3
$\begingroup$

I was wondering where does the formula for redshift $$z=\frac vc$$ come from? Can it be derived from the definition of redshift $$z={\lambda_{observed} - \lambda_{emitted}\over \lambda_{emitted}}?$$

$\endgroup$
3
$\begingroup$

The non-relativistic formula can be derived analogously to the derivation of the Doppler effect for sound. Namely, draw waves as consecutive parallel lines moving at velocity $c$ whose distance is $\lambda$ (if the source is not moving) and let the source move away at $v$. You will find that the distance has increased and became the observed wavelength, which is $\lambda$ - $vt$ = $\lambda + v\lambda/c$ = $\lambda(1+\frac{v}{c})$.
Note that this formula is not relativistic and that there is cosmological (as pointed out by @Alchimista in the comment below) as well as gravitational redshift, so the formula above only describes only one of the effects that cause redshift or blueshift.

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.