What is the Period of the Sun's Rotation Based on Doppler Shift of Light?

[P3X-018]

I have to calculate the suns period time, when given the following information;

"The H_{alpha} line has the wavelength \lambda_0 = 656.1~nm. Measuring this spectrum from opposite sites of the suns equator, shows that there is a difference between that is \Delta \lambda=9\times 10^{-12}~m. Asume that this effect is due to the rotation of the sun. Find the period, when the suns radius is 1.4 x 10^6 km."

Wouldn't the difference just be (if calculated relativisticly)

\Delta \lambda = \left( \sqrt{\frac{1+v/c}{1-v/c}} - \sqrt{\frac{1-v/c}{1+v/c}} \right)\lambda_0

Then just solving for v in that equation, and the periode would then be 2\pi r/v? I just want to know if my assumption is correct, because I keep getting the wrong answer. If the assumption is correct then I just have better check my math.

 

[berkeman]

Why do you need to calculate it relativistically? It's just a doppler frequency shift, not a gravitational red shift.

 

[P3X-018]

Yea why wouldn't I just calculate it classical, a lot less algebra, and gives the right answer. But even though calculating relativisticly I should get and answer almost equal to the classical one. But then again, I must have made an error in the calculation. Thanks any way.