The terrible physics of Julia Donaldson

Julia Donaldson writes some excellent childrens books, but sadly vital plot points rely on a strange alternative world with entirely different physics to our own.

Gruffalos Child

At the end of the story the mouse jumps on a branch and the moon rises to cast a massive shadow of 'The Big Bad Mouse' which scares the Gruffalo's child away.

Anyone who's looked at a shadow outside at night cast by the moon knows that they're pretty much the same size as you, with a bit of elongation based on how low in the sky the moon is. You definitely don't get a massive projection which is the key plot point because the moon is far away.

To demonstrate, I took some mouse photos with a light source both near and far (albeit a lot closer than the moon!).

Light source close to the mouse gives a big shadow Light source far from the mouse (like the moon)

In reality the moon is a lot further away than my light source, if the branch is 1m up the moon is around 250 million times further away from the branch than the branch is from the ground. The shadow would be exactly the same size as the mouse.

Troll

At the end of the book Troll, the troll empties out the treasure chest of gold and gets in it to try and trap a goat. The pirates discover the chest and take it back to their ship. Obviously they would notice, trolls weigh a lot less than gold because gold is very heavy. But Peg Polkadot says..

The chest was heavy, it must be full of gold.

This is rubbish. You can fill a chest with gold pieces whereas it's rather hard to do that with bipeds, and gold is a lot more dense than flesh.

To give an idea, I have a 47L Really Useful Box and a 17kg stunt troll called Ben that doesn't quite fit in the box.

How heavy is 47L of gold coins? If you stack gold coins next to each oether you can get one gold coin of radius 1cm (area 3.14cm^2) in a 2cm by 2cm square (area 4cm^2). So that's a packing density of roughly 3.14/4 = 0.78, so we've roughly 36.9L of gold. How heavy is 37L of gold? Gold has a density of 19.3kg per L, so this is 712kg of gold, 41x heavier than my stunt troll.

As a picture, this is the difference in weight between a chest with a troll and a chest full of gold.

Weight of chest with troll inside. Weight of chest with gold inside