)
λ is the rest wavelength of the spectral line (in this case, 6562.8 Angstrom)
v is the velocity of the star (600 km/s)
c is the speed of light (299,792 km/s)

First, we need to convert the velocity of the star from km/s to m/s to match the units of the speed of light. We can do this by multiplying 600 km/s by 1000 to get 600,000 m/s.

Now we can plug the values into the formula:

Δλ / 6562.8 = 600,000 / 299,792

To solve for Δλ, we rearrange the equation:

Δλ = (6562.8 * 600,000) / 299,792

Simplifying the equation:

Δλ ≈ 131.101 Angstrom

The Doppler shift (Δλ) is approximately 131.101 Angstrom.

To determine if the spectral line is located to the red or the blue of its rest wavelength, we need to compare the Doppler shift with the rest wavelength (6562.8 Angstrom).

Since the Doppler shift is positive, the spectral line is located to the red (longer wavelength) side of its rest wavelength.