Sunday, September 14, 2008

Ten Things You Don’t Know About the Earth

1) The Earth is smoother than a billiard ball.

Maybe you’ve heard this statement: if the Earth were shrunk down to the size of a billiard ball, it would actually be smoother than one. When I was in third grade, my teacher said basketball, but it’s the same concept. But is it true? Let’s see. Strap in, there’s a wee bit of math (like, a really wee bit).

OK, first, how smooth is a billiard ball? According to the World Pool-Billiard Association, 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.

The highest point on Earth is the top of Mt. Everest, at 8.85 km. The deepest point on Earth is the Marianas Trench, at about 11 km deep.

Hey, those are within the tolerances! So for once, an urban legend is correct. If you shrank the Earth down to the size of a billiard ball, it would be smoother.

But would it be round enough to qualify?

2) The Earth is an oblate spheroid

The Earth is round! Despite common knowledge, people knew that the Earth was spherical thousands of years ago. Eratosthenes even calculated the circumference to very good accuracy!

But it’s not a perfect sphere. It spins, and because it spins, it bulges due to centrifugal force (yes, dagnappit, I said centrifugal). That is an outwards-directed force, the same thing that makes you lean to the right when turning left in a car. Since the Earth spins, there is a force outward that is a maximum at the Earth’s equator, making our Blue Marble bulge out, like a basketball with a guy sitting on it. This type of shape is called an oblate spheroid.

If you measure between the north and south poles, the Earth’s diameter is 12,713.6 km. If you measure across the Equator it’s 12,756.2 km, a difference of about 42.6 kilometers. Uh-oh! That’s more than our tolerance for a billiard ball. So the Earth is smooth enough, but not round enough, to qualify as a billiard ball.

Bummer. Of course, that’s assuming the tolerance for being out-of-round for a billiard ball is the same as it is for pits and bumps. The WPA site doesn’t say. I guess some things remain a mystery.

3) The Earth isn’t an oblate spheroid.

But we’re not done. The Earth is more complicated than an oblate spheroid. The Moon is out there too, and the Sun. They have gravity, and pull on us. The details are complicated (sate yourself here), but gravity (in the form of tides) raises bulges in the Earth’s surface as well. The tides from the Moon have an amplitude (height) of roughly a meter in the water, and maybe 30 cm in the solid Earth. The Sun is more massive than the Moon, but much farther away, and so its tides are only about half as high.

This is much smaller than the distortion due to the Earth’s spin, but it’s still there.

Other forces are at work as well, including pressure caused by the weight of the continents, upheaval due to tectonic forces, and so on. The Earth is actually a bit of a lumpy mess, but if you were to say it’s a sphere, you’d be pretty close. If you held the billiard-ball-sized Earth in your hand, I doubt you’d notice it isn’t a perfect sphere.

A professional pool player sure would though. I won’t tell Allison Fisher if you won’t.

4) OK, one more surfacey thing: the Earth is not exactly aligned with its geoid

If the Earth were infinitely elastic, then it would respond freely to all these different forces, and take on a weird, distorted shape called a geoid. For example, if the Earth’s surface were completely deluged with water (give it a few decades) then the surface shape would be a geoid. But the continents are not infinitely ductile, so the Earth’s surface is only approximately a geoid. It’s pretty close, though.

Precise measurements of the Earth’s surface are calibrated against this geoid, but the geoid itself is hard to measure. The best we can do right now is to model it using complicated mathematical functions. That’s why ESA is launching a satellite called GOCE (Gravity field and steady-state Ocean Circulation Explorer) in the next few months, to directly determine the geoid’s shape.

Who knew just getting the shape of the Earth would be such a pain?

5) Jumping into hole through the Earth is like orbiting it.

I grew up thinking that if you dug a hole through the Earth (for those in the US) you’d wind up in China. Turns out that’s not true; in fact note that the US and China are both entirely in the northern hemisphere which makes it impossible, so as a kid I guess I was pretty stupid.

You can prove it to yourself with this cool but otherwise worthless mapping tool.

But what if you did dig a hole through the Earth and jump in? What would happen?

Where my own hole through the Earth ends up.
Well, you’d die (see below). But if you had some magic material coating the walls of your 13,000 km deep well, you’d have quite a trip. You’d accelerate all the way down to the center, taking about 20 minutes to get there. Then, when you passed the center, you’d start falling up for another 20 minutes, slowing the whole way. You’d just reach the surface, then you’d fall again. Assuming you evacuated the air and compensated for Coriolis forces, you’d repeat the trip over and over again, much to your enjoyment and/or terror. Actually, this would go on forever, with you bouncing up and down. I hope you remember to pack a lunch.

Note that as you fell, you accelerate all the way down, but the acceleration itself would decrease as you fell: there is less mass between you and the center of the Earth as you head down, so the acceleration due to gravity decreases as you approach the center. However, the speed with which you pass the center is considerable: about 7.7 km/sec (5 miles/second).

In fact, the math driving your motion is the same as for an orbiting object. It takes the same amount of time to fall all the way through the Earth and back as it does to orbit it, if your orbit were right at the Earth’s surface (orbits slow down as the orbital radius increases). Even weirder, it doesn’t matter where your hole goes: a straight line through the Earth from any point to any other (shallow chord, through the diameter, or whatever) gives you the same travel time of 42 or so minutes.

Gravity is bizarre. But there you go. And if you do go take the long jump, well, your trip may be a wee bit unpleasant.

6) The Earth’s interior is hot due to impacts, shrinkage, sinkage, and radioactive decay.

A long time ago, you, me, and everything else on Earth was scattered in a disk around the Sun several billion kilometers across. Over time, this aggregated into tiny bodies called planetesimals, like dinky asteroids. These would smack together, and some would stick, forming a larger body. Eventually, this object got massive enough that its gravity actively drew in more bodies. As these impacted, they released their energy of motion (kinetic energy) as heat, and the young Earth became a molten ball. Ding! One source of heat.

As the gravity increased, its force tried to crush the Earth into a more compact ball. When you squeeze an object it heats up. Ding ding! The second heat source.

Since the Earth was mostly liquid, heavy stuff fell to the center and lighter stuff rose to the top. So the core of the Earth has lots of iron, nickel, osmium, and the like. As this stuff falls, heat is generated (ding ding ding!) because the potential energy is converted to kinetic energy, which in turn is converted to thermal energy due to friction.

And hey, some of those heavy elements are radioactive, like uranium. As they decay, they release heat (ding ding ding ding!). This accounts for probably more than half of the heat inside the planet.

So the Earth is hot in the inside due to at least four sources. But it’s still hot after all this time because the crust is a decent insulator. It prevents the heat from escaping efficiently, so even after 4.55 billion years, the Earth’s interior is still an unpleasantly warm place to be.

Incidentally, the amount of heat flowing out from the Earth’s surface due to internal sources is about 45 trillion Watts. That’s about three times the total global human energy consumption. If we could capture all that heat and convert it with 100% efficiency into electricity, it would literally power all of humanity. Too bad that’s an insurmountable if.

7) The Earth has at least five natural moons. But not really.

Most people think the Earth has one natural moon, which is why we call it the Moon. These people are right. But there are four other objects — at least — that stick near the Earth in the solar system. They’re not really moons, but they’re cool.

The biggest is called Cruithne (pronounced MRPH-mmmph-glug, or something similar). It’s about 5 kilometers across, and has an elliptical orbit that takes it inside and outside Earth’s solar orbit. The orbital period of Cruithne is about the same as the Earth’s, and due to the peculiarities of orbits, this means it is always on the same side of the Sun we are. From our perspective, it makes a weird bean-shaped orbit, sometimes closer, sometimes farther from the Earth, but never really far away.

That’s why some people say it’s a moon of the Earth. But it actually orbits the Sun, so it’s not a moon of ours. Same goes for the other three objects discovered, too.

Oh– these guys can’t hit the Earth. Although they stick near us, more or less, their orbits don’t physically cross ours. So we’re safe. From them.

8) The Earth is getting more massive.

Sure, we’re safe from Cruithne. But space is littered with detritus, and the Earth cuts a wide path (125 million square km in area, actually). As we plow through this material, we accumulate on average 20-40 tons of it per day! [Note: your mileage may vary; this number is difficult to determine, but it’s probably good within a factor of 2 or so.] Most of it is in the form of teeny dust particles which burn up in our atmosphere, what we call meteors (or shooting stars, but doesn’t "meteor" sound more sciencey?). These eventually fall to the ground (generally transported by rain drops) and pile up. They probably mostly wash down streams and rivers and then go into the oceans.

40 tons per day may sound like a lot, but it’s only 0.0000000000000000006% the mass of the Earth (in case I miscounted zeroes, that’s 2×10-26 6×10-21 times the Earth’s mass). It would take 140,000 million 450,000 trillion years to double the mass of the Earth this way, so again, you might want to pack a lunch. In a year, it’s enough cosmic junk to fill a six-story office building, if that’s a more palatable analogy.

I’ll note the Earth is losing mass, too: the atmosphere is leaking away due to a number of different processes. But this is far slower than the rate of mass accumulation, so the net affect is a gain of mass.

9) Mt. Everest isn’t the biggest mountain.

The height of a mountain may have an actual definition, but I think it’s fair to say that it should be measured from the base to the apex. Mt. Everest stretches 8850 meters above sea level, but it has a head start due to the general uplift from the Himalayas. The Hawaiian volcano Mauna Kea is 10,314 meters from stem to stern (um, OK, bad word usagement, but you get my point), so even though it only reaches to 4205 meters above sea level, it’s a bigger mountain than Everest.

Plus, Mauna Kea has telescopes on top of it, so that makes it cooler.

10) Destroying the Earth is hard.

Considering I wrote a book about destroying the Earth a dozen different ways (available for pre-order on!), it turns out the phrase "destroying the Earth" is a bit misleading. I actually write about wiping out life, which is easy. Physically destroying the Earth is hard.

What would it take to vaporize the planet? Let’s define vaporization as blowing it up so hard that it disperses and cannot recollect due to gravity. How much energy would that take?

Think of it this way: take a rock. Throw it up so hard it escapes from the Earth. That takes quite a bit of energy! Now do it again. And again. Lather, rinse, repeat… a quadrillion times, until the Earth is gone. That’s a lot of energy! But we have one advantage: every rock we get rid of decreases the gravity of the Earth a little bit (because the mass of the Earth is smaller by the mass of the rock). As gravity decreases, it gets easier to remove rocks.

You can use math to calculate this; how much energy it takes to remove a rock and simultaneously account for the lowering of gravity. If you make some basic assumptions, it takes roughly 2 x 1032 Joules, or 200 million trillion trillion Joules. That’s a lot. For comparison, that’s the total amount of energy the Sun emits in a week. It’s also about a trillion times the destructive energy yield of detonating every nuclear weapon on Earth.

If you want to vaporize the Earth by nuking it, you’d better have quite an arsenal, and time on your hands. If you blew up every nuclear weapon on the planet once every second, it would take 160,000 years to turn the Earth into a cloud of expanding gas.

And this is only if you account for gravity! There are chemical bonds holding the Earth’s matter together as well, so it takes even more energy.

This is why Star Wars is not science fiction, it’s fantasy. The Death Star wouldn’t be able to have a weapon that powerful. The energy storage alone is a bit much, even for the power of the Dark Side.

Even giant collisions can’t vaporize the planet. An object roughly the size of Mars impacted the Earth more than 4.5 billion years ago, and the ejected debris formed the Moon (the rest of the collider merged with the Earth). But the Earth wasn’t vaporized. Even smacking a whole planet into another one doesn’t destroy them!

Of course, the collision melted the Earth all the way down to the core, so the damage is, um, considerable. But the Earth is still around.

The Sun will eventually become a red giant (Chapter 7!), and while it probably won’t consume the Earth, it’ll put the hurt on us for sure. But even then, total vaporization is unlikely (though Mercury is doomed).

Planets tend to be sturdy. Good thing, too. We live on one.

[Via Discover Magazine]

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