Why does the sun have to be a lot further from us than the moon? A deduction.

Remember the hands-on demo of the phase of the moon?

Mondphase
In both pictures: Model of the moon between my fingers on the left, and moon in the background on the right. See how the lit and dark sides of both spheres are in the same position?

Holding a sphere up in the sunlight in the direction of the moon, the sphere will show the same phase as does the moon. Of course it has to, because the sun is so far away that its rays hitting the moon and the ones hitting the sphere are pretty much parallel.

If the sun wasn’t so far away, what would we see?

Schematic of how the Earth, your little sphere you are holding up in the direction of the moon (marked X) and the Moon would be lit if the Sun was not very far away (left) and very far away from Earth and Moon. See how the phase of the moon differs from that of your little sphere when the sun is “close”?

So the only way we can explain that the lit and dark sides of the sphere and the moon are the same is that the light lighting both of them comes in parallel, which can only be the case of the sun is very very very far away compared to the distance of earth, sphere and moon.

Isn’t that a nice little thought experiment?

Phase of the moon

Relating the phases of the moon to one side of the moon being lit by the sun and the other side being in the dark sometimes appears a bit unintuitive. One thing that books and “the internet” always recommend is holding up a sphere in the direction of the moon and pointing out how the same side of the sphere and the moon are lit.

I’ve tried this before using apples or other fruit that I had on me when I happened to see the moon in the sky, but it is not really satisfying. Fruit in the sun always look like fruit in the sun, plus it is really hard to photograph (or can you spot the moon above the nectarine in the picture below?).

IMG_1911
See the tiny moon right above the nectarine and how its light and dark sides are the same as those of the nectarine?

So I was really happy when I managed to take the pictures below:

Mondphase
In both pictures: Model of the moon between my fingers on the left, and moon in the background on the right. See how the lit and dark sides of both spheres are in the same position?

This is the first time I felt like it actually worked for me.