# Homework Help: Rearranging equation - Relativistic doppler

1. Sep 16, 2009

### roberto85

1. The problem statement, all variables and given/known data
The hydra cluster is 900 Mpc (3x10^9 light years) away. Calcium atoms emit a spectral line of wavelength 396.8 nm. This line is observed at 487.5 nm. The velocity of the cluster, v, is given by ($$\lambda$$ =c/f)

487.5 = 396.8 SQRT((1+v/c)/(1-v/c))

How do i find v please?

2. Relevant equations

3. The attempt at a solution I need to rearrange and this example says take v/c to one side and solve but i dont know how. Well i have taken the numbers to one side, squared them and left with (1+v/c)/(1-v/c) on the other side, how do i find v? Thanks

2. Sep 16, 2009

### Staff: Mentor

1. Divide both sides by 396.8.
2. Square both sides.
3. Multiply both sides by (1 - v/c).
4. Carry out the multiplication on the left side.
5. Get all terms involving v on one side.
6. Factor v out.
7. Divide both sides by the coefficient of v.
That should pretty much do it

3. Sep 23, 2009

Thanks :)