Dropping a dime on the Moon

By Phil Plait | May 5, 2012 10:59 am

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.


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!]

A video that came out a little while back hammers this home as well:

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.


Related Posts:

Supermoon Supercomic
The Supermoon stuff? AGAIN?
Why does the Moon look so huge on the horizon?
In which I disagree with cartoon Neil Tyson

Comments (34)

  1. Druhim

    You’re not being a jerk at all. Some people just hate being shown their assumptions are wrong, so to deal with the cognitive dissonance some have to make you the bad guy and turn your education into something mean spirited or elitist.

  2. Michael Ben Silva

    Hey Phil! How long would your arms have to be to make the dime appear the same size as the moon at its apogee? Could that comparison help us understand the moon’s change in perceived size? Thanks!

  3. Wzrd1

    I’ll be out and looking at the moon tonight. As I did last night. As I did a month ago. As I did a year ago.
    I go outside to have a smoke, when I do, I look up. Where one SHOULD look when outside at night and not navigating. :)

    Phil, there is another math to consider, regarding holding that dime at a distance. The aging eyes math, where one’s arms are NEVER long enough to read the thing. ;)

  4. Bryan

    First of all, correct me if I’m wrong but the moon has been near perigee for a few days now, so is it not going to look about the same size it has for a while?

    And aslo, don’t you love how all these news stories about the “super moon” include photos that are clearly cropped or long-lens shots to make it appear huge?

  5. MacRat

    The way the press is hyping the super moon, you would think it is about to crash into the earth.

  6. Wzrd1

    Our local press hyped it as an exceptionally rare event that “won’t be seen for another two years”.
    Now, if I were a mayfly, I’d pay close attention to it. As I saw the supermoon last year, saw this one and expect to live longer than two years longer…
    But, hype and sex sells. As the supermoon cannot fill a sexual title to titillate the juvenile mind, they have to stick with hype.

  7. Zack

    Ah, but the most important question is: how will this affect werewolves? :P

    I do in fact intend to take a look at the ‘Supermoon’, Phil, but only as much as I try to take a look at the full moon whenever I get a chance.

  8. antiavenger

    @Michael Ben Silva: The math is actually doable by you since he showed how to do it! If you want the apogee distance this little link should help: http://www.fourmilab.ch/earthview/pacalc.html

    Thankfully, I haven’t heard much about this locally… but my twitter is getting some weird mentions of it that I’m calling somewhat of a BS on. At least it’s a good excuse to get people outside to watch the skies.

  9. fedra

    All of these great expectations are plaguing astronomical observatories… People just write to us, going like “Why the hell haven’t you organized a Moon-observing night if this phenomenon is so huge and rare? I thought you were scientifically educated people, but I guess I was wrong”. I try to make them understand the true story, also explaining that a full Moon is not exactly an exciting Moon phase to observe through a telescope, but… Who am I to state my case against what was said on TV? Cheers from Italy.

  10. Pete Jackson

    I looked at the nearly full moon last night, and, while it didn’t necessarily look bigger than usual, I could definitely see more details of the Maria than I normally do. I did an experiment looking at a globe of the Earth from across the room, and then moving 1/7 of the distance closer, and you really do pick up significantly more detail!

    So try tonight to see if you can see more of the ‘Man in the Moon’ than you have seen before.

  11. Other Paul

    Since the moon’s closer – and therefore brighter – than usual, maybe it’s best to look at it only through smoked glass. Or – even better – projected onto a white card. Just to be on the safe side y’understand. No need to go overboard.

    ->cough<-

    In the UK, a 5p piece is 18mm and you'd need to hold it 1849 mm away to cover the 356953km distant moon. To cover the averagely remote and apparently smaller moon, at 385000km, you'd need to stretch your rubber arm another 145mm – that's a little over six extra inches to just over six and a half feet.

  12. Alex

    Where was that video shot? The face to camera segments look a lot like Centennial Park in Sydney, but I don’t recognise the segments on the path with others asking about their estimated distance scale for the basketball and tennis ball.

  13. Lusus Naturae

    Like the man said, any reason to go look at the moon is a good one. Unfortunately, I CAN’T because I live in the Pacific Northwest, and it’s sterotypically overcast right now. Maybe I’ll luck out later in the night.

  14. Messier Tidy Upper

    @9. fedra :

    All of these great expectations are plaguing astronomical observatories… People just write to us, going like “Why the hell haven’t you organized a Moon-observing night if this phenomenon is so huge and rare? I thought you were scientifically educated people, but I guess I was wrong”. I try to make them understand the true story, also explaining that a full Moon is not exactly an exciting Moon phase to observe through a telescope, but… Who am I to state my case against what was said on TV? Cheers from Italy.

    Guess you’ve tried explaining to them that the Full Moon is actually often the bane of astronomers because it’s brilliant light washes out the fainter stars and deep sky objects and actually makes it more difficult to see the “faint fuzzies” a lot of astronomers really prize? That the best nights for doing astronomy (well many forms of astronomy anyhow – not specifically Lunar astronomy natch!) are the darkest New Moon nights instead?

    Also that a Moon filter is needed / helpful to reduce the lunar glare?

  15. Infinite123Lifer

    I really enjoyed everything about this article, especially the “Here comes the math” portion. Since I am not required to calculate much anymore and was never great to begin with I enjoy the simple reminders and the ‘calculate a long at home’ fun, I found it very relevant, doable and interesting.

    You’ve been sharing your passion for the skies and encouraging folks of all walks of Life to look up for more than a decade and probably longer and I am guessing its been a Life’s constant for you to share your experiences and to inspire skygazing. It is more absurd than even ignorant to suggest that you’ve done anything but. I personally have NEVER felt discouraged to explore here at BA, quite the contrary in point of fact.

    Much appreciated Dr. Plait.

  16. @Lusus — I feel your pain. You, Al Boyle, and I share the same affliction: the ubiquitous and confounding Pacific Northwest cloud bank. I’ve become used to setting the alarm for meteor showers or other celestial events, taking a peek at the clouds, and going right back to sleep. It is frustrating as all hell. I have two telescopes that have just been standing indoors on their tripods for so long, they’re starting to tap their feet. I think earlier this week I actually heard one of them humming the Final Jeopardy music over and over and over…. I keep telling myself it could be worse; I could be in Los Angeles.

  17. Walt Donovan

    I dragged my wife outside and actually did the experiment using a flashlight, a quarter (24mm diameter) and a stiff tape measure. We shined the flashlight on the quarter so we could see it, held it on its edge, and moved it visually adjacent to the moon until the two diameters appeared to match. Both distance measurements (eye to quarter, my wife and me viewing) came out to about 6.5 feet, which seems fairly far away from the theoretical 9 feet. Note that the moon had just peeked over the trees, so was about oh 30 degrees above the horizon (local time 10:15 PM, California, U.S.)

    I’d be interested to see what other people actually measure.

  18. Wzrd1

    @Warren, I feel your pain. In the Philadelphia area, it’s socked in, like when REAL astronomic events occur.
    But, if I had two telescopes that want a good view, I’d build a temperature controlled enclosure for them and set the automation to good use. Of course, I’d also have the automation to control them.
    And if I ever hit the big bucks in the lottery (which would REALLY be something, as I don’t play the thing), said telescopes would be on a high mountain peak. ;)
    As for worse places than LA, I CAN think of a few, but they’re underground and observing neutrinos… ;)

  19. Kevin N

    I had a girl today tell me that the supermoon was “like four times bigger than normal,” which I think is definitely worth going outside for.

    A rule of thumb (ha ha) is that the width of the pinkie finger subtends 1 degree when held at arm’s length. You wouldn’t think it, but its width could cover two full moons, as the moon subtends only half a degree.

  20. Regarding the “jerk” aspect, this is what I posted on Facebook (along with a link to your earlier supermoon article):

    Last night’s moon was absolutely beautiful. I am glad so many people looked up and appreciated it. You should do the same every time there is a full moon and the sky is as clear as it was last night — because *it looks exactly the same*. Yes, the moon really is that awesome, even the normal non-super variety! Don’t wait for a misleading news story to tell you to look at it. Look at it every chance you get.

    (It was a particularly clear night last night in my city, very very beautiful for moongazing)

  21. Phil, no, you are not being a jerk then or now. This “supermoon” stuff has been bugging the crap out of me for the last week. I’ve seen it on “news” sites… hell, I’ve even seen it on sites that are just astronomy. The aggravating thing is that friends and family know that amateur astronomy is a hobby of mine. I’ve shown a bunch of them marvels with my puny 114mm scope, so they try to keep me “informed” about stuff like this. As I told my beautiful Irish other half though… we really won’t be able to see an significant difference since the distance is so large. It would take a much larger difference in scale for us to pick it up with just the naked eye.

    As an aside, I prefer to see my astronomy in pictures on the Interweebs! for the sole reason that I can take the time to study what i’m seeing. When I go huntin with my 114mm reflector, I prefer targets like the moon or the planets. I literally can stay up all night looking at our neighbors. of big interest are Luna, Mars, Jupiter, and Saturn, although any others are gonna catch my eye if they are up. Sue me if our own neighborhood is of bigger interest to me than stuff far away… ;-)

  22. Ironically, I went through this math at my kids’ Elementary School (where I volunteer) on Friday when I brought my “big dog” lens in and talked about how one can use math for photography as I was trying to get a picture with a foreground object about the same relative size as the Moon.

    Being an engineer (not an Astrophysicist), we like ballpark solutions (as one does not need to be exact here) and the ratio is actually pretty close to 100-1 … which you might have mentioned Phil is pretty close to what the Sun’s distance/diameter is … and what effect that has on Solar Eclipses! ;-)

    Here’s what that Full Moon looked like from the Republic of Boulder using a Canon 7D with a 500m lens and 1.4x tele-extender … i.e. 1,120mm effective reach.

    http://www.komar.org/sound-of-freedom/rocky-mountain-airport-airshow/#fullmoon

  23. Pete Jackson

    I had another thought about how you can see more detail with the naked eye on the perigee Moon than on the apogee Moon. In the early days of TV, the gold standard was a 21-inch television, on which you could definitely see things better than on an 18-inch television. Nowadays, it would be like a 40-inch TV against a 35-inch TV.

  24. Malcolm

    SUPERMOON – making Lycans more powerful than a speeding locomotive and able to leap tall buildings with a single bound. They are pretty rare so let’s not do the bullet thing, okay.

  25. Eric

    As an additional factoid, if you were on the moon Sat night, you’d have to hold a dime 501mm (just over 19″) from your eye to eclipse the earth.

  26. It’s interesting how the “moon illusion” is lost when you take a photo. One evening I was at a theme park in Orlando. I had brought a tripod and SLR camera to get pictures of the park at night. The full moon over one of the attractions looked incredible. So, I set up the tripod and took several photos. When I got them back, I was disappointed at how small the moon appeared. Of course, a visit to nasa.gov to find a high-res image of the moon and a few minutes using Photoshop fixed the photos!

  27. Nigel Depledge

    Pete JAckson (10) said:

    I looked at the nearly full moon last night, and, while it didn’t necessarily look bigger than usual, I could definitely see more details of the Maria than I normally do. I did an experiment looking at a globe of the Earth from across the room, and then moving 1/7 of the distance closer, and you really do pick up significantly more detail!

    So try tonight to see if you can see more of the ‘Man in the Moon’ than you have seen before.

    OK, that’s a comparison between the perigean full moon and the apogean full moon.

    But last month’s full moon, being reasonably close to perigee, was only about 1% farther away than the “supermoon”. So the “supermoon” will look pretty much no different from last month’s full moon.

  28. Nigel Depledge

    Alek (23) said:

    . . . using a Canon 7D with a 500m lens . . .

    Whoa! That’s a monster lens.

    Oh.

    You meant mm.

    ;-)

  29. Nigel Depledge

    Alek (23) said:

    a 500m lens and 1.4x tele-extender … i.e. 1,120mm effective reach.

    Surely that makes a 700 mm equivalent, isn’t it?

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