every seashore demonstrates the influence of celestial bodies. It’s vivid but old news: Ancient cultures knew that tides are mainly controlled by the Moon, not the Sun. Yet nowadays, many are mystified by this supposed disparity.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.?

每一個海岸都展示著天體的影響。古代文化知道，潮汐主要是由月亮控制的，而不是由太陽控制的?！疤柕囊Ρ仍虑虻囊蟮枚唷覀兩踔晾@著它運行，對吧？”然而，月亮控制著潮汐，所以它對我們的潮汐影響更大。這意味著潮汐力和引力是不同的力。但該如何區(qū)分呢？“你找不到一個人能告訴你的。太陽對地球的引力大約是月球的175倍。但它對海洋的影響甚至還不到月球的一半。

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 7percent 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.?

這是因為重力本身并不能使水移動。關(guān)鍵是月球要與海洋極端接近。由于重力大小隨著距離的增加而迅速下降，近距離的微小變化就會產(chǎn)生力的巨大變化。月球在靠近地球一側(cè)3.4%的地方盤旋，其對全球的引力影響產(chǎn)生了7%的傾斜。這種差異不會產(chǎn)生潮汐；它是潮汐效應(yīng)。所以潮汐效應(yīng)就是重力差。月球在地球半球的強(qiáng)度有7%的差異。但是太陽的巨大距離對半球的拉力只有0.0.18%的變化。

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.這還不到二分之一。相比較弱的太陽潮汐。更有趣的是地球本身的重力。在經(jīng)常被誤解的方面，比如逃逸速度：它是每秒7英里。在被大炮擊中后，繼續(xù)前進(jìn)，無視空中阻力。許多人認(rèn)為，如果一枚火箭不能達(dá)到這個速度，它就永遠(yuǎn)無法逃離地球。

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.

那個才華橫溢的人堅持認(rèn)為，如果火箭只以每秒2英里的速度上升，它的路徑總是會向下彎曲?！澳遣皇钦娴模蔽腋嬖V他，你甚至可以以每小時2英里的速度繼續(xù)上升，只要引擎繼續(xù)燃燒，你就可以穿越宇宙。”“他不同意，因為他顯然忘記了，如果你為任務(wù)提供更多的能量，逃逸速度根本不適用?！?/span>

The?concept that a speed greater than the escape velocity is?needed is only valid in a oneshot 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 (9.8meters) 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.

所需要的速度大于逃逸速度的概念只有在一次性的交易中才有效，之后你的火箭就會自己滑行。如果你從遠(yuǎn)處墜落在地面上，逃逸速度等于撞擊速度。如果你拋出一個橙子，它會回來擊中你的手掌，速度和你碰巧向上投擲的速度完全一樣。向上等于向下。墜落的身體每秒會加速32英尺（9.8米）。但如果我們說從懸崖上掉下來的巖石每經(jīng)過一秒后每小時快22英里（35.4公里），如果它下降了兩秒鐘，它就會以每小時44英里的速度撞到地面上。三秒，時速每小時66英里。

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.

簡單來說，空氣阻力在某個點阻止了速度的增加，這就是為什么降雨量只有每小時22英里。以及為什么松鼠沒有致命的終端速度。這就是一個49層以上的高空跳投者仍然以每小時120英里的速度下降。這解釋了為什么流星體以每小時72,000英里（115,873 km/h）的速度尖叫進(jìn)入我們的大氣層，以每小時250到300英里（402到483 km/h）的速度撞擊屋頂。忽略空氣阻力，你可以通過將你的高度乘以64.4，然后按下平方根按鈕來找到你最終的下降速度。

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.

結(jié)果以每秒英尺為單位，幾乎等于每小時公里。每小時數(shù)英里，再乘以0.68。這個方程顯示，從1英尺跳躍會讓你以8 km/h或8 fps的速度撞擊地面。這是每小時5英里。從5英尺以上開始，以每小時12英里的速度降落。這些都是在冰上滑倒后的典型撞擊速度。從10英尺一層樓看，你達(dá)到每小時17英里。從兩層樓來看，它是24.4英里每小時，所以最好降落在一些非常柔軟的東西上，以避免嚴(yán)重的傷害。大約35英里每小時，時速為35英里，相當(dāng)于4層樓。但我們有點吹毛求疵了。還是停下來吧。