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Why can we, as earth habitats, observe stars further than the speed of light /earth's rotational angular speed? I think it should be in the order of 10^14 m? As, relative to us, stars further than that should have a tangential speed that is more than light speed?

Maybe it is a stupid question!

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    $\begingroup$ See en.wikipedia.org/wiki/Faster-than-light#Daily_sky_motion As explained immediately above this section, “Certain influences may appear to travel faster than light, but they do not convey energy or information faster than light, so they do not violate special relativity.” $\endgroup$ – G. Smith May 27 at 16:35
  • $\begingroup$ Please put your comment in separate answer to vote for it as it was useful to me. $\endgroup$ – Ahmed Kamal Kassem May 28 at 3:53
  • $\begingroup$ OK, I’ve provided an answer. $\endgroup$ – G. Smith May 28 at 4:04
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Your question is a good one and is not stupid.

As Wikipedia’s “Faster-than-light” article explains under the section “Superluminal travel of non-information”,

Certain influences may appear to travel faster than light, but they do not convey energy or information faster than light, so they do not violate special relativity.

The subsection “Daily sky motion” mentions how stars appear to move faster than light because of the rotation of the Earth. The article provides numerous other examples of allowed superluminal “motion”.

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I think what you mean is that stars in other galaxies are moving away from us at enormous speeds,& the further away they are,the faster they recede. What you seem to be asking is: do the most distant stars/galaxies recede faster than the speed of light? No,they don't,but some of them get very close to it. There may be galaxies further away than the furthest we can detect at present,but it is not thought that they exceed c (speed of light).

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    $\begingroup$ No, actually I don't mean the radial speed due to universe expansion, which is proportional to the distance from us. I mean the relative tangential speed due earth rotation, which, at least classically, should = omega* R $\endgroup$ – Ahmed Kamal Kassem May 27 at 14:50
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    $\begingroup$ Sorry, but this answer is totally wrong. Speed of light is not a limit for galaxies' recession velocities, or any other distant object in general relativity. $\endgroup$ – D. Halsey May 27 at 21:00

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