How fast is this star moving?

Question

A line in a star's spectrum lies at 400.0 nm. In the laboratory, that same line lies at 400.2 nm. How fast is this star moving? Is it moving towards or away from us?

Answer 1

If its speed is small compared to the speed of light, you can use the following approximation for the Doppler shift:

 

Δλ/λ = v/c ⇒ 

 

v = (Δλ/λ)c = [(400.2 - 400.0)/400.2](3 x 10⁸) m/s ≅ 1.499 x 10⁵ m/s

 

The wavelength dropped, so this is a blue shift, and the star is moving toward us.