The question follows from xkcd cartoon "Depth Perception (941)". I've isolated the frames that describe the concept here.
In words, one could theoretically point two cameras at the sky, and displace them so that, if viewed as components of a projected 3D image, the starfield of the night sky would have a perceivable depth. That is, Sirius or Alpha Centauri would appear closer than, say, Betelgeuse.
The idea sounds interesting, but I was wondering whether it's actually possible. That is, how large would the displacement of the cameras need to be to create a perceivable depth? To quantify, let's say we're trying to reduce the scale from 5 light-years to 100 m. Would this require a displacement of 5 light-years / 100 m$\times$(separation of eyes)$\approx1/400$ light-years $\approx136$ AU or is it more complicated than that?
I guess the maximum we could achieve is by taking two images of the same field of stars, one year apart and combining them, to give a separation of the "eyes" of about 2 AU. I don't know enough astrometry myself to be sure.
Best Answer
Parallax is linearly proportional to separation, so to get meaningful depth perception to even one star, your eyes would have to be (present eye separation)*(distance to Proxima Centauri)/(longest distance at which we naturally have meaningful depth perception). Having been to Meteor Crater, I can tell you that the last quantity is definitely under a half mile, i.e. distance from rim to center, but for a conservative estimate we'll call it that.
Our formula, then, is sep=3 inches * 4.2 l-yr / 2640 feet = .0004 l-yr = 25 au. That is past Uranus, almost to Neptune.