Getting the supermoon out of proportion

I’ve enjoyed looking at the many news-website photo galleries of last week’s ‘supermoon’. Many of the shots purport to show how unusually large the moon looked last Saturday night, and some are quite remarkable. Here’s a photo shown prominently on Gizmodo, under the headline ‘The Supermoon really was super huge!’:

Gizmodo supermoon

That does indeed look impressive, but the commenters quickly realised there was a problem, because they knew the size difference was overhyped. The ‘supermoon’ was a rare-ish conjunction of a full moon and the moon’s closest approach to the earth. The latter happens every three years, and the conjunction about every 20. The moon was 2% closer, its gravity 3% stronger, and the spring tides here on earth were 5% higher than usual as a result. NASA reckon the moon appears 14% bigger at its closest position than at its furthest, but most of the time the moon is somewhere inbetween, and the differences aren’t noticeable. Yet the above shot definitely shows a huge moon hovering by the Lincoln Memorial, so what’s happening?

There are a couple of things going on here. First of all, when you’re physically outside and looking into the sky, the apparent size of the moon is way more affected by its position than its distance. For reasons not entirely understood, the moon appears far larger when nearer the horizon. This is the moon illusion, and is illusory because there’s no actual difference – if you hold up a ruler, or take a series of photos, it’s obvious the size never changes (in fact the moon is 1.5% smaller nearer the horizon, but that’s too small to notice anyway). Many Gizmodo commenters concluded that the photos were showing this illusion. But this can’t be correct, as the moon illusion doesn’t work in photos1. At one point someone suggests that the moon will always look big if you point a telephoto lens at it, and they were immediately shot down – after all, there’s the Lincoln memorial for comparison, isn’t there? But I’m pretty sure this person was correct and the naysayers were wrong.

It is a telephoto lens. It took me a little while to get the optics straight in my head, but the size of the building makes no difference. If the moon’s as tall as the building, it just means the photo was taken from further back. Writing this out now, it all seems obvious and I’m worried the following will seem patronising. But both I and some commenters were clearly confused for a while, so I figure it’s worth explaining.

Imagine you’re standing on a flat plain. The moon is always the same size in the sky, no matter where it is (ignoring the effects of the moon illusion). Now imagine there’s a single, distant tree on the horizon. If the moon sets behind it, the moon is going to appear substantially bigger than the tree, simply because the tree is far away. If you were to use a telephoto lens to zoom in until the moon filled your photo, the moon and the tree would both get proportionally bigger as you zoomed, and the moon would look much larger than the tree. But as you walk closer to the tree, the size of the moon will stay the same while the tree gets bigger. Eventually you’ll obviously be standing next to a tree which seems far, far bigger than the moon.

So it’s the same with the Lincoln Memorial photo. It’s been taken from far enough away that the memorial appears small in relation to the moon, but zoomed in enough that you can only see the two objects. If you’d taken a photo with a regular lens, you’d see far more of the city and the moon would look its normal size. If you’d walked closer, the Memorial would have quickly dwarfed the moon.

Most supermoon galleries are full of photos using this same trick. Probably because the newsdesk photo editors had to show something. Which I don’t mind at all – anything that makes people look at the moon more closely is fine with me.

  1. Phil Plait suggests the Ponzo illusion might contribute, but I’m skeptical in general, and I don’t think there’s enough depth in these photos for it to kick in anyway []