by Bob Berman
Beaufort force 10 is a “storm” or “whole gale.” Winds roar at 55–63 mph (89–102 km / hr). Weak trees are blown down or uprooted. Saplings are bent and deformed. Weak or old asphalt shingles are peeled off roofs. Large waves of 20–30 feet have overhanging crests. There is a heavy rolling of the sea, which is white with foam. Visibility is reduced.
Beaufort force 11 is a “violent storm,” with winds of 64–72 mph (103–117 km / hr). There is widespread damage to trees and crops. Many trees are blown over. Many roofs are damaged. Many objects left unsecured are blown away and can break glass. The sea has very high waves of 37–52 feet and extensive foam, and there is restricted visibility.
Beaufort force 11 winds of around seventy miles per hour are slightly below hurricane strength but have easily destroyed half the trees in this forest.
Beaufort force 12 is a “hurricane.” Winds are above 72 mph (above 118 km / hr). Crops, plants, and trees suffer widespread damage. Some windows may break; mobile homes and weak sheds and barns are damaged. Heavy debris is hurled about. Waves are huge; over 50 feet. The sea is completely white with foam and spray. Visibility is negligible, thanks to driving spray.
I’m offering the entire Beaufort scale for one reason only: because to recognize what is happening and be able to label it means that you can watch air motion with more attention. And better observation creates better enjoyment. This way if you see branches swaying yet large tree trunks are steady, and overhead wires are whistling, and your plastic garbage pail just blew over, you can say with confidence: “Hey, honey, there’s a strong breeze outside. The wind is between twenty-five and thirty miles per hour.” And you’ll earn a perfunctory nod from your spouse, who really doesn’t care.
No matter. You and your fellow nature lovers are enraptured by the magic of the wind. And perhaps reminded of Alhazen, who figured out a thousand years ago where it ends. And of Evangelista Torricelli, whose words still linger:
“We live submerged at the bottom of an ocean of… air.”
CHAPTER 10: Falling
Enigmas of the Most Far-Reaching Force
The whole damn thing, the universe,
Must one day fall.
—HOWARD NEMEROV, “COSMIC COMICS” (1975)
We take for granted the tinkle of falling rain. And we stick to Earth’s surface without giving it a thought. Yet can anyone honestly explain gravity or claim to know what’s going on? The otherwise perspicacious cultures of the ancient Greeks, Chinese, and Mayans didn’t even try.
Even today, how many of us ever really pay attention to the act of falling? Any kid who has belly flopped into a swimming hole knows that the higher the dive, the more it hurts. That’s because the farther up we jump from, the faster we hit the water. In fifth grade they used to cite thirty-two feet per second per second as the rate at which a plummeting body accelerates, until primary school science switched to the metric system, and then it became 9.8 meters squared. Too bad. We might have paid attention if they’d expressed it in everyday language.
Fall for a single second and you hit the ground going twenty-two miles an hour. Simple.
Each additional second you’re airborne makes you land another twenty-two miles an hour faster. Still simple.
If you want to stay in the air for exactly one second, you have to jump from a height of sixteen feet. One and a half stories. If you land on a trampoline this might not hurt. But you should not, as they say on TV, try this at home. To stay aloft for two seconds, however, means leaping from a six-story roof, and you’d then accelerate to forty-four miles an hour, the impact from which is usually not survivable. So humans, unlike squirrels, have a very narrow available range of safe falling. One second of plummeting can sometimes be okay. Two seconds means death.1
This is the hard-nosed reality all people and animals confront from the moment they take their first baby steps. Our motions are a contest between our muscles and the ground beneath us, as it eternally holds us as closely as possible.
As we’ve seen, Aristotle and his friends tackled downward motion by saying that everything made of the elements water and earth wants to fall. In a straight line. After all, a stone tossed off a cliff angles more and more toward a linear trajectory with every second it keeps plummeting.
Watching the sky, the ancients decided that up in the heavens, objects want to move in circles. The sun and moon daily circle around us. The stars nightly wheel around the North Star.2
Moreover, the only celestial objects that aren’t dots are the disks of the sun and moon—more circles. Clearly, the gods like circles in their realm. You can’t blame them. The circle, according to the Greeks, is the perfect geometric form—so perfect it was divine, with a legacy that lingers to this day in traditions such as the exchange of rings at weddings and engagements. It’s the only shape whose boundary contains no special points or direction changes and whose edge is at every point equidistant from the center.
So according to the Greeks, all motion is either linear or circular. Circular up there, linear down here. There was no word for gravity. There wasn’t even the concept of a downward-pulling force. Instead, objects themselves “want” to head downward and will do so the moment obstacles are removed.
That’s how things stood for century after century while children tripped and scraped knees and old men idly threw pebbles into ponds.
It took until modern times for this gravity business to become central to space exploration and bungee jumping and such. Meanwhile the parallel topic of air resistance developed into a major study of its own. It’s a central tenet of aircraft engineering and parachuting and was always a design feature in the animal kingdom—which explains why cats and squirrels usually never accelerate to lethal speeds no matter how far they fall.3
All that technological fun stuff was still to come when the ancient Greeks were alive. But when the sixteenth century dawned, science was dealing with old Greek views that had since been incorporated into Church dogma and was trying to make those square Plato-idea pegs fit into the round holes of actual planet movement.
The problem was that the holes were not round. They were oval. To chart planetary motion against the background stars was to observe loopy trajectories that didn’t jibe with anything circling a stationary Earth. Then in the sixteenth century, nightly observations performed meticulously for twenty years by the obsessive Danish astronomer Tycho Brahe refined the length of the year to within an accuracy of one second, which proves he was a type-A fanatic who refused to “round off” anything. He was good. Yet he failed to unlock the simplest underlying secrets of celestial choreography.
It did not appear as if planets moved in circular paths. But Tycho assumed all sorts of comically jury-rigged systems—planets moving in circles around empty spots of space that in turn orbited still more circles that then circled us—to preserve the traditional Holy Roundness. And to keep a motionless Earth at the center of it all. All his mental gymnastics, a pathetic purgatory of years of intellectual labor, served the single desperate purpose of trying to make the universe jibe with the clergy’s mistaken view of natural motion.
When Tycho died in 1601, his assistant, Johannes Kepler, inherited his notes and pondered them for the next ten years, right through and beyond Galileo’s first telescope discoveries in 1610. Kepler, a brilliant mathematician, came to a startling conclusion. The celestial minuet made sense only if the sun lay at the center of all motion, and the planets—including Earth—moved in elliptical paths.
Ellipses were not sexy, then or now. But they are the fact of the cosmos. They are the way gravity makes nearly all celestial bodies move.
Understanding ellipses is easy if you draw one. Push two thumbtacks partway into a piece of plywood or cardboard and loosely put a loop of string around them. Insert a pencil within the loop, pull it firmly sideways, and you’ll draw an ellipse. In the actual universe, each of those tacks is called a focus, and the sun occupies one focus of every planet’s orbit. (The other is just an empty spot o
f space. This bothers some people, who feel that such a vital mathematical point merits more than mere vacuity. Well, perhaps some enterprising space-travel company will someday erect a floating café there with a catchy name like the Focal Point.) This is the simple and complete reality of every planet’s path through space.
Kepler found that each planet speeds up as it approaches the sun in its oval path but decelerates as it heads away. Holy cow: Earth and all other worlds continually change their speeds. Nobody had seen that coming.
Obviously, something about the sun pulls on the planets. It was a puzzle pondered at that same time—the opening decade of the seventeenth century—by Galileo Galilei.
Galileo, who, like Kepler, was a longtime subscriber to Heliocentrism Today, decided to study the way things move and fall. He built ramps that had various kinds of slopes, set balls rolling, and watched what happened. He timed things carefully and concluded that, regardless of how steep or gentle the slopes were or how high a ball was when it was released, it would speed down one incline and then up another until it reached the same height as the one from which it was dropped.
If the second ramp was perfectly flat—horizontal—the rolling ball would just keep going and finally stop only, Galileo correctly determined, because of friction. He was struck by an amazing thought. Maybe the moon and planets were rolling sideways, too. In which case they’d continue in motion forever, which is exactly what they appear to be doing.
He used simple math, and the numbers added up as long as planets were not slowed down by any air resistance. They must be orbiting in a realm of emptiness!
These days we’re accustomed to the idea of space being a vacuum. But back then, “nothing” had a long, bumpy history in philosophy and never came out smelling like a rose. The Greeks, for example, made many intriguing arguments as to why nothingness was impossible, while Renaissance clergymen reasoned that “God is everywhere, so there can be no vacuum.”4
Galileo, in the opening years of the seventeenth century, became the very first person who was sure he knew what existed “up there” in the heavens. Nothing.
In his heretical publication The Starry Messenger, Galileo didn’t make much ado about nothingness only because it was the least of his revelations. He also boldly claimed that Aristotle was wrong when he said that massive objects fall faster than skimpy ones. After all, Galileo’s biggest metal balls rolled no faster than his lighter models. Instead, he proclaimed, it was merely air resistance that slowed down spread-out objects, such as feathers. (We got to see Galileo’s breakthrough notions come true on the moon when astronaut David Scott simultaneously dropped a hammer and feather and both plummeted in perfect sync. He did this near the end of the Apollo 15 mission in 1971.)
And now we come, inevitably and predictably, to Isaac Newton. Who, by the way, indeed told at least four people that he got his inspiration about gravity from watching a falling apple. The only false aspect of his popularized, American Idol–like bio is the business about a Golden Delicious bonking him on the head.
Pondering the way the moon and apples behave, Newton realized that Galileo had been onto something. Both objects move the same way. Abandoning the Greeks’ longstanding linear-versus-circular reasoning, he unified the heavens and the earth by coining a new word: gravity. He created it from gravitas, the Latin word for “heaviness.” What exactly it was he could not say. But how it acted—ah, this he could quantify perfectly.
Actually, his contemporaries, including Robert Hooke and Edmond Halley, also assumed that some mysterious force pulled objects toward the center of the earth. Halley even presumed it grew less powerful with distance and, in a now-forgotten experiment, carried a pendulum to the top of a 2,500-foot hill, where, he claimed, he watched it swing a bit more slowly there. These natural philosophers, as scientists were then called, not only believed the planets were yanked by the sun but also correctly said that this force grew proportionally weaker with the square of their distance. Meaning an object that’s three times farther away from the sun than you are experiences three times three, or nine, times less of a pull.5
So Newton hardly came up with the idea of the force, even though he named it and introduced it to the Western world. Rather, he accurately described how it behaved.
Isaac Newton was born in 1643, in Lincolnshire, England, one year after Galileo died. He studied at Trinity College in Cambridge and later became professor of mathematics there. In a paper published in 1687 that soon became widely known as the Principia, Newton mathematically proved that the sun’s gravity should make planets travel in elliptical paths, thus effectively awarding Kepler a posthumous 1600 SAT score. It was here that he offered his famous three laws of motion, although in fairness Galileo had already pretty much stated the first two:
Every body continues in a state of rest, or of uniform motion in a straight line, unless it is impelled to change that state by forces impressed upon it.
The change of motion is proportional to the force impressed, and it is made in the direction of the straight line in which that force acts.
To every action there is an equal and opposite reaction.
In plain language, a moving body tends to keep moving. And a stationary body likes to remain at rest. Both of these tendencies are called inertia. Newton also introduced the concept of momentum. Momentum involves exactly two things: the mass of an object (what one perceives as its weight) multiplied by its speed. A slow-moving truck may move at the same speed as a bicycle, but the truck has more mass and hence more momentum. It’s harder to stop.
Newton was also the first to state the obvious—that the strength of a force is determined by how it influences a body’s motion. He also spoke of acceleration as a change in movement, whether of speed or of direction.
Newton regarded gravity as a force simply because it changes the way objects move. It pulls them ever faster. Here on Earth, we know that gravity yanks things toward Earth’s center at the rate of twenty-two miles per hour faster every second. Newton’s brilliance was in understanding that a falling apple behaves exactly the same way as the moon orbiting around us does.6
Newton’s third law expressed something totally new: the notion of equal and opposite reactions. This means that any object exerting a force also feels it acting on itself. If you push a stalled car, you feel that same force upon your hands, pushing back at you.
The exploding charge propelling a bullet forward also creates a recoil in the rifle. Because the bullet weighs less than the rifle, one object enjoys more forward speed while the heavier one moves backward with less oomph. This inequality business goes off the scale when it comes to events that involve our planet. If you jump up, you are simultaneously pushing Earth backward in the opposite direction. However, since Earth weighs an octillion times more than you, it moves an octillion times less than you do when you jump.
That equal-but-opposite law showed why a rocket sending a stream of high-speed gas out its bottom end, even in the vacuum of space, moves the opposite way—upward. There’s no need for those gases to push against anything.
Using Newton’s figures and just a tiny bit of math we can figure out how fast a bar of bullion would fall if tossed exuberantly from the Fort Knox roof by a gold-standard extremist. Or how fast a midlife-crisis bungee jumper falls when leaping from a twenty-story bridge. Grab a one-dollar calculator. Don’t be afraid. It’s time for the “fun with math” segment.
Multiply the jumper’s altitude (in feet) by 64.4, then hit the square root button. That’s his final speed in feet per second. If you prefer miles per hour, multiply this by 0.68.
Let’s consider one example. Our bungee jumper leaps from two hundred feet, so this figure times 64.4 is 12,880. The square root of this is 113. And that’s his final speed: 113 feet per second. Multiplying that by 0.68 yields seventy-seven miles per hour. Not so difficult.
The greatest speed you’d reach if you jumped from the highest possible perch—by falling toward Earth from even beyond the moon, say
—would be 25,031 miles an hour, ignoring air resistance. It’s exactly the same speed needed to escape from Earth with a single upward blast, as though you were a circus performer fired from a cannon. So the velocity needed to escape any celestial body is also the velocity at which you’d land if you fell there from a great height.
This up-speed-equals-down-speed business is pretty cool. Toss an orange up and let it land back in your hand. Interestingly, the exact speed at which you chose to toss it up is the same speed at which it’s coming down when you catch it.
Each celestial body has its own impact speed, or escape speed, predetermined by its mass and its diameter. For the moon that’s 5,368 miles an hour. For the sun it’s more than a million miles an hour, or 384 miles per second. That’s how fast a drifting, out-of-fuel spacecraft piloted by incompetent aliens would be pulled into the sun by its gravity.
On Earth, air resistance slows things down. In skydiving class they make you practice spreading your arms and legs to let your body present its maximum surface area to the wind. If you do that you won’t gain any additional speed beyond 120 miles an hour. This is the famous “terminal velocity.”7
It’s reached pretty quickly, after jumping from a height of just five hundred feet, or fifty stories. So, perhaps surprisingly, you’ll not go any faster if you jump from the 110th floor than you would if you jump from the fiftieth floor. Daredevils who bypass the fiftieth floor in favor of leaping from the roof much higher up merely want to buy themselves extra air time for their parachutes to open—an excellent idea.8
But we still haven’t explained why all this happens. So let’s fast-forward to Albert Einstein, born in 1879.
In his 1905 and, especially, his 1915 relativity theories, Albert Einstein did not just tweak Newtonian mechanics. He tossed it out, replacing it with concepts so bizarre that even now, a century later, they remain mind-twisting. It was a brand-new way of thinking about movement in the universe.