🍎 万有引力：苹果与月亮同一条定律🍎 Gravity: the Apple and the Moon, One Law
上一片里，向心力拉着小球转圈。可这只“看不见的手”到底是谁？牛顿说：是引力——苹果和月亮，都握在它的手里。Last leaf, a centripetal force kept a ball circling. But whose hand is it? Newton's answer: gravity — the same hand holds the apple and the Moon.
第 1 步：苹果落地，月亮绕地Step 1: The apple falls, the Moon orbits
先看这张图——苹果和月亮，看起来毫不相干。Look at this picture first — the apple and the Moon seem worlds apart.
苹果熟了往下掉，月亮却绕着地球转圈。牛顿把它们画进同一张图：都是地球在拉。苹果离得近，被拉向地面；月亮离得远，被拉弯了路线，正好绕成一圈。同一个引力，两种结果。A ripe apple falls down, while the Moon circles the Earth. Newton put both in one picture: the Earth pulls on both. The apple is close, so it is pulled to the ground; the Moon is far, so its path is bent just enough to circle forever. One force, two outcomes.
那引力是地球的“专利”吗？So is gravity Earth's private property?
第 2 步：万物互吸，天体才明显Step 2: Everything attracts, but only stars show it
不是。任何两个有质量的东西都会互相吸引，这叫万有引力：你和我之间也有，只是太小，小到感觉不到。质量越大，拉力越大——地球和月亮拉出了潮汐；两颗恒星质量惊人，拉成了双星，互相绕着转。No. Any two things with mass pull on each other — that is universal gravitation. You and I feel it too, but far too weakly to notice. More mass means more pull: Earth and Moon raise the tides; two massive stars become a binary and swing around each other.
既然万物都互吸，月亮为什么没被吸下来？If everything attracts, why doesn't the Moon fall down onto us?
第 3 步：距离翻倍，引力砍到四分之一Step 3: Double the distance, quarter the force
秘密在距离。引力公式的分母上是 r²：距离 ×2，引力 ÷4；距离 ×3，引力 ÷9。这就是平方反比。月亮离地球 38 万千米，引力已经很弱；再加上它跑得快，一边被拉一边“往前掉”，就绕成了圈。The secret is distance. The denominator of the gravity formula carries r²: double the distance, divide the force by 4; triple it, divide by 9. That is the inverse-square law. The Moon sits 384,000 km away, where the pull is weak — and it moves fast enough that falling forward becomes circling.
🎮 你来当实验员（30 秒）🎮 Your turn: lab assistant (30 seconds)
拖动质量与距离滑块，看引力 F 怎么实时变化；再把 4 个任务的 F 调到目标值。Drag the mass and distance sliders to watch F react live — then dial F to the target in 4 tasks.
一句话记住它：万有引力 = 万物互吸，F = G·m₁m₂/r²。质量越大，引力越大；距离在分母的平方上，距离翻倍，引力砍到四分之一。Remember it in one line: universal gravitation = everything attracts, F = G·m₁m₂/r². More mass, more pull — and distance sits squared in the denominator, so double the distance, quarter the force.
万物都有引力：质量越大，拉力越大（对质量成正比）Everything attracts: more mass means more pull (proportional to mass)距离在分母的平方上：距离 ×2，引力 ÷4；距离 ×3，引力 ÷9Distance is squared: ×2 distance → ÷4 force; ×3 distance → ÷9 force苹果和月亮服从同一条定律：近处落地、远处绕圈，都是引力的结果The apple and the Moon obey one law: fall nearby, orbit far away — gravity does both
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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