Down With Gravity!
I’m sure you’ve all heard the tongue-in-cheek expression “GRAVITY SUCKS,” or seen it on a t-shirt, or a bumper sticker. But truth be known, GRAVITY SUCKS BADLY. And by “bad”, I don’t mean that it’s really great at sucking, but rather, it does a pretty poor job of sucking. Of course, gravity doesn’t actually “suck,” it attracts. Anything that has mass, such as stars, planets, asteroids, mountains, even people, bugs, or the tiniest of bacteria, will attract other bits of mass, and it’s this force of attraction that we call gravity. It’s actually a bit more complicated than that but for our purposes this explanation will do. But you need a whole lot of mass before gravity is truly noticeable, which is why people usually think of it applying to really large things, such as planets, stars or black holes. And therein lies the first clue that gravity isn’t all it’s made out to be.
Frankly, gravity is a push-over. Don’t believe me? It’s really easy to prove. Just get up and walk to the middle of the room. Make sure you’ve got several feet of head clearance. Now jump up in the air. You’ve just beaten gravity. With your own two relatively weak, meat powered legs, you managed to defy the gravity of an object with a diameter of 12,756 kilometers (7,926 miles) and a mass of 598,000,000,000,000,000,000,000 metric tons. Just little ol’ you vs. the Earth. And you win! But before you get all full of your own bad self, pause to consider: a flea is capable of the same feat.
Of course your victory is short lived, because, gravity just doesn’t know when to quit. It’s there 24/7 and has been (near as we can tell) for the last 13+ billion years (or in the case of the earth, 4.5 billion). And that’s why you quickly come right back down. In order to stay up, you have to continue to counteract gravity and, once you’re up in the air, you’ve got nothing substantial to push against. So gravity’s dogged staying power allows it to lose the battle but win the war. But what if we had some sort of anti-gravity device that would allow us to continually push against gravity? As a matter fact, many of us do, right in our homes and places of business. They’re called stairs, and we use them every day to defy gravity (well, at least until we get to the top). In theory, as long as you’ve got stairs to climb, you can continue to rub your defiance in the face of gravity.
In fact, if you had a tall enough set of stairs you could walk right off the planet, up into space, and into orbit.
Right about now is when people start looking at me like I’m a complete loon. Go ahead, I’m used to it. A few seconds later you’ll be telling me about how we have to use huge rockets that go thousands of miles per hour just to a get a small satellite into orbit. Well, yes, I reply, but that’s because the folks who put up the satellites are in a big hurry to get them up there, and they’re using a relatively brute force method for doing it. They just don’t want to go to all the time and effort to build that stairway. You’re still looking at me like I’m a complete loon, aren’t you…
So humor me here (after all you never know what a complete loon will do if you push him over the edge). Let’s just assume that someone could and would build a spiral stairway to orbit. Just how tall would those stairs have to be? As it turns out, quite a bit taller than many of us would suspect. Even if you said several hundred miles or kilometers, you’d be way off. You see, the big problem with going into orbit is not just getting above the atmosphere and into space, it’s getting up enough orbital speed that centrifugal force just balances out the pull of gravity, and instead of flying off into space or falling back to Earth you just keep falling around and around it.
At altitudes of a few hundred miles, that speed (known as orbital velocity) is pretty enormous. The shuttle typically orbits at an altitude of around 300 kilometers (185 miles) and that works out (I’ll spare you the math) to an orbital velocity of a bit over 28,000 kilometers per hour (17,000 mph). Our stairwy, however, is anchored on the planet Earth, so its speed is governed by how fast the Earth is rotating. Since we want to get the best speed we can, we’ll want to build our stairway on the equator where it rotates the fastest. Alas, the best we can do is a paltry 1,670 kilometers per hour (1,070 mph), or roughly 17 times slower than we would need to orbit at the shuttles altitude.
But wait…because the top of our stairway is 300 kilometers higher than the surface of the Earth, we’ll be going faster than we were at the bottom. So how does that work? Well you can see for yourself. Get a broom. Put your feet together and place the handle of the broom between your feet so it’s anchored there. Now move the broom back and forth. Notice how much farther the top of the broom moves compared to the bottom near your feet? Our stairway is like that, and it turns out that every kilometer we move the bottom of the stairway (via the rotation of the Earth), we move 1.047 kilometers at the top. This pushes us to a whopping…1748 kilometers per hour…still well shy of orbital velocity. The moral is, if you step off the top of a 300 kilometer high stairway, you won’t go into orbit around the Earth, but you WILL fall back to the bottom.
Well, “duh,” you say. Ah, but you see there IS a height at which the increasing speed at the top of the stairway will exactly match the speed you need to orbit the Earth. At that altitude you can gently step off the stairway and into orbit around the earth, all under the power of your own two legs. It’s even got its own special name: geostationary orbit. Something placed in this orbit will always stay over the same place on the Earth below. Conveniently enough, that’s exactly what our stairway does, since it’s actually anchored to the Earth. The reason this works is that the farther you get from Earth, the slower the speed needed to stay in orbit. So eventually — as the top of the stairs get taller and faster and the orbit gets farther and slower — they meet.
At 35,786 kilometers (22,236 miles) above the Earth’s surface.
Now, see, you’re looking at me like that again. We’ve been through this before; remember, you’re humoring me. In fact let’s humor me a lot and assume a number of things. Let’s continue to assume that you could actually build a stairway that tall. Let’s assume that there were a number of oxygen stands along the way as well as a spacesuit shop (the kind that probably silkscreens their suits with; “I walked into space and all I got was this lousy spacesuit”). Lets assume the existence of a string of hotels, restaurants, rest stops and vending machines to keep you stoked and fresh for each day’s assent. Let’s assume you could survive the Van Allen radiation belt and any solar flares that happened to blow through. Given all of this, how long would it take to climb the stairway and step off into orbit?
Let’s further assume that our stairway zigzags straight up, each flight of stairs ascending 4.5 meters (roughly 15 feet) with landings as needed to connect to the next flight; pretty much the same as you would find in your average office building stairwell. If we divide that into the height of the stairway we get approximately 7,952,444 flights. Let’s assume that it takes you 30 seconds to ascend each flight (this leaves you a minute to catch your breath every 10 or 15 flights). This works out to a total ascent time of 66,270 hours. Let’s also assume that you’re in pretty good shape and that you can do 12 hours of stair-climbing a day. This works out to 5,522.5 days or 15.13 years. Wow, Stairmaster hell.
Actually, though, I don’t think it would take that long, for the simple reason that, as you go higher, you get lighter. There are a couple of reasons for this: 1) The farther from Earth you get, the less gravity pulls at you, and 2) as your altitude increases, so does your speed and the associated centrifugal force acting to counteract gravity. At the same altitude that the shuttle flies, your weight would drop by 10% and you would weigh about the same as you would on Venus (about 91% of your Earth weight). The reason you wouldn’t be weightless, like the shuttle astronauts, is that the shuttle whizzes around the Earth about 17 times faster than you do on the stairs.
At 1,000 kilometers (621 miles) you’d be down around 3/4 of your original weight and by the time you reached 2,600 kilometers (1,616 miles) you would weigh half as much as you do at the Earth’s surface. At around 3,900 kilometers (2,423 miles), a little over a tenth of the way to the top, you would weigh about 1/3 your normal weight — the same as you would on Mars. At 9,000 kilometers (5,592 miles) you’d be down to your lunar weight at 1/6 of Earth’s gravity. By the time you finally reached the top of the stairway you’d actually be weightless, which makes sense considering that you’ll be in orbit and what little gravity there is (about two hundredths of one percent of normal) would be canceled out by the centrifugal force generated by the stairways movement. So for well over half of your trip you would weigh less than you would on the moon and you would probably be bounding up whole flights (or even several flights) at a time, which is why I suspect the trip would take somewhat less than the 15 years estimated above.
Not that anyone would be crazy enough to climb it, let alone build such a thing. I mean, let’s get real (see, I can sound almost rational). The whole thing is pretty farfetched. Well…maybe not as farfetched as you might think…
You see, there are a number of people who think something like this might just be possible…even practical. Of course they’ve already concluded that using a stairway which takes years to climb isn’t very efficient. They propose to use something a bit faster. An elevator. That’s right, they want to build a space elevator into geostationary orbit and beyond. And it’s not just a bunch of crackpots. NASA is interested and there are several companies that are working on the technology and a competition created to encourage development.
So the next time you climb the stairs or take an elevator (or other anti-gravity device of your choice), just imagine: what if you didn’t have to stop? Before you know it, people will be looking at you like a loon too! Down with gravity!
© 2006 Daniel C. Carver
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