I remember a discussion a while back where Grant Hutchison (and Selden?) was pointing out that the closer you get to a nebula, the dimmer it actually gets because of the same amount of light coming from a larger area of sky.
Can someone explain that in a bit more detail, and also describe how to figure out at what point a nebula (let's say it's 10 ly across) would become invisible?
How far would you need to be from a Nebula to see it?
How far would you need to be from a Nebula to see it?
My Celestia page: Spica system, planetary magnitudes script, updated demo.cel, Quad system
Grant's explanation is in this thread:
http://www.celestiaproject.net/forum/viewtopic.php?p=43381
it depends on whether the nebula is optically thick (you can't see through it) or optically thin (you can see through it to the empty space beyond).
An optically thick nebula stays the same brightness (the same number of photons reach you per square steradian of nebula) no matter how much of the sky it covers. As you get closer, the atoms in the front region are spread farther apart on the sky, but there are always more glowing atoms being revealed between them.
An optically thin nebula gets dimmer as you get closer, because, again, the same number of emmitting atoms spread out over a larger area of sky, but this time you see the blackness of space in between them, not more glowing atoms.
So the answer to your question isn't a fixed value. It's a function of the nebula's density, among other things.
I'm lousy at 3D trig, so I won't try to write down the formula. The luminosity should be inversely proportional to the angular area of sky that the nebula covers, though. That should be 1/ a tangent function, I think.
http://www.celestiaproject.net/forum/viewtopic.php?p=43381
it depends on whether the nebula is optically thick (you can't see through it) or optically thin (you can see through it to the empty space beyond).
An optically thick nebula stays the same brightness (the same number of photons reach you per square steradian of nebula) no matter how much of the sky it covers. As you get closer, the atoms in the front region are spread farther apart on the sky, but there are always more glowing atoms being revealed between them.
An optically thin nebula gets dimmer as you get closer, because, again, the same number of emmitting atoms spread out over a larger area of sky, but this time you see the blackness of space in between them, not more glowing atoms.
So the answer to your question isn't a fixed value. It's a function of the nebula's density, among other things.
I'm lousy at 3D trig, so I won't try to write down the formula. The luminosity should be inversely proportional to the angular area of sky that the nebula covers, though. That should be 1/ a tangent function, I think.
Selden
Thanks Selden 
My Celestia page: Spica system, planetary magnitudes script, updated demo.cel, Quad system