Stellar aberration without relative motion between source and observer

According to SR, there should be no aberration if source and observer move uniformely (as would be the case in terrestrial aberration). In this case we should find at least some celestial bodies that show no aberration at all, while moving by chance uniformely witht earth. Was ever any celestial body found out there, that does not underlay aberration?

I would be very happy to receive some answers, kind Regards Florian Michael Schmitt

• SR is not needed for aberration. Commented Oct 1, 2022 at 14:21
• Can you provide a reference wjich states there is no aberation for objects with no relative motion? Commented Oct 1, 2022 at 21:26
• If Relative motion meant that there is no aberration, then the Michelson Morley experiment would have excluded aberration from the light-path explanation, Commented Nov 2, 2022 at 14:12

It's impossible to measure instantaneous aberration because there is no reference angle to compare against.

What can be measured is the variation of aberration over the course of a year. In 6 months, Earth's velocity relative to the Sun changes by about 60 km/s, and that slightly changes the apparent direction of all stars in the sky. The change of relative velocity is the same 60 km/s for every star, and the change of angle only depends on that, and not on the "absolute relative" velocity.

There are three sources of abberation: annual (due to the orbit of the Earth) diurnal (due to its rotation) and secular (due to the relative motion of the solar system.

The secular aberration is generally ignored. That is to say, the position of a star is the position it appears to be in as a result of secular aberration. It is generally not possible to determine the secular aberration by direct measurement, as there is nothing to compare the position of the star to. If the relative velocity of a star is known, the secular aberration could be calculated, but it isn't usually done.

And so, it isn't possible to identify stars that happen to have close to zero relative velocity by measuring secular aberration.

The crucial point with stellar aberration is that the light does actually not travel in a vacuum (as assumed by Special Relativity) but in a physical medium. And according to the Ewald–Oseen extinction theorem, any information relating to the source will be lost after a certain distance traveling in a medium, with the latter basically now having taken over the role of the light source. For the interstellar medium, this distance amounts to about 2 light years for visible light, so any stellar aberration you see is effectively referred to the local interstellar medium. Of course, as pointed out already in some of the other answers, only changes in the aberration are actually noticeable, so even though the Sun may move relatively to the local interstellar medium, you would not notice this in the short term, but only the motion of the Earth around the Sun.

from your answers I am afraid, I din't put the question right. Of course I am aware that stellar aberration can be seen only conparing one stars position on the course of over one year (drawing a small ellipse actually over a year). But the point is:

If any celestial body (say some thousand lightyears away) would have exactly the same path around its sun as earth, and its sun the same path as our sun, than according to SR no aberration should occur and also no change of position within a year (no relative speed between source and observer). Eventually this is the only way how SR can explain terrestrial aberration. In other words: According to SR it should be likely that there must be some celestial body out there showing no aberration. Otherwise earth would be very special in the universe...

• The motion of the star is irrelevant for stellar aberration. See my own answer above Commented Oct 2, 2022 at 18:40
• Unless you meant to answer your own question, please edit this content into your original Question post. Commented Oct 3, 2022 at 22:13