Use doppler shift to find star velocity

[Covenant32]

Homework Statement

How fast would a star have to travel to make violet light (λ = 400 nm) appear to be blue (λ = 450 nm)? Assume the star is moving along the line that connects the star to the Earth.

Homework Equations

λr = λc / (c-Vr)

f= fo (c +- Vr / c +- Vs)

The Attempt at a Solution

Well, to be honest I am completely confused with this problem. It is the last problem in a homework set, so it is most likely the most difficult.

First attempt:
400-450 = -5e-8.
Now solve for v:
Δf = fs*((1+v)/c)
v = Δf*c/fs-1 = -5e-8*3e8/(4e-7) - 1 = -3.75E7 m/s, so the star would have to be moving away from you at 37,500,000 m/s.

Second attempt:

Vr = 450 * 3e8 / 400 * 3e8 = 1.125.


Neither are correct. Any assistance or guidance is truly appreciated. Thank you.

 

[Covenant32]

I have no idea why the template is copied multiple times. Sorry about that.

 

[Covenant32]

The answer is in terms of "c". So, I thought that perhaps I could just find the ratio of 3.75e7 to 3e8, which is .125, but that is incorrect.

I'm really lost on this blasted problem. It is the last one of close to 40 I've done.

 

[netgypsy]

I don't see how you're using the equations. Define the variables in the first equation and give the units of measure please.