# Doppler shift and red/blue shift

Tyro
Suppose we have a weightless light source that is moving. Its output light will therefore undergo a Doppler shift. Now, if the lightsource had weight but were static, its light would undergo a red shift. If the light source had weight and were moving, would it undergo both a red shift and a Doppler shift, with the end frequency being the linear superposition of both effects?

Also, if:
• The relative velocity of the transmitter and recepient is the same, will the apparent Doppler shift be zero?
• If the weight of both the transmitter and the recepient is the same, will the apparent red/blue shift be zero?

## Answers and Replies

Gold Member
Dearly Missed
Originally posted by Tyro
Suppose we have a weightless light source that is moving. Its output light will therefore undergo a Doppler shift. Now, if the lightsource had weight but were static, its light would undergo a red shift. If the light source had weight and were moving, would it undergo both a red shift and a Doppler shift, with the end frequency being the linear superposition of both effects?

Also, if:
• The relative velocity of the transmitter and recepient is the same, will the apparent Doppler shift be zero?
• If the weight of both the transmitter and the recepient is the same, will the apparent red/blue shift be zero?

there are two formulas, one for the gravitational redshift and one for the doppler, and they each give you a ratio of wavelengths----you can just multiply the two factors together.

"superposition" suggests adding two effects together, so it is not quite the right word-----combining the effects in this case means to multiply the two factors

if the gravitational effect is to extend wavelengths by a factor of 1.5
and on top of that the thing is speeding away so fast that the doppler effect extends wavelengths by a factor of 2
then the combined effect is to make the wavelengths 3 times longer (multiply them first by 1.5 and then by 2 gives the same as multiplying them by 3)

the two formulas are each for a factor 1+z
1 + z = received wvlngth/emitted wvlngth = extension factor

so if the factor by which wavelengths get longer is 1.5
then the "z" astronomers talk about is 0.5
it is just a custom that that they have to subtract 1.0 from the
ratio and call it "z"-----it is handy for some purposes

but the fundamental thing is the factor 1+z, and that is what the formulas give

doppler:
wavelngth ratio = 1+z = sqrt((1 + v/c)/(1 - v/c))

Here v is the radial velocity of one relative to the other (by convention, speed towards is negative, speed away is positive).
For small velocities the formula gives approximately 1 + v/c

grav:
wavelngth ratio = 1+z = 1/sqrt(1 - RS/r)

Here r is the radius of the body and RS is the Schwarzschild radius 2GM/c2

WHAT YOU SAY IS TRUE except maybe for the way you said it. If someone one one planet sends a signal to someone on another planet, then the redshift of rising out of the potential well of the sender will just cancel the blueshift of falling down into the potential well of the receiver (if the planets are the same size and mass) other things being equal.
You said the same "weight" and I guess it would be a bit clearer to say the same size and density, but I understood what you meant it I believe its quite true

ABOUT THE DOPPLER if the two are not moving relative to each other----yes, what you say is true, the doppler shift would be zero. They can both be moving relative to some third-party observer but that does not matter. In the doppler formula the only thing that matters is the motion of one relative to the other

Last edited:
Tyro
Oh my God, I just graduated from uni and already I am making mistakes like that, re: the "weight" thing.

This here, is proof that your brain shrinks after leaving skool. (Is that how I spell it? )

Thanks for clarifying re: the superposition thing as well.

Gold Member
Dearly Missed
Originally posted by Tyro
Oh my God, I just graduated from uni and already I am making mistakes like that, re: the "weight" thing.

This here, is proof that your brain shrinks after leaving skool. (Is that how I spell it? )

Thanks for clarifying re: the superposition thing as well.

no problem, nobody needs to be sticklers about terminology as
long as we understand each other and maybe your brain is
growing and becoming more relaxed in the process since you
stopped taking classes which might be a good thing, who knows

anyway as long as you are satisfied with the explanations given
ask more questions if you feel like it, we dont have a heck of a
lot to do besides explore questions that people come up with

I'm trying to understand a book by Carlo Rovelli which is very hard
and I had to put it down and take a break. It is called "Quantum Gravity". Interestingly enough it is not all formulas, there some
actual non-technical thought in the book like what is space, what does it mean for something to be someplace. I thought it was out of date to think about philosophical questions in physics, but maybe it isnt.

Rovelli is in Marseilles. Have you ever been there?

Tyro
Can't say I have been to Marseilles, or intend to. The local atmosphere just gets on my nerves - I mean the people .