Tag Archives: parallax


An idea coming from the below xkcd, Depth Perception, and a few working examples[1,2], I wondered what it would take to get the parallax to look at the Moon or even the Sun in 3D as if they were the size of a bungalow as seen from the sidewalk.

xkcd 941, Depth Perception

Let’s take this bungalow to be about 5 m tall ($d_2$), 40 ft from the sidewalk, and the space between our eyes to be 7 cm ($d_1$). That’s right, I can mix units haphazardly. The angle to a point 40 ft away will differ by a small amount as viewed from each eye — I’ll call this difference $beta_0$. It looks familiar, and probably has a standard name and definition in optics.

beta_0 = dfrac{d_2-d_1} {d_2+d_1}
= dfrac{5 m – 7 cm}{5 m + 7 cm}
approx 0.972386588

The relation between object size and image size becomes this:

d_1 = d_2 dfrac{1-beta_0}{1+beta_0}
approx d_2 times 0.014

The Moon would require images 48 km apart; the Sun, 19’488 km (3x radius of Earth) apart. The Earth orbits the Sun at about 30 km/s, so those 19’488 km would conveniently go by in under 11 minutes. If there weren’t any clouds, you could have a setup that films the Sun and displays two output streams: one delayed 11 minutes behind the other. Any surface details that had changed during that time would be lost or at least blurry. As for the Moon, it would take a bit of planning with a friend that lives 50 km away and similar cameras with identical settings.

Something tells me that this only works for objects far away, as that distance isn’t in the calculations.

What’s that? I’m supposed to be doing homework? Oops.