Simple Redshift Question/Orbital Velocity

[bmb2009]

Homework Statement

When studying the optical spectrum of a very distant quasar (quasi stellar object), they found that a certain spectral line appears at a wavelength of 559 nm instead of the regular 446 nm. In terms of the speed of the light, what is the radial speed of the quasar with respect to Earth?

Homework Equations

The Attempt at a Solution

I tried using the fact that the redshift z= (λ_observed - λ_emitted)/(λ_emitted) and then
1 + z = 1/(sqrt(1-(v^2/c^2)) and then solving for v.. But is this "v" the orbital velocity? And I did convert my answer into terms of the speed of light so that's not the part that's wrong. Any help? Thanks!

 

[mfb]

There is no orbital velocity.

1 + z = 1/(sqrt(1-(v^2/c^2))

Where does that formula come from? That looks like the transversal doppler effect, which is not relevant here.
A calculated v would be the radial velocity of the quasar, if redshift would come from moving objects (it does not, but you have to assume this here as it seems).

 

[bmb2009]

what velocity equation is relevant here then?

 

[gneill]

For high recession velocities (like those of quasars) you're probably expected to employ the relativistic Doppler effect relationship.

 

[bmb2009]

Ahhh good idea... and yep it worked.. Thank you!