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A possible answer for this is that, light emitted from the galaxies travelled a billion miles all the way to earth, where the hubble space telescope picked up this light through its sensors, and was able to construct an image of the galaxy

but if this is true, and galaxies are billions of miles away, shouldn't the light particles emitted from the galaxies be scattered all over the place? after all they have been travelling from millions of years, and have probably collided with asteroids and other foreign objects. What were the chances that about 95% of the photons actually reached earth, giving us a very detailed image.

Consider the andromeda galaxy which has a distance of 1.492 × 10^19 mi from earth. If light emitted from the galaxy travels in all directions, then how is it that we can still map out the entire galaxy, evident from the photo below?

Shouldn't like half of the galaxy be missing since photons could have hit other objects, and "never have reached earth"?

enter image description here

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    $\begingroup$ Because space is largely just that. The entire premise of your question - that light is likely to interact with something - is incorrect. $\endgroup$ – Rob Jeffries Sep 10 '17 at 19:04
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    $\begingroup$ @KSplitX You're going about it the wrong way. We can see the galaxy from here because there's nothing in between. (That is, the fact that we can see it from here is evidence that nothing is.) If there are galaxies that are obscured by something in between, then we couldn't see those, no. $\endgroup$ – Mr Lister Sep 10 '17 at 20:12
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    $\begingroup$ Light from galaxies travelled a billion miles? Sorry, but a billion miles barely gets you past the orbit of Saturn :-) As for why we can see galaxies a billion or more light years away, 1) They emit a lot of photons; 2) We use big mirrors to catch as many photons as possible; and 3) We stare at the same patch of sky for hundreds of hours (for the Hubble Deep fField images) to collect photons. Indeed, in real time there is pretty much nothing to be seen in the patches of sky they look at - that's part of the reason why they were chosen. $\endgroup$ – jamesqf Sep 11 '17 at 4:43
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    $\begingroup$ The premise of this question is a rather good example of an Argument from Personal Incredulity (I can't understand how X can be true, therefore, I doubt X to be true). $\endgroup$ – Oscar Bravo Sep 11 '17 at 7:37
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    $\begingroup$ "Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is." $\endgroup$ – PlasmaHH Sep 11 '17 at 9:31
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There are two reasons that often — but not always — light from galaxies millions and even billions of lightyears away make it through the Universe and down to us:

Particle number and particle size
  1. First, the intergalactic medium (IGM) is extremely dilute. The number density of particles out there is of the order $n\sim10^{-7}\,\mathrm{cm}^{-3}$, or roughly 26 orders of magnitude lower that the air at sea level! That means that if you consider a tube from Andromeda to the Milky Way with cross-sectional area of $1\,\mathrm{cm}^{2}$, it will contain roughly one microgram of matter (thanks to Rob Jeffries for catching a factor $10^6$ error).

  2. Second, even if a photon comes close to an atom, it will only be absorbed if its energy matches closely some transition in the atom. Since most of the atoms are ionized (and thus should be called plasma instead, but in astronomy the distinction if often not made), there are no electrons to absorb the photon. The photons are more likely to interact with the free electrons via Thomson scattering, but the Thomson cross section is immensely small $(\sim10^{-24}\,\mathrm{cm}^{2})$, so even if you consider the CMB photons — which have traveled through the Universe almost since the Big Bang — only around 5% of them have interacted with electrons on their way.

In other words: The amount of transmitted light depends on two factors: 1) The amount of matter along the line of sight, and 2) that matter's ability to absorb the light. In the IGM, both are tremendously small. When the light enters the interstellar medium (ISM) inside our galaxy, it may encounter denser clouds with atoms that are able to absorb the light. But usually (although not always) "dense" is still very dilute compared to Earth's atmosphere.

Mathematical expression

In general, if a beam of light traverses a region of particles, each with a cross section $\sigma$ (measured e.g. in cm$^2$), passing $N$ particles per area of the beam (measured e.g. in cm$^{-2}$), then the opacity of the medium is given by the optical depth $\tau$, defined by $$ \tau \equiv N \, \sigma. $$ The transmitted fraction $f$ of photons is then $$ f = e^{-\tau}. $$ In general $\sigma$ depends on the wavelength, and thus part of the spectrum may pass unhindered, while another part may be completely absorbed.

The figure below (from here) shows the spectrum of a quasar lying at a distance of 22 billion lightyears, i.e. $10\,000$ times farther away than Andromeda. You see that there are several thin absorption lines (caused by intervening hydrogen clouds whose densities are a factor of 10-100 higher than the IGM), but still most of the light makes it down to us.

qso

Because the light we see from this quasar was emitted so long ago, the Universe was considerably smaller at that time, and thus the density was larger. Nonetheless, only a small fraction is absorbed. The farther away the light is emitted, the longer ago it was, which means smaller Universe, and higher density, and thus the more light is absorbed. If you consider this quasar (from here) which lies 27 billion lightyears away, you see that much more light is absorbed in part of the spectrum. Still, however, much light make it through to us.

qso2

The reason that it is only the short wavelengths that are absorbed is quite interesting — but that's another story.

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    $\begingroup$ The distance to Andromeda is $2\times 10^{24}$ cm. A 1cm$^2$ cylinder contains $2\times 10^{18}$ H atoms/ions, with mass $4\times 10^{-6}$ g ? If you had this surface density of tinfoil it would be a micron thick and I suspect not opaque to light, however the tinfoil argument is a red herring since the reflectivity of tin arises directly from its density (and electron degeneracy), not the total number of atoms present along the line of sight. @user18458 $\endgroup$ – Rob Jeffries Sep 11 '17 at 12:00
  • $\begingroup$ Oops, thanks @RobJeffries. I don't know how I missed a factor of a million. Guess I should stop doing calculations in my head. I'll edit. $\endgroup$ – pela Sep 11 '17 at 12:34
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    $\begingroup$ Is it correct to say the quasar is >20 billion ly away when the universe is <14 billion years old? It may now be that far away, but we are talking about the light we are measuring from it, which was not emitted from that distance. Just a bit misleading I think. $\endgroup$ – mao47 Sep 11 '17 at 15:38
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    $\begingroup$ @mao47: It is quite customary, when talking about distances to a given cosmological object, to refer to the distance to that object now. The distance it had when it emitted the light we see today is less commonly of interest, but is easily found: For instance, the last quasar I mention lies at redshift z = 5.82. At a given redshift z, everything was a factor (1+z) closer to each other than today, so the distance to that quasar was 27 Gly / (1+5.82) = 4 Gly (despite the Universe only being 1 Gyr old at the time). $\endgroup$ – pela Sep 11 '17 at 18:56
  • $\begingroup$ Do you have a link to the explanation of why only short wavelengths are absorbed? $\endgroup$ – Beta Decay Sep 12 '17 at 11:24
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As Rob Jeffries says, the universe is mostly empty space. A photon can easily travel thousands of light years without interacting with anything. Most of the interaction would occur when photons entered the earth's atmosphere. The Hubble avoids this. These photos were most likely from combining several viewing sessions giving basically an extended time period for observing the galaxy.

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    $\begingroup$ Galaxies were observed more than 200 years before Hubble, which just shows that light can travel a long way through even a relatively dense medium (our atmosphere) without being absorbed to a great extent. $\endgroup$ – Dr Chuck Sep 10 '17 at 19:42
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    $\begingroup$ @DrChuck The Andromeda galaxy has been observed for much longer than that since it's very well visible with the naked eye. If there's one thing I'm jealous of the good old days, it's the lack of light pollution. $\endgroup$ – Eric Duminil Sep 11 '17 at 20:22
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    $\begingroup$ Or as Douglas Adams said, "Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space." $\endgroup$ – T.E.D. Sep 11 '17 at 22:26
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There's a misconception in your question I don't think the other answers have addressed.

If light emitted from the galaxy travels in all directions, then how is it that we can still map out the entire galaxy

Light is emitted from the galaxy in all directions. Only a tiny, tiny fraction of it is directed to Earth, and of that, an even tinier fraction is collected by any given telescope. But we can still see it, because galaxies are very, very bright. Andromeda contains about a trillion stars.

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    $\begingroup$ This is a useful point to make. If you spend the effort to calculate the total number of photons Andromeda emits per second, you'll find an astronomically high number (think $10^{60}\:\mathrm{photons/s}$ at a minimum). So its no wonder we can collect $\sim 10^3\:\mathrm{photons/pixel}$ in a single, longer-than-a-second observation with a telescope. $\endgroup$ – zephyr Sep 11 '17 at 12:57
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Sorry if this logic seems a bit circular, but we can get unobscured pictures of galaxies because they are unobscured.

As has been mentioned - space is really, really big and really, really empty. This is hard for us to contemplate, because there's so much stuff right next to us - but this is actually a really unusual condition. The next star to the Sun is over 4 light-years away, but we get almost all (99.9999999999...%) the light from it that heads in our direction - the same with light from further away - we get a huge number of photons sent to us from objects very far away.

Hubble also uses the simple camera techniques of lensing and long exposures to take images of distant objects - so more light is received to construct the image.

But, the other part of this, it is almost impossible to take a picture of a galaxy (or star) that is behind another galaxy or dust cloud. For example, we can't easily see past the centre of our own galaxy, because there's a lot of dust and gas and stars in the way. The picture in your question, on the other, seems to be Andromeda, which is above the plane of the galaxy. Our galaxy is quite thin compared to its diameter, and we're a decent way out of the galactic centre, meaning there's a lot less stuff in the way.

And there are some galaxies we've taken images of which are obscured by dust:

enter image description here

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    $\begingroup$ "a lot less crap in the way" -- can we try to answer without so much technical jargon? $\endgroup$ – Barmar Sep 12 '17 at 20:45
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There's been some good answers already, but I'd like to add my two-pennyworth:

How do we have photos of galaxies so far away?

Because there's nothing much between them and us that interferes with the light that reaches our cameras.

A possible answer for this is that, light emitted from the galaxies travelled a billion miles all the way to earth, where the Hubble space telescope picked up this light through its sensors, and was able to construct an image of the galaxy

It's a billion miles to Saturn. Well actually the distance varies with the orbits, but see this Space.com article: "At their most distant, when they lie on opposite sides of the sun from one another, they are just over a billion miles (1.7 billion km) apart". The Andromeda galaxy is circa fifteen billion billion miles away. Or circa fifteen quintillion miles.

but if this is true, and galaxies are billions of miles away, shouldn't the light particles emitted from the galaxies be scattered all over the place?

Don't forget that photons have an E=hf wave nature. And that even though they are scattered in the air, you can still see the Moon. Yes, there's a bit of light going astray in space. But not so much that the night-time sky is some blank foggy fug. You can see Saturn too. And the stars. And the galaxies, but they are rather dim.

after all they have been travelling from millions of years, and have probably collided with asteroids and other foreign objects. What were the chances that about 95% of the photons actually reached earth, giving us a very detailed image.

The chances are high. We have pictures of planets and things because the chances are high.

Consider the Andromeda galaxy which has a distance of 1.492 × 10^19 mi from earth. If light emitted from the galaxy travels in all directions, then how is it that we can still map out the entire galaxy, evident from the photo below?

If I was covered in lights, I would emit light in all directions, and you would see me because some of that light goes into your eye. The Andomeda galaxy is similar.

Shouldn't like half of the galaxy be missing since photons could have hit other objects, and "never have reached earth"?

No. And if half the photons didn't reach Earth, you'd just see a dimmer galaxy, that's all.

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Let me give some simple explanations.

No, no, no. 95% of the photons don’t reach Earth. Even if 5% of photons emitted (within a few seconds) just by one star, say, by our Sun had reached Earth, our planet would have been completely scorched! Now then, Andromeda has hundreds of billions of stars (or suns). Nothing of that reaches us, except for an infinitesimally small number. It’s mind-boggling how small the percentage of photons that reach us is! You can try to calculate that very roughly. It is very easy to calculate what percentage of photons emitted by the Sun reaches Earth. And the Sun is only 8 minutes away from Earth, while Andromeda is more than 2.5 million years away! So, actually, it’s not that difficult to imagine how many photons reach us.

Now, why don't asteroids, planets or stars block everything? Andromeda is way too large to be blocked like that! It’s easier to block the view of the Pacific Ocean from space by placing a few specks of dust in between! The diameter of Andromeda is more than 200 million light years. Can we block it from view? Actually it can be blocked by something as large as a nebula close to our solar system. Such a nebula must be many light years in diameter; it must be dense enough; and not too far away. Thankfully nothing like that blocks this beautiful galaxy from our view. However it happens with some other galaxies and deep space objects. As to very distant nebulas, they won’t block Andromeda from our view because they will look way too small against the background of Andromeda which is much further away.

Why is light not scattered? Why should it be scattered that much to make Andromeda blurry? When the Moon is on the horizon, its light travels through many hundreds of miles of dense atmosphere almost parallel to the surface of Earth; yet, we can still train our telescopes on it and see the various features of the Moon. It would not be a very clean view but we would still see a lot. Now, in space light travels through an almost complete vacuum, especially empty is the void between galaxies. So, there’s no reason for light to be scattered too much. Photons and many other particles are stable enough and can travel much larger distances: billions of light years. Another way to look at it is to ask a question how much photons should deviate from their straight path so that Andromeda becomes blurry to us. Well, they have to go sideways a lot, and the diameter of Andromeda is too huge for that. That doesn’t seem logical, as photons travel in straight lines. Large objects, like stars and black holes will affect their path but the diameter of Andromeda is so huge that it is not an option, unless we artificially place trillions of black holes along the line between Andromeda and our solar system in an attempt to warp the image of Andromeda or to make these black holes gobble up all the light from the galaxy! So, when astronomers say most of the light reaches us, they mean that intergalactic space is almost complete vacuum, and the photons that go exactly in our direction are “free” to go. Yet, only an infinitesimally small number of them go exactly in our direction and it is still enough for nice photos. Why? That's why:

The absolute magnitude (relative luminosity against that of an object $40$ times brighter than the Sun at a distance of $33$ light years away) of Andromeda is around $-21.5$. Our Sun is only around $5$. The higher the number the dimmer the object. An object with an absolute magnitute of $1$ would be $2.5^{5-1}=40$ times brighter than the Sun. The difference between Andromeda and our Sun is $-21.5-5=-26.5$. This means Andromeda is very roughly $2.5^{26.5}\approx 40,000,000,000$ times brighter than the Sun.

As to how large it is in the night sky, well, lengthwise it is roughly six times the diameter of the moon but you can only see the bright central part. To see the whole extent you need a large aperture telescope and long exposure photography to gather more light and produce a better, more detailed image.

Hope, this primitive explanation will be of some help. Andromeda is visible today if weather permits :)

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    $\begingroup$ What do you mean by "95% of the photons don't reach Earth"? If you mean "most photons are emitted in other directions than Earth", then it's quite obvious (since Earth only spans a solid angle of $R_\oplus^2/d_\mathrm{And}^2 \sim 10^{-31}$). If you mean "95% of the photons are absorbed on their way", then it's not true. $\endgroup$ – pela Sep 14 '17 at 14:21
  • $\begingroup$ I thought I were polite. I asked because I don't understand why you write that sentence. If for reason #1, then I think it's so obvious that writing it only adds to confuse (especially since you write "95% don't reach Earth", when in fact the fraction that do reach Earth is $10^{-31}$). If for reason #2, then I think you should remove it or edit, because it is not true. For instance, in the visual the extinction toward Andromeda is roughly $A_V=0.2\!-\!0.25$, so the fraction of photons that do reach Earth is much higher than 5%, more like 80-85%. $\endgroup$ – pela Sep 17 '17 at 21:32
  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – called2voyage Sep 20 '17 at 13:58

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