### From the Height of the Pacific to the Depths of Everest

Earth may not be flat, but it is smoother than a billiard ball. I’ll justify that sentence in a bit, but first, I want to tell you a story involving Kansas, my grandmother, topography, and the Mariana Trench.

My maternal grandmother died last summer. She deserves a full tribute from me at another time, but I have one great story to tell about her that’s all the better for being a little atypical. Though she had a great sense of humor, she also had the tendency to take things literally, so her favorite funny stuff didn’t tend to be wry or sarcastic…except for this one incident that I recall.

Left: a pancake. Right: Kansas.

In 2003, the august journal Annals of Improbable Research published a paper entitled “Kansas is Flatter than a Pancake“. They analyzed the surface both of a pancake and of Kansas, along the way having to answer the question of what “flat” actually means (not a minor matter, as it turns out). Since my grandparents both grew up in Kansas, it was absolutely imperative they learn of said paper as soon as possible.

I really didn’t expect the response I got, though: a wide envelope from my grandmother containing the two panoramic photos below:

Evidently she drove from her northwestern Missouri home into Kansas just for the purpose of taking these photos. The tags, of course, are her own, and her letter (which I can’t find, unfortunately) said something like “We can now lay these slanders to rest!”

So, why am I thinking of Kansas and pancakes now (other than the fact that I often think of pancakes with longing)? We shall yet arrive, so patience.

In many ways, it’s harder to study the deep ocean than it is to explore space. Going from sea level to hard vacuum is a difference in one atmospheric pressure, but going into the depths requires withstanding huge pressures: every 10 meters (roughly 33 feet), the pressure increases by about one atmosphere. The submersible Alvin has gone as deep as 4.5 kilometers (2.8 miles), but dives that deep can take 10 hours, most of which is spent on descent and ascent for safety’s sake. You can look up into the sky at night and see many stars, and a relatively small investment in binoculars or telescopes reveals a lot to study; to go deep isn’t a matter as simple as building bigger telescopes.

Measuring the depth of the ocean and maping the ocean floor requires using sound rather than light: you don’t have to dive very deep before things get dark. So it’s not surprising that the depth of the Mariana Trench—the deepest point on the ocean floor—has been found to be just a little deeper than before. The deepest point, known as Challenger Deep, is 10,994 meters (about 6.8 miles) below the surface, 75 meters more than previously estimated. (For reference, that’s about the same as the thickness of the breathable part of our atmosphere, known as the troposphere, at middle latitudes.) The highest point on Earth, Mount Everest, stands about 8.8 kilometers (5.5 miles) above sea level.

Everest isn’t the tallest mountain in the Solar System: that honor goes to a formation on Vesta (or to Olympus Mons on Mars, if you restrict yourself to planets). Likewise, the Valles Marineris on Mars is deeper than the Mariana Trench, so we have to find our planetary chauvinistic pride elsewhere. That’s not really my concern, here, though: as with the case of Kansas, I simply wish to point out that the Earth is very smooth.

Well, relatively speaking. From our perspective, it isn’t smooth at all: the bumps and creases, the heights and depths are large on our scale. Because of the crushing pressures, a human being is not capable of going to the bottom of the Mariana Trench at the current time, and climbing Everest is still a major investment of energy with huge risks to life and health. Yet compared to the curvature of Earth, Everest and Mariana, the Andes and the deep Atlantic, all the mountains and valleys are tiny wrinkles, smaller than the imperfections of a billiard ball. The Earth’s radius is about 6,400 kilometers, so the difference between the height of Everest to the depth of Mariana is about 0.3% of that. We do indeed live on a blue marble.

I think my grandmother would be pleased to know all of this.

(The title of this post is from “Everest”, a song by Ani DiFranco.)

#### 3 Responses to “From the Height of the Pacific to the Depths of Everest”

1. December 11, 2011 at 15:42

To add a little mathematical justification to the claim, the following is from BAD ASTRONOMY at Discover Magazine :
“a pool ball is 2.25 inches in diameter, and has a tolerance of +/- 0.005 inches. In other words, it must have no pits or bumps more than 0.005 inches in height. That’s pretty smooth. The ratio of the size of an allowable bump to the size of the ball is 0.005/2.25 = about 0.002.

The Earth has a diameter of about 12,735 kilometers (on average, see below for more on this). Using the smoothness ratio from above, the Earth would be an acceptable pool ball if it had no bumps (mountains) or pits (trenches) more than 12,735 km x 0.00222 = about 28 km in size.”

Note both Mountains and Ocean Trenches are far short of these numbers… The earth really is smoother than a billiard ball (IF the billiard ball is at the upper boundary of its tolerance.)

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