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I'd be interested to know how far from the sun you'd have to be for it to feel 100% dark, as the human eye sees it.

But also, are there places in space so far removed that there is nothing visible there even if you had very fine measuring instruments. I guess I'm asking if there are places in space where there is nothing at all.

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The answer to the second question is a qualified no (unless you find a really dark and opaque cloud or box to hide in). The reason is that the largest voids in the cosmic web are a few hundred megaparsec wide. That means that you will see light from galaxies on the outside since there has been enough time for it to reach you there.

The apparent magnitude of the milky way seen at 300 megaparsec is $−20.8 + 5\log_{10}(300\cdot 10^6)-5=16.59$. Now this is too faint to see with the naked eye or binoculars (even when ignoring redshift). But if you have a telescope this should be visible.

The first question is tricky since as you move away from the sun will see a lot of stars. The point where it gets naked eye dark will presumably be where the milky way reaches the limit $M_{lim}\approx 7$ magnitude, which would be 3.7 Mpc (just invert the above formula: $d=10^{(M_{MW}+M_{lim}+5)/5}$). At that point you are somewhere just outside the Local Cluster, and there will be other galaxies present. So I think the nearest really naked eye dark point is in the Local Void.

Here is a crude sketch, using the Karentchev catalog of nearby galaxies, assuming each is as bright as the Milky Way and plotting an isosurface where there is no galaxy with more apparent magnitude than 7. Red regions are dark places. The closest dark point is 4.6 Mpc away from us. Estimate of dark regions among nearby galaxies.

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In order to receive randomly a single photon from the sun at a time you would have to place the sun ~1000 light years away from you.

The universe is relatively homogeneous and isotropic. No matter where you go in our observable universe you will have about the same quantity of light from the stars. There are places that are more devoid of matter, but light can travel with almost no dissipation to these places too.

If you want no light it is better to hide in a bunker, but you would have thermal radiation from the walls. But even if you have no visible light somewhere in outer space, you'll still have blackbody radiation from the cosmic microwave background (microwave radiation) from the Big Bang that you cannot escape because it fills the universe.

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