## Opacity of Space?

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snow5379
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### Opacity of Space?

Imagine if you travel 100 million light years in one direction. What are the odds you'd hit a star or something? I'm getting ~1.9% by just counting galaxies at various distances... has anyone ever calculated this before?

I'm trying to figure out specifically what percentage of objects are hidden from view by objects in front of them. My calculations say every 100 million light years of space blocks ~1.9% of the space behind it from view but I'm not exactly an astronomer and I was wondering if any actual astronomers have ever produced a number regarding this.
Last edited by snow5379 on Tue Feb 28, 2012 12:26 am UTC, edited 3 times in total.

LaserGuy
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### Re: Opacity of Space?

The observed stellar density appears to be on the order of 1 star per 1000x1000x1000 light year cube.

The largest stars have a diameter of ~900,000,000 km, or about 0.00001 ly. So if there is one star in a 1000x1000 field, it would make up a 10^-12 of the total area. In your 10^3x10^3x10^11 block, there would be 100,000 stars, so if you were to send a ray through the field, the odds of hitting one would be ~10^-7 or 10^-5%.

In reality it would be much less than this, because I'm using the value of the largest observed diameter, rather than the average. I'd guess that the real value is probably 1-2 orders of magnitude smaller.

Izawwlgood
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### Re: Opacity of Space?

Sweet zombie void dragons... Space is big.
... with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandalled feet.

starslayer
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### Re: Opacity of Space?

A related question you could ask (the answer of which could easily be modified for your original question) is "How far do I have to go before I hit a star?" Taking the number density of stars to be ~1E9 Mpc-3, and the typical radius of a star to be Rstar = 7E10 cm = 2E-14 Mpc, the average distance you travel before hitting a star is just the mean free path, or $\lambda = \frac{P}{n_{\star}\pi R^2_{\star}}$ Here, P is the probability we hit a star (1, in this case), and nstar is the number density of stars. In this case, we get ~1E18 Mpc or ~3E24 ly. Yowza. Note that this is some 15 orders of magnitude larger than the currently observable universe.

To get the answer to your original question (what is the probability of hitting a star if I travel 30 Mpc?), just set lambda to 30 Mpc and solve. This gives a result of 5E-17, or 5E-15%. Space is freakin' empty.

Note that my answer is so much smaller than LaserGuy's because I used the solar radius, while he used the radius of the largest star, which is some 1000 times larger. Our number densities were also somewhat different.

snow5379
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### Re: Opacity of Space?

Why does the galaxy density seem to drop off so quickly the farther you go? Is it because far away galaxies are harder to detect? I'm trying to do a statistical analysis of the universe using star and galaxy catalogs and I'm having a lot of trouble.

mfb
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### Re: Opacity of Space?

LaserGuy wrote:The largest stars have a diameter of ~900,000,000 km, or about 0.00001 ly. So if there is one star in a 1000x1000 field, it would make up a 10^-12 of the total area.

I don't get this number. 9*108 km are 10-4 ly diameter (not 10-5) and 10-7 of your side length, which is 10-14 of the area (pi/4 ~ 1).

However, large stars are rare, something close to the solar radius looks like a better approximation.
Unless you aim for a specific star, it is unlikely that you ever hit one, even if the path goes through a galactic center.

If you are very slow, things are a bit different due to gravity - the chance to hit a star can increase a lot in that case.

@snow5379: The galaxy density is the same everywhere if the scale is large enough. It is lower in voids and higher at their borders, but apart from that you don't have significant larger structures. Maybe you mixed "hit a galaxy" with "hit a star"? The probability to fly through a galaxy is much larger.

Twistar
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### Re: Opacity of Space?

What about the probability if you travel towards the center of the milky way? I feel like realistically if you travel a random direction in space the properties of the galaxy will dominate the probability of hitting something (and then you could compare this to the probability of hitting something if you end up missing everything in the galaxy)

scarecrovv
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### Re: Opacity of Space?

@snow5379: I'm not sure what distance scale you're referring to as "so quickly" here, but there could be a variety of causes. I am not a cosmologist, so take my advice with a grain of salt, but:

• There's a lot of galaxies out there, and only so much time to observe them and write them all down.
• The universe has only been around for 14 billion years, give or take. Once you look further away than (age of universe - (time between big bang and first galaxies)) light years, you're not going to see any.
• Galaxies are drawn together by gravity. Our galaxy is in a cluster of other galaxies, which itself is part of a supercluster of galaxy clusters. Once you travel beyond the Local group, density goes down until you hit another group in the supercluster. Once you travel beyond the Local Supercluster, density goes way down until you hit another supercluster. If your search volume is larger than the Local Supercluster, but too small to contain any other superclusters, you might be led to believe that we were in the only high density region of the universe. It's possible that your list of galaxies has been purposefully pruned to contain only the local supercluster. It's something to check on.

Incidentally, I'm curious about where you're getting your data. Care to share?

snow5379
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### Re: Opacity of Space?

http://www.sdss.org/

It's a site with lots of pictures of stars and galaxies. They also have catalogs of all their pictures which I've been using to try to learn about the universe.

Also I've thought about it more... star brightness would have a bigger impact than star size. A bright star would block much more from view than a large star... so I don't think size estimates are useful here.

starslayer
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### Re: Opacity of Space?

snow5379 wrote:Why does the galaxy density seem to drop off so quickly the farther you go? Is it because far away galaxies are harder to detect? I'm trying to do a statistical analysis of the universe using star and galaxy catalogs and I'm having a lot of trouble.
Well, your first problem is that you're using Sloan, which is a magnitude-limited search (~22 in all bands, for reference). This isn't a knock against Sloan, really, since any sky survey we do is going to be magnitude-limited just due to our instruments, but you need to keep it in mind - as you go further out, you naturally expect to see fewer galaxies, since they're getting (apparently) fainter and smaller. Plus, even at z=1, you're not exactly in the local universe - you're looking at something that is presently some 13 billion light years away.

It's also worth noting that there should be several hundred billion galaxies in the observable universe, based on surveys of the local Gpc or so plus the assumption that the universe is homogenous and isotropic on large scales, but SDSS, by their own admission, catalog only 930,000 of them. We have a very nice representative sample of galaxies that we have observed and cataloged, but we're nowhere close to bagging them all, even out to z=0.1.

Also I've thought about it more... star brightness would have a bigger impact than star size. A bright star would block much more from view than a large star... so I don't think size estimates are useful here.
Why?

Twistar wrote:What about the probability if you travel towards the center of the milky way? I feel like realistically if you travel a random direction in space the properties of the galaxy will dominate the probability of hitting something (and then you could compare this to the probability of hitting something if you end up missing everything in the galaxy)
Still horrifically low; the average density of stars in the Galaxy is something like ~10 pc-3 (it's about 1 near the Sun, and about 100 in the Bulge, so split the difference), and we need to go ~20 kpc to go through the center of the Galaxy and out the other side, so the probability of hitting a star is about 3E-10, or something like a one in a billion chance of actually hitting anything.

LaserGuy
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### Re: Opacity of Space?

mfb wrote:
LaserGuy wrote:The largest stars have a diameter of ~900,000,000 km, or about 0.00001 ly. So if there is one star in a 1000x1000 field, it would make up a 10^-12 of the total area.

I don't get this number. 9*108 km are 10-4 ly diameter (not 10-5) and 10-7 of your side length, which is 10-14 of the area (pi/4 ~ 1).

Yes, you're right, it looks like I dropped a factor of 10. Serves me right to trying to do math in my head

Jplus
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### Re: Opacity of Space?

Why are we only considering stars? I have a gut feeling you're much more likely to bump into a rock or get sucked into a black hole if you're going to travel in a random direction.
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Tass
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### Re: Opacity of Space?

Jplus wrote:Why are we only considering stars? I have a gut feeling you're much more likely to bump into a rock or get sucked into a black hole dust particle if you're going to travel in a random direction.

Fixed

snow5379
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### Re: Opacity of Space?

Is the consensus here that objects in the foreground blocking out objects in the background isn't a significant issue for statistical analysis then?

LaserGuy
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### Re: Opacity of Space?

snow5379 wrote:Is the consensus here that objects in the foreground blocking out objects in the background isn't a significant issue for statistical analysis then?

Given the extremely low density of objects in space, this effect is going to be quite insignificant, I think. Since objects in space are correlated to each other, it would be a bit higher than chance, but the effect is still probably pretty small. For example, suppose you were looking at the solar system from some distant point, in the orbital plane of the Earth around the Sun. From your point of view, the Earth would travel back and forth along a line 2 AU (300,000,000 km) long. The Sun has a diameter of 1,400,000 km, so Sun would eclipse the Earth ~0.47% of the time. If you were out of the line of sight even by a small angle, however, the Sun would not eclipse the Earth at all.

mfb
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### Re: Opacity of Space?

Kepler searches for these alignments of objects to find exoplanets. Stuff which orbits around stars (or whatever is left from a star) in front of or behind these stars is probably the only interesting case in that respect.
And of course objects in our solar system, which can be in front of something else. The moon can block a lot, and so does the sun. Other objects in the solar system are a much smaller part of our sky.

>> I have a gut feeling you're much more likely to bump into a rock or get sucked into a black hole if you're going to travel in a random direction.
Black holes are smaller than stars with the same mass, and have the same gravitational pull at the same distance. So they are less likely to get hit.
And rocks... only a really small fraction of mass which is not in some clouds consists of rocks. So small that the lower depth of them does not help, the stars remain bigger objects.
If you look for smaller stuff - dust particles or even single molecules, you get a much higher density. However, the particles smaller than the wavelength of visible light do not really "block" this light like large objects do.

Tass
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### Re: Opacity of Space?

Also note the darkness of the night sky. That means that all stars we see in all galaxies combined take up much less of the sky than the suns disc (except for the aforementioned dust, which does play a role, but not a huge one).