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The Wikipedia article "Relativistic Doppler effect - One object in circular motion around the other" confused me.

Relativistic Doppler Effect when One object in a circular motion around the other

There they say that when the light source orbits the observer, the observation of the observer would be different than the case where the observer orbits the light source.

Now, what I knew from my basic physics background is that there is no such thing as "orbiting" because despite from the outside the earth seems like it is orbiting around the sun, that is just a misinterpretation. If we fix the sun at the center, the earth will seem like orbiting around the sun and if we fix the earth at the center, the sun will seem like orbiting around the earth. In essence, they both are rotating around their overall center of mass.

So, how is it possible that when I and the sun are rotating around our overall center of mass, I could observe redshift and blueshift at the same time?

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The center of mass is well within the sun because the sun is so much more massive than the Earth, so it's OK to say "orbiting the sun". We can likewise assume that if the sun were orbiting the Earth, then the Earth would be much more massive than the sun.

And that is the answer to your problem: the massive object has outgoing radiation redshifted and the incoming radiation blueshift much more than the less massive object has incoming radiation blue shifted and the outgoing radiation redshifted.

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  • $\begingroup$ If the question is about special relativity, the mass can be neglected. The reason why the orbiting object is objectively redshifted has to do with the constant acceleration $\endgroup$ – Yukterez Aug 18 at 23:23
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In special relativity rotation and acceleration means that you are constantly switching your inertial frame. The object in the center is unaccelerated, so it stays in its inertial frame. The object in orbit is rotating and therefore constantly accelerating, so its light will be redshifted relatively to the unaccelerated object in the center, and the object in the center will be blueshifted relative to the orbiting object. That is because the accelerating object on a circular orbit is constantly switching into a frame in which the proper time of the unaccelerated object in the center runs faster than its own. For more information see https://en.wikipedia.org/wiki/Born_coordinates and the references therein.

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