The Question

As I was watching videos on my YouTube account, this SciShow video was among the recommendations. Now, I love reading the comments as much as watching the video itself; there is usually a comment that simply makes me roll over laughing. Every so often though, something golden comes up, like the following question which has become one of the top comments.

If Pinocchio's nose is 1 inch long, how many lies does Pinocchio need to tell to get into near earth orbit, remembering that at some point Pinocchio will fall over because his nose is too long?

The Short Answers

First, we need to assume the diameter of Pinocchio's nose, otherwise the calculations can have many different answers. So to make things easier, we will set the diameter to 0.50 inches (1.27 cm). Another assumption we will make is that Earth's gravitational field strength is uniform for the distances covered. A short calculation will reveal that this assumption is a very good approximation, since the value of g at 160 km above the earth is 95% of that on the surface.

There are many possible answers, depending on how Pinocchio is positioned. If he was lying down with his nose pointing up, then one of the following would occur.

It would take around 6.5 million lies for his nose to get to low earth orbit, assuming the nose is massless.

If the mass of the nose changes with length, his face gets crushed after ___ lies.

If Pinocchio was standing up with his nose level to the ground, either of the following may happen

About 56 million lies are required to get to low earth orbit. This assumes the nose is massless.

If the mass of the nose changes with length, he falls over somewhere between 700 and 800 lies. As he continues to lie, his nose will keep growing until it surrounds the earth, hugging the ground.

These are all the simple answers possible, and we'll look at why on the next page.

The Long Answers

For the simplest possible answer, we will ignore everything else and just look at the length of the nose needed to reach low Earth orbit, which sits at 160 km (100 miles). If Pinocchio lies down, his nose only needs to travel 160 km to get to low earth orbit.

image of nose going vertically out of atmosphere

Since an inch is defined to be 2.54 cm in length, we convert it and use the value to find the number of lies needed.

The situation is slightly different when Pinocchio's nose is horizontal to the ground. In this case, his nose has to travel 1434 km, since it has to go through a thicker later of atmosphere, as shown below.

image

Calculating the number of lies is pretty straightforward though.

For the other questions, let's assume that Pinocchio is still a marionette made of wood. Most types of wood have a density ofÂ 700 kilograms per cubic metre, which is about half that of flesh. We can assume that Pinocchio has the same mass as an 8-year-old boy who has twice his volume. Since an average 8-year-old would have a mass of 30 kg, Pinocchio should have the same mass. Furthermore, Pinocchio's nose should be 300 g in mass and 3.0 cm in length.

This

asd