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I can't comprehend this: 10 light years away there is an explosion. 10 years later we see it. But, what about the hazardous rays (like gamma or something)? When it took us 10 years to see the explosion, in the meantime negative effect is already here, so we don't actually see the process of exploding (+10 years until incoming wave arrive since the event), but whole image at once (beginning of explosion and incoming ray in the same time)? So if something happens in deep space, we don't have time, because the moment we see something happened the consequences are already here? Because they were already coming, while we were waiting for any images in the first place! Or does it works differently? What actually happens?

Explain like I'm 5 (or 10, but not more, because science classes were too much for me since middle school, so don't even try any formulas :P).

Bonus question: If the Universe expands, doesn't that 10 years travel of light stretch in the meantime (if expanding is faster than speed of light it should never reach us!?) to 10,0(+whatever 0 it takes)1 years?

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Gamma rays and other forms of radiation are light. Just because we can't see gamma rays doesn't mean that it's not a type of light. Everything in the electromagnetic spectrum travels at the speed of light. This includes x-rays, gamma rays, microwaves, radio waves, viable light, infared, ultraviolet, and long waves. All of these things are just photos with different wavelengths. So they all travel at the same speed.

So to a awnser your question if a sun did explode really far away the light from it and he bad effects would happen at the same time.

Even though if you wereally on earth while a gamma ray burst hit it wouldn't instantly destroy the planet. A gamma ray burat would probably tear a massive hole in our ozone cooking half our planet but on the other side of the world people could survive a bit longer until the suns radiation killed them. It all depends on how far the bust came from. The father away he more dangerous. The further away a bust come from the more it expands over time. So in theory a super far dying star could roast out whole solar system if it traveled long enough. You can learn more about gamma rays here: Gamma ray busts explained - Death from above

Any particular damage would hit us long after a gamma ray burst and by that time we all may be dead.

Also expansion of the universe wouldn't really change anything, I don't really get what you tried to say here but the universe'a expansion effects all light in the same way. The universe is expanding outwards but the universe is so large that expansion is speak out so it would male little difference in the light's time of arrival.

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The radiation from an explosion all travels at the same speed, so nothing will actually occur to us before we see it. We may not have much time to do much about, say a gamma ray burst, but it will been seen first (or at worst at the same time) as long as we look in the right place.

If the damage is going to be caused by particles rather than radiation, since these particles have mass, they will travel more slowly than the light rays.

An example of this are Coronal Mass Ejections from the sun, which we can see before the particles actually affect us.

enter image description here

A coronal mass ejection, is a giant cloud of solar plasma, that is particles such as protons and electrons, which we will see up to a day before it interacts with the Earth's magnetic field.

Image credit: Spaceweatherlive.com

Bonus question: If the Universe expands, doesn't that 10 years travel of light stretch in the meantime (if expanding is faster than speed of light it should never reach us!?) to 10,0(+whatever 0 it takes)1 years?

The expansion of space affects all radiation at the same rate, increasing the wavelength of the radiation by the time it reaches us. So 10 years before it reaches us, at the time of the bang, the radiation will have a shorter wavelength (higher frequency).

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