# Is the Moon Really One Quarter the Size of the Earth?

• 12/14/2016
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Are you ready for the supermoon on December 14? This will actually be the 3rd supermoon in 2016! With these big-looking full moons we're having this year, I got to wondering exactly how big is the moon compared to Earth? This seems like a good question to answer with some SAS graphs!...

But before we get started, here's a picture my friend David took of the a supermoon this year. The weather wasn't great, but he managed to get a pretty decent shot!

As with most things I'm curious about, I started my quest for knowledge with a Google search. I asked Google "How big is the moon compared to Earth?" Google found about 1.8 million results, and showed me the following summary at the top:

I have often heard that the moon is about 1/4 (25%) the size of the Earth, but I was a little distrusting of that number. For example, look at the picture in the Google summary - the moon doesn't look 25% the size of Earth, does it? As with many things, it depends...

The 25% number comes from comparing the diameters. The moon's diameter is indeed about 25% the size of Earth's diameter, which is easily shown in a simple bar chart:

But if you look at the earth and moon side-by-side (as in the image in the Google results above), does your brain compare the diameter, or does it compare the amount of area taken up in the image? Here's a visualization of the cross section area of the moon and Earth laid out on a gridded graph, so it is easy to visually compare them (each square area in the grid represents 1,000 x 1,000 = 1 million square miles).

The above graph is a nice visual comparison that people can relate to (since the circular shapes correspond to the moon and Earth), but let's make it even easier to compare the areas, by plotting the them in a bar chart. Here, you can see that the cross-sectional area of the moon is much less than 25% the size of the Earth.

And what about the volume of the spheres? As you've probably guessed by now, that's an even bigger difference!

So, when somebody asks how big the moon is compared to Earth, the answer is "It depends!"

If you're a data analyst, you might be thinking ... "Hmm, I wonder if this same issue might affect bubble chart visual perception? - Should I be sizing the bubbles based on the diameter, the area, or the volume of the bubbles?" (and yes, this is an important issue that many people creating bubble charts don't even think about). Feel free to leave a comment with your thoughts/preferences on bubble chart sizing!

This content was reposted from the SAS Learning Post. Go there to view the original.

#### Robert Allison, The Graph Guy!, SAS

Robert Allison has worked at SAS for more than 20 years and is perhaps the foremost expert in creating custom graphs using SAS/GRAPH. His educational background is in computer science, and he holds a BS, MS, and PhD from North Carolina State University. He is the author of several conference papers, has won a few graphic competitions, and has written a book calledSAS/GRAPH: Beyond the Basics.

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Re: Earth is the big cheese
• 12/27/2016 8:11:46 AM
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It's great that not only analytics is revolutionizing what humanity is discovering, it is also allowing people to participate in the analysis through open source platforms, programming, and communities.

Re: Earth is the big cheese
• 12/26/2016 5:03:54 PM
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..

Thinking about the relative size of the moon makes me think of how profoundly the analytics/big data revolution has been impacting astronomical research. Today the amount of data being gathered and analyzed about the universe is approximately doubling each year.

Here are a couple of articles about the subject – one fairly technical, the other oriented to more of a layperson audience ...

Astronomy in the Big Data Era

How Big Data Is Changing Astronomy (Again)

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Re: Earth is the big cheese
• 12/22/2016 4:16:51 PM
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It's always been funny to me to see journalists write stories about the super moons, which one would think occur very rarely, or the eclipses, or just about any astronomical event, which as it turns out aren't all that rare at all. At least if you define these events so superficially, or so generally that a super moon could be more common than we might expect, without a good definition of just what "super" means, or how the size is truely different than usual.

Re: Earth is the big cheese
• 12/20/2016 9:32:32 AM
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Whaddaya know ... Huffington Post UK has just posted an article this AM (Tuesday, Dec. 20th) on a major discovery about the Earth's molten core, involving its influence on the outer magnetic field. In fact it was changes in the magnetic field that led to the discovery of the core phenomena ...

Re: Earth is the big cheese
• 12/19/2016 9:53:04 PM
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T Sweeney asks "do you know if the difference in weight/mass has anything to do with the earth's molten core, which also circulates and is thought to be the source of our planet's magnetic field?"

Regarding the mass issue, I don't have a ready answer; I'd need to research this. Earth's core is about 30% molten iron, which is pretty dense, so maybe that's a factor in the higher density affecting the mass comparison.

Regarding the Earth's magnetic field, I understand that convection within the core, plus Earth's rotation, does play a significant role in generating this (it's called the geodynamo).

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Re: Earth is the big cheese
• 12/19/2016 9:16:17 PM
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One other question, Lyndon... do you know if the difference in weight/mass has anything to do with the earth's molten core, which also circulates and is thought to be the source of our planet's magnetic field? I'm no astrophsicist, but it makes sense to me that a body with a molten core would weigh more than one that doesn't.

Re: Earth is the big cheese
• 12/19/2016 9:13:18 PM
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You make an excellent point about volume, Lyndon. And in this instance, I can see where my own preference for visual data might keep me from grasping the bigger picture (as it were). In any case, this is a great representation about how one set of data doesn't tell the whole story.

Earth is the big cheese
• 12/19/2016 6:28:11 AM
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I dabble only cautiously in astronomical physics, but it seems to me the volume comparison has more validity than visual diameter or circumference.

However, mass is probably the metric that beats all three. In terms of mass, the moon has just 1.2% of the Earth's mass. Earth "weighs" 81 times more than the moon. A major reason is that the moon has just 60% of the Earth's density.

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