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 and explanation for studying 

Answer 1

Hi James!

 

The relationship you can use for this is an approximation based on the Doppler effect:

 

Δλ/λ ≅ v/c

 

where

 

Δλ = (absolute value of) the shift in the spectral emission from its laboratory wavelength

λ = the laboratory wavelength

v = speed of the object (toward or away)

c = speed of light (= 2.99 x 10⁸ m/s)

 

Δλ = 0.2 nm  ( = |400.2 - 400|)

λ = 400.2 nm

 

So it is plug-and-play after this.  I get v = 1.49 x 10⁵ m/s.

 

Since the observed wavelength is SHORTER than the laboratory wavelength, this represents a "blue" shift (because blue is the shortest of the visible wavelengths).  Blue shift means that the star is moving toward us.

 

Hope this helps!  Let me know if you have any other questions or problems with this.