Why Do The Sun And The Moon Look The Same Size?

This question was inspired by this post on the Oatmeal blog (look about 3/4 of the way down in the black ‘for example’ box), and referred to me by Colin.

This question could be interpreted in two ways (that I can think of) and, being a generally helpful and amiable chap* I’m going to have a go at both. Firstly…

Why do the Sun and the Moon look the same size?
 

The Sun is about 1.392 x 10⁶ km in diameter, and is about 1.496 x 10⁸ km away from us.
The Moon is about about 3474 km in diameter, and 384,399 km away from us.
Using some gadgetry, we can measure the Sun’s angular diameter as seen from Earth as being between 31 and 33 arcminutes. The Moon’s angular diameter can be observed to be between 29 and 34 arcminutes.

Remember that angular diameter is a measure of how big things look as opposed to how big they actually are: the fact that the Moon’s and Sun’s angular diameters are so close means that they look pretty much the same size from where we’re standing. But why is this?

If we look at the info I provided at the beginning of this section regarding the Sun and Moon’s respective distances from Earth and diameters, we can work out (by appropriate use of division) that the Sun is almost exactly 400 times further away from us than the Moon is, and about 390 times bigger.

Here’s a practical demonstration for you to do: Grab a couple of tennis balls (or any object, as long as they’re about the same size) and go outside. Place one tennis ball ten steps away from you, and place the other one twenty steps away. The second one should look, from your vantage point, as if it’s half the size of the first one: if two identically sized objects are placed so that one is twice as far away from you as the other, it will appear to be half the size. If you placed the second ball ten times further away, it would appear to be a tenth of the size.

Now imagine (or actually find) two balls, one twice the size of the other. If you place the bigger ball twice as far away from you as the first, it will appear to have halved in size, and therefore will look, to you, exactly the same size as the first. If you could find a ball ten times bigger than the first, you’d have to place it ten times further away from you than the first ball in order to make them appear to be the same size.

This is exactly what’s happening with the Sun and Moon: being 400 times bigger but also 400 times further away means that the Sun looks almost exactly the same size as the Moon.

Is there a reason for this?

Humans seem to have brains that just cant accept that coincidences happen. This is great in some cases- it helps to fuel our sense of wonder, and to encourage us to further our own understanding of how the universe works. It is probably, without being too conceited, one of the main reasons why you’re reading this blog.

However, in this case it really is just a coincidence. A coincidence with beautiful consequences, but a coincidence nevertheless. Here on Earth is the only place in the solar system that total solar eclipses can be seen. Yes, other planets have moons and many of these moons are bound to block out the Sun from time to time, but most of them block out out completely while others just block out a small portion of it. Earth is the only vantage point from which we see such a perfect fit when our Moon passes between us and our Sun.

In fact, it hasn’t even always been that way here: the Moon is, and has been since its formation, moving away from the Earth. This means that in the distant past the Moon appeared bigger than it does now, and blocked the Sun entirely; in the future the Moon will appear smaller, and total eclipses will no longer be able to occur. I’ve already blogged about that, though, and you can read it here.

* At least I try to be. It doesn’t always work out that way.

Blogstronomy: answering YOUR space questions.

Read more at Blogstronomy