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Are there stars, galaxies etc that we cannot see because they are traveling too fast and their spectrum is shifted below our visible range? From what I understand, red shift is caused by stars and such moving away from the viewer. At what speed does a star etc have to travel to be invisible to us?

What if you are in one galaxy on one side of the universe that is expanding looking at a galaxy on the other expanding edge side. They would be traveling faster than the speed of light away from each other. Would they be invisible to each other?

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    $\begingroup$ Do you mean invisible to human vision? Your question is not very well defined. Note that cosmological redshift is not caused by motion. $\endgroup$ – Rob Jeffries Jul 17 '18 at 22:35
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    $\begingroup$ To repeat @RobJeffries, do you just mean “visible light”? Cosmic microwave background radiation, for example, is highly redshifted and isn’t in the “visible” frequencies. $\endgroup$ – Chappo Jul 18 '18 at 0:31
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    $\begingroup$ The answer is still going to depend on the object, or more specifically on the type(s) of electromagnetic radiation that it is emitting or reflecting. A strong gamma ray source, such as an exploding supernova, would still be visible at very high redshifts because the gamma rays would be redshifted down to visible light. $\endgroup$ – Steve Linton Jul 18 '18 at 12:08
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    $\begingroup$ Also, stars that are far enough away to have an appreciable redshift are by no means visible to the human eye in the first place, simply because they're too far away and hence too faint. You can still detect them in a telescope, but since telescopes can "see" infrared anyway, they won't redshift out of a telescope's visible range. $\endgroup$ – pela Jul 18 '18 at 12:31
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    $\begingroup$ The question has now been edited into something that is quite different from the original and it is not clear that this was the intent of the OP. $\endgroup$ – Rob Jeffries Jul 18 '18 at 13:05
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The following deals only with redshift caused by motion (Doppler effect).

Wavelength (wl) shift for an object moving away from a stationary observer is calculated by following formula: shift = wl x V/C with V speed of the moving object and C speed of light (source: https://en.wikipedia.org/wiki/Doppler_effect)

Let's say we want a Sun-like star to become invisible to the human eye. Our Sun's emission starts around 250 nm and human vision ends around 700 nm (source: https://en.wikipedia.org/wiki/Sunlight#/media/File:Solar_spectrum_en.svg).

So we want a minimum shift of 700 - 250 = 450 nm for wl 250 nm. Formula yields V/C = 450 / 250 = 1,8 which (1) is impossible because nothing moves faster than light (2) makes the classical formula irrelevant

The relativistic formula (for objects moving at speeds > C/10) is: shift / wl = SQRT( (1 + V/C) / (1 - V/C) ) -1 with SQRT the square root (source: https://en.wikipedia.org/wiki/Relativistic_Doppler_effect)

Rounding (shift / wl) up to 2, the relativistic formula yields V/C = 8/10

The speed V would have to be even higher for a hotter (white to bluish) star with UV emission starting below 250 nm.

So my answer to the question is: very close to the speed of light (80% in above calculation) and therefore not a real-life scenario (see below).

"Among the nearby stars, the largest radial velocities with respect to the Sun are +308 km/s" (source: https://en.wikipedia.org/wiki/Doppler_effect), that is 1000 times smaller than C = 3e5 km/s. Rounding down to 300 km/s, it would produce a maximum shift of 700 x 300 / 3e5 = 0,7 nm, several hundred times smaller than required for invisibility.

Besides, the star would still appear on an infrared image.

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    $\begingroup$ Hi, welcome on the Astronomy SE! Note, the site supports Latex, just write $5\cdot 5$ and you will get $5\cdot 5$. $\endgroup$ – peterh Jul 26 '18 at 12:38
  • $\begingroup$ I really liked your answer. Please come back and look at some others. $\endgroup$ – Muze the good Troll. Jul 26 '18 at 20:25
  • $\begingroup$ Among stars which are not "nearby" there are many whose light is red-shifted by a factor of 3 or more, so that 250nm UV would be shifted to 700nm or longer IR. Such galaxies will also contain stars (and other things) that emit much shorter wavelength radiation, though, so some visible light will probably reach Earth. That said such a galaxy will be much too faint to see with the naked eye. $\endgroup$ – Steve Linton Jul 27 '18 at 21:40

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