YJL

Stumbled on an interesting Gist about a fact

If you could fold a piece of paper in half 50 times, its thickness will be 3/4 the distance from the Earth to the Sun (71 million miles¹).

I forked the Gist and simplified it:

How many folds? 50
 1 folds, thickness = 2.000000E-04 m = 0.000000 AU
 2 folds, thickness = 4.000000E-04 m = 0.000000 AU
 3 folds, thickness = 8.000000E-04 m = 0.000000 AU
[snip]
46 folds, thickness = 7.036874E+09 m = 0.047039 AU
47 folds, thickness = 1.407375E+10 m = 0.094077 AU
48 folds, thickness = 2.814750E+10 m = 0.188154 AU
49 folds, thickness = 5.629500E+10 m = 0.376309 AU
50 folds, thickness = 1.125900E+11 m = 0.752618 AU

But I am not sure if you can fold a paper even you did get a huge piece of paper. First of all, 3/4 to our Sun, the closet planet, Mercury is about 0.4 AU from the Sun. That means the paper will burn since Mercury could be heated up to 427°C. I do not know much about astronomy, but I am pretty sure that folded paper will burn to ashes. Wait, if lack of oxygen, will it still burn?

If I can fold this special piece of paper without compressing, stretching, then I’d imagine that it would be like a half mood, onion-like shape to have minimal amount of paper.

So, the volume will be $\frac{\pi r^2}{2}h$. The paper has a very long length for folding, thickness (or diameter of the disc) is $2r$, and $h$ is the last side, height of this half-disc.

Say $h$ is also 0.1 mm as the thickness of a sheet of paper, and if 5g for a sheet of A4, then the mass of this half moon shape would be 3.963E20 kg. If it’s 10 cm, then it’s even heavier than Mercury, whose mass is 3.302E23 kg.

Anyway, it would be a very skinny half-disc looking space object and I am just too bored.

[1]	I beileve it actually means AU (Astronomical unit), that is 92,955,807.3 miles, not 71 million miles, or it won’t be 3/4.