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Stars being flung from black holes in the news made me question if something were heading directly for us at the speed of light, would we even know?

Update: Since it's impossible for a star to travel at the speed of light, would we see it coming if it were traveling at 99% the speed of light? and if so, how much warning would we have?

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    $\begingroup$ Ah ok sorry I didn't know I'll update the question $\endgroup$ – Jake Graham Arnold Nov 16 at 13:40
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Processes energetic enough to accelerate a star to 99% of the speed of light are not known. A close interaction and ejection from a multiple black hole system could perhaps provide enough energy, but such close interaction with black holes would probably rip the star apart before it could reach such excessive speeds. Hypervelocity stars are known. They have speeds less than about 1% of the speed of light.

A star travelling through space at such speeds would also have problems. It would be slamming into interstellar gas. I have no idea if it could even survive, or would it be eroded by the interaction with the thin gases in interstellar space.

A star at that speed would be significantly blue-shifted. This would make its spectrum very odd. A small dim star could be visible, catalogued and observed to have a very odd spectrum at a distance of about several hundred light-years. It is likely that we would first observe such a star several hundred years before it got close to us. However such high speed objects probably don't exist.

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  • $\begingroup$ That's incredible thank you :) $\endgroup$ – Jake Graham Arnold Nov 16 at 22:40
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    $\begingroup$ Despite the "problems" the poor star would be having, I'd still like to know the answer to the question; "...would we see it?" if it were traveling near the speed of light. $\endgroup$ – uhoh Nov 16 at 22:48
  • $\begingroup$ See paragraph 3: Yes, but it would be blue shifted. $\endgroup$ – James K Nov 17 at 7:13
  • $\begingroup$ Carl Sagan video on "what if the speed of light were slower". $\endgroup$ – Keith McClary Nov 18 at 20:04
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    $\begingroup$ How do you get a blueshift of ~2? It should be more like 14 at v = 0.99c. $\endgroup$ – pela Nov 19 at 22:05
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We would have $$\tau = d/0.99c - d/c,$$ of warning, where $d$ is the distance to the star when we first detect its light and $c$ is the speed of light.

Would we see it - yes indeed. Since $$\lambda_{\rm obs} = \lambda_0 \left( \frac{1 - v/c}{1+ v/c}\right)^{1/2},$$ the light from the star would be blueshifted by a factor of 14, so for a solar type star, the peak of its emission would be shifted into the ultraviolet.

However, it will still be much brighter than a stationary star at all wavelengths. If we assume the star emits roughly blackbody radiation, then it will look like a blackbody at 14 times the temperature, with an integrated luminosity that is $14^4 = 38,000$ times higher!

See the results/derivations at https://en.m.wikipedia.org/wiki/Relativistic_Doppler_effect

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  • $\begingroup$ So if it travelled at the speed of light wouldn't it have infinite mass and then turn into a black hole?? :-) $\endgroup$ – MiguelH Nov 19 at 16:48
  • $\begingroup$ @MiguelH It cannot travel "at the speed of light". The question asks what it would look like if it travelled at 99% the speed of light. $\endgroup$ – Rob Jeffries Nov 19 at 16:53
  • $\begingroup$ @uhoh "It will still be much brighter than a stationary star at all wavelengths". ?? $\endgroup$ – Rob Jeffries Nov 19 at 16:54
  • $\begingroup$ @RobJeffries. Fair cop! Well then, almost infinite mass ... $\endgroup$ – MiguelH Nov 19 at 16:58
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    $\begingroup$ @MiguelH You are out of date. "Mass" is a relativistic invariant, such that $(mc^2)^2 = E^2 - p^2c^2$. What you mean is that its momentum is very large. $\endgroup$ – Rob Jeffries Nov 19 at 17:05

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