Every seashore demonstrates the influence of celestial bodies.
It’s vivid but old news: Ancient cultures knew that tides were mainly controlled by the Moon. Yet, nowadays, many are mystified.
After all, the Sun’s gravity is much greater than the Moon’s — we even orbit it. 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 if you’re into astronomy. Yes, the massive but more distant Sun pulls on Earth 176 times more forcefully than the Moon does. 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 if there’s a difference in the gravity 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 its power. The Moon hovering a few percent closer to one side of Earth yields a 7% inequality. 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% disparity in lunar strength acting on Earth’s hemispheres. But the Sun’s great distance yields only a 0.018% variation in its pull on our world’s opposite hemispheres. Less than one twentieth of one percent. Result: Wimpy solar tides.
Even more fun is dealing with our own gravity. Like our escape velocity. It’s seven miles a 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.
What’s cool is that escape velocity equals the impact speed if you fell here 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 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 an hour faster after each 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 hit rooftops at just 300 mph, 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 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 five mph. Starting five feet up, you’d land at 12 mph. These are typical maximum impact speeds after slipping on ice or off a stepladder.
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 a four-story fall. An insurance table says the chance of death increases by 1% after that, for each additional foot you plunge. But four-stories and up are where your odds of surviving go below 50/50. Good thing so few of our readers have any windows that high.
Enlightening, perhaps, but we’re now getting morbid. Let’s stop.