Doppler Shift of Light

Question

A hydrogen line in a star's spectrum has a frequency of 6.17*10^14 Hz when stationary. In Rigel's spectrum, it is shifted downward by 4.26*10^10 Hz. What is Rigel's velocity relative to us?

Answer 1

 

I will show you how to work this and you can do the math.

 

For a source moving away from the observer,

 

f = f₀ √[(c - v)/(c + v)]

 

c = speed of light = 3 x 10⁸ m/s

 

v = speed of Rigel moving away from the earth

 

From the equation for f, get

 

v = c [1 - (f/f₀)²] / [1 + (f/f₀)²]

 

f₀ = frequency when stationary = 6.17 x 10¹⁴ Hz

 

f = shifted frequency = (6.17 x 10¹⁴ Hz) - (4.26 x 10¹⁰ Hz)  [Be sure to keep several decimal places here.]

 

You now have c, f, and f₀.  Compute f/f₀, and plug everything into 

 

v = c [1 - (f/f₀)²] / [1 + (f/f₀)²]

 

You should be able to finish from here.