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How functionaly dense are nebulae? Are they so sparse they are only visible from an interstellar or intergalactic perspective or would you be unable to see your hand in one?

Do they vary widely in density, between nebulae or even within a single one?

What would it look like from the inside of one?

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They are very sparse. Typical densities are in the range of 100 to 10,000 particles per $\textrm{cm}^3$.

This is much more dense than the general interstellar medium (1 particle per $\textrm{cm}^3$), but much, much less dense than anything you are used to - air is around $10^{19}$ particles per $\textrm{cm}^3$. You would very easily see your own hand in a nebula.

Density variations can be quite sharp within the nebula; in star-forming regions, the variations are strong and the density variations appear to be organized like a fractal, produced by turbulence within the cloud.

However, most nebulae are basically the same, and there aren't huge differences between the densities of different starforming regions. Planetary nebulae and supernova remnants, of course, can have very different densities depending on their ages, since they are expanding balls of gas rather than broad molecular clouds loosely bound by gravity.

If you were within a nebula, it is hard to say what it would look like. But nebulae are so large that the optical depth of the cloud would actually probably be quite high, and I would guess that it would look like you were surrounded by glowing green and red gas in the far distance - instead of space looking black and dark, it would be colored all over. But this would only be an effect caused by the fact that you are looking through so much gas - even if your spaceship were a thousand kilometers away, it probably wouldn't look much different if you were inside a nebula versus outside of it.

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3… says that the mean free path in a nebula is about 5800 km. The mean free path is the distance at which things start to get "lost in the fog." – Andrew Jul 4 '11 at 21:25
5800km as the mean free path for what? Depending on whether its for gas particles, photons of a particular wavelength (absorption line?) or visible photons as a whole wound make a pretty big difference to visibility. – Kyle Oman Jan 24 '13 at 16:41

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