Earth’s gravity: A downer?理解重力

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. 

每一个海岸都展示着天体的影响。古代文化知道，潮汐主要是由月亮控制的，而不是由太阳控制的。“太阳的引力比月球的要大得多——我们甚至绕着它运行，对吧？”然而，月亮控制着潮汐，所以它对我们的潮汐影响更大。这意味着潮汐力和引力是不同的力。但该如何区分呢？“你找不到一个人能告诉你的。太阳对地球的引力大约是月球的175倍。但它对海洋的影响甚至还不到月球的一半。

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. 

这是因为重力本身并不能使水移动。关键是月球要与海洋极端接近。由于重力大小随着距离的增加而迅速下降，近距离的微小变化就会产生力的巨大变化。月球在靠近地球一侧3.4%的地方盘旋，其对全球的引力影响产生了7%的倾斜。这种差异不会产生潮汐；它是潮汐效应。所以潮汐效应就是重力差。月球在地球半球的强度有7%的差异。但是太阳的巨大距离对半球的拉力只有0.0.18%的变化。

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.这还不到二分之一。相比较弱的太阳潮汐。更有趣的是地球本身的重力。在经常被误解的方面，比如逃逸速度：它是每秒7英里。在被大炮击中后，继续前进，无视空中阻力。许多人认为，如果一枚火箭不能达到这个速度，它就永远无法逃离地球。

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.

那个才华横溢的人坚持认为，如果火箭只以每秒2英里的速度上升，它的路径总是会向下弯曲。“那不是真的，”我告诉他，你甚至可以以每小时2英里的速度继续上升，只要引擎继续燃烧，你就可以穿越宇宙。”“他不同意，因为他显然忘记了，如果你为任务提供更多的能量，逃逸速度根本不适用。”

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，之后你的火箭就会自己滑行。如果你从远处坠落在地面上，逃逸速度等于撞击速度。如果你抛出一个橙子，它会回来击中你的手掌，速度和你碰巧向上投掷的速度完全一样。向上等于向下。坠落的身体每秒会加速32英尺（9.8米）。但如果我们说从悬崖上掉下来的岩石每经过一秒后每小时快22英里（35.4公里），如果它下降了两秒钟，它就会以每小时44英里的速度撞到地面上。三秒，时速每小时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.

简单来说，空气阻力在某个点阻止了速度的增加，这就是为什么降雨量只有每小时22英里。以及为什么松鼠没有致命的终端速度。这就是一个49层以上的高空跳投者仍然以每小时120英里的速度下降。这解释了为什么流星体以每小时72,000英里（115,873 km/h）的速度尖叫进入我们的大气层，以每小时250到300英里（402到483 km/h）的速度撞击屋顶。忽略空气阻力，你可以通过将你的高度乘以64.4，然后按下平方根按钮来找到你最终的下降速度。

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.

结果以每秒英尺为单位，几乎等于每小时公里。每小时数英里，再乘以0.68。这个方程显示，从1英尺跳跃会让你以8 km/h或8 fps的速度撞击地面。这是每小时5英里。从5英尺以上开始，以每小时12英里的速度降落。这些都是在冰上滑倒后的典型撞击速度。从10英尺一层楼看，你达到每小时17英里。从两层楼来看，它是24.4英里每小时，所以最好降落在一些非常柔软的东西上，以避免严重的伤害。大约35英里每小时，时速为35英里，相当于4层楼。但我们有点吹毛求疵了。还是停下来吧。