Dropping a dime on the Moon

Bad Astronomy
The entire universe in blog form
May 5 2012 10:59 AM

Dropping a dime on the Moon

So, tonight is the so-called Supermoon, when the Moon happens to be full at the same time it's at perigee, the point in its orbit closest to the Earth. This makes it somewhat larger and brighter than normal, and that's getting a lot of attention in the press. I pointed out a few days ago that in reality, you almost certainly won't notice the difference between this full Moon and any other, mostly because the difference is small, and our eyes and brain are terrible at judging things like that without something to directly compare it to.

I was thinking about this last night as I watched the almost-full Moon rise in the east (which, I'll add, ironically looked huge due to the Moon Illusion!), and thought of something that might help illustrate this last point.

Phil Plait Phil Plait

Phil Plait writes Slate’s Bad Astronomy blog and is an astronomer, public speaker, science evangelizer, and author of Death From the Skies!  

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Monetary eclipse

Imagine you go outside tonight to look at the full Supermoon rising in the east. Imagine also you're holding a US dime in your hand (if you live in another country, feel free to substitute your local currency, but beware of the math; hang on a minute to see).

Let me ask you this: How far away would you have to hold the dime so that it appears as big as the Moon to you?

A few inches? A foot? (Convert to metric if you wish). Go ahead, guess!

... OK, ready? [Answer is below the fold so as not to spoil it.]

Here's the answer: 6 feet. That's right: unless you're 12 feet tall, you literally cannot hold a dime in your hand far enough away to be as small as the Moon in the sky!



Here comes the math

The math isn't that hard.

The size an object appears to your eye depends on how big the object is and how far away it is. This is pretty intuitive, right? If you have two objects that are the same size, the closer one will look bigger. If you have two objects at the same distance, the bigger one will look bigger. Duh.

Stretch your memory way back to grade school math, and the rule of proportions. We want to know how far away you need to hold a dime so it looks as big as the Moon. The size of the dime divided by that distance will be equal to the physical size of the Moon divided by its distance:

diameter(dime) / distance (dime) = diameter(Moon) / distance(Moon)


I can rearrange that to solve for the dime's distance to get:

distance (dime) = diameter(dime) / ( diameter(Moon) / distance(Moon) )


OK, plug and chug! The Moon is about 3475 kilometers across (yeah, I'm using metric now. Sue me). Tonight, it'll be 356,953 km away. A dime is 17.91 mm across. So...

distance (dime) = 17.91 mm / (3475 km / 356,953 km) = 1840 mm


1840 mm is almost exactly 6 feet! So to get a dime to look as big as the Moon in the sky, it has to be six feet (1.8 meters) away from your eye. [If you live in another country, simply substitute whatever coin you like, and swap out the numbers.]

I bet that's a lot farther than you guessed. So even tonight, when the Moon is as close as it gets to the Earth, it's still smaller than you think. Like I said, our brains are actually pretty bad at judging things like this. [Bonus challenge for math/astronomy geeks: how much bigger than the Moon does a dime look at arm's length? I can hold a dime about 50 cm away from my eye, so to me it's about 3.5 times bigger. Check my math!]


Cool, huh?



Super viewing

Having said all this, let me be clear: observing the Moon is awesome! In my "Supermoon" article earlier in the week I'm getting some feedback from folks who think I'm being a jerk about this and discouraging people from going out and looking at the Moon. Maybe I am being a jerk; that's your call. But I would NEVER tell people not to go out and look! I love watching the Moon, whether it's a fingernail-thin crescent setting in the west, or a fat silvery disk swimming through the haze as it struggles upwards in the east.

Our Moon is gorgeous. And if this Supermoon stuff gets people outside looking up, then great! But don't let the hype fool you, and certainly don't let it this be a flash in the pan. If you do go out to look at the Moon tonight, don't stop when the weekend's over. Over the next few days or so, if you get up early, you'll see the waning Moon setting in the west around sunrise, which is always lovely. And then, in two weeks, the cycle starts again with the new Moon... and even better, there is a solar eclipse on May 20th that'll be visible for a lot of the planet. I'll have more info on that in a few days as well.

Observing the Moon is easy. You don't even need fancy-schmancy equipment to do it; your own eyes will do. But through binoculars or even a small telescope it's an amazing sight. So please do go out and take a look, and make sure you always take the chance to gaze at the sky. There's a lot up there to see, and it's always surprising, delightful, and awe-inspiring.

Moonrise image from Jorge-11's Flickr photostream.



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