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Earth's gravity: A downer?

Gravity’s pull influences life — and the potential for death — on the planet.
bob_berman_2009
Ask your smartest friends, “The Sun’s gravity is much greater than the Moon’s — we even orbit it, right? Yet the Moon controls the tides, so it boasts a greater tidal influence on us. This means tidal and gravitational pulls are different animals. But how?”

You’ll find no one who can tell you. Maybe you yourself know, since you’re into astronomy. Yes, the Sun pulls on Earth about 175 times more forcefully than the Moon. But its effect on the oceans isn’t even half that of the Moon. That’s because gravity alone won’t make water move. What does the job is the difference in the gravitational pull on various parts of the ocean.

The Moon’s extreme nearness is the key. Since gravity’s grip falls quickly with distance, a little change in nearness yields a big shift in power. The Moon hovering 3.4 percent closer to one side of Earth yields a 7 percent inequality in its gravitational influence across the globe. This difference doesn’t produce the tidal effect; it is the tidal effect.

So a tidal effect is a gravity difference. There’s a 7 percent disparity in lunar strength acting on Earth’s hemispheres. But the Sun’s great distance yields only a 0.018 percent variation in its pull on opposite hemispheres. That’s less than one-twentieth of a percent. Result: comparatively wimpy solar tides.

Even more fun is dealing with Earth’s own gravity. Especially in ways often misunderstood, like escape velocity: It’s 7 miles per second. That’s the speed you’d need, after being shot from a cannon, to keep going and never be pulled back, ignoring air resistance. Many imagine that if a rocket failed to achieve that speed, it could never escape the planet.

Berman0118
Boats sit directly on the exposed ocean floor during low tide in Gorey Harbour, Jersey. Water levels around Jersey, an island between England and France, can differ by more than 40 feet (12 m) between low and high tide.
Foxyorange on wikipedia
In the ’90s, I had that debate with the astrophysics chair at Columbia University. That otherwise brilliant man insisted that if a rocket headed upward at only, say, 2 miles per second, its path would invariably curve back down. “That’s not true,” I told him, in what was surely the only instance of me being right and him being wrong about anything. “You could keep heading upward at even 2 miles an hour, and as long as the engines kept firing, you could go clear across the universe.”

He disagreed because he’d apparently forgotten that escape velocity simply doesn’t apply if you’re supplying further energy to the job. The concept that a speed greater than the escape velocity is needed is only valid in a one-shot deal, after which your rocket then coasts on its own.

What’s cool is that escape velocity equals the impact speed if you fell to the ground from a great distance. If you toss an orange up, it comes back to strike your palm at exactly the same speed you happened to hurl it upward. Up equals down.

Schools teach that falling bodies accelerate by 32 feet (9.8 meters) per second squared. But most people grasp that more easily if we instead say a rock tossed off a cliff falls 22 miles (35.4 kilometers) an hour faster after each passing second. If it falls for two seconds, it hits the ground at 44 mph. Three seconds, and it’s 66 mph. Simple.

Air resistance stops the speed gain at some point, which is why rain falls at just 22 mph. And why squirrels have no lethal terminal velocity. It’s why an arms-and-legs-out base jumper leaping from any height above 49 stories remains falling at 120 mph. It explains why meteoroids screaming into our atmosphere at 72,000 mph (115,873 km/h) hit rooftops at just 250 to 300 mph (402 to 483 km/h), and penetrate no farther than one or two floors.

Ignoring air resistance, you can find your final falling speed by multiplying your height in feet times 64.4 and then hitting the square root button. The result is in feet per second, which very nearly equals kilometers per hour. For miles per hour, multiply again by 0.68. This equation reveals that jumping from 1 foot (times 64 is still 64, whose square root is 8) makes you strike the ground at 8 km/h or 8 fps. That’s 5 mph. From 5 feet up, you’d land at 12 mph. These are typical impact speeds after slipping on ice.

From 10 feet, a single house story, you hit at 17 mph. From two stories it’s 24.4 mph, and now you’d better land on something very soft to avoid serious injury. Fatal impacts become more likely than not at around 35 mph, which corresponds to four stories. An old insurance table says the chance of death increases by 1 percent for each additional foot you fall.

Enlightening, perhaps, but we’re now getting morbid. Let’s stop.

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