of gravity is stronger the closer you are to the sun, so you'd think that if the earth

地心引力的拉力隨著物體與之距離愈近而增強，所以你可能會覺得如果地球

got bumped slightly towards the sun (like, if you jumped, or something), then the sun

稍微離太陽靠近一些些（像是你跳起來，離天花板就比站立時近一些，之類的），然後太陽

would pull just a little bit stronger, tugging the earth yet closer still, at which point

對地球的拉力就會增加一點點，將地球往太陽拉近一些，然後，

the sun's pull would be stronger yet again, … and the earth would spiral in to its eventual

隨著距離拉近一些，太陽對地球的拉力又再次微幅增加，直到地球會以螺旋軌跡方式，最終撞上太陽，

doom.

而毀滅。

But you and I and swiss cheese are clearly evidence that the earth doesn't just spiral

但你、我和瑞士起司都是明顯的證據說明地球不會以上述方式運行

in to its doom – so why not? Well, when the earth does get pushed a little bit towards

最終毀滅 - 那為什麼不會呢？嗯哼，這樣說好了，當地球真的受到來自太陽引力影響往太陽靠近時，

the sun, the sun's pull speeds it up a little bit, too - so even though the nearby sun's

太陽拉力也會使得地球運行速度相對增加一些些。所以，就算愈靠近太陽，所受引力愈強。

pull is stronger, the earth will be going fast enough that it overshoots and ends up

地球也會因為速度夠快，以致於產生所謂"過衝"現象，且最後

farther away from the sun. Of course, the sun's pull slows it down again in the process…

遠遠離開太陽。當然，太陽引力在地球遠離時漸漸拉住地球，使著地球速度再度降低。

at which point the earth turns back and starts the cycle all over again.

在某個時間點，地球會轉向，然後朝著太陽再度加速，如此週而復始。

The amazing thing is that the two effects of speeding up plus stronger gravitational

值得驚嘆的是：加速和增強的地心引力的雙重影響效果達到完美的均衡，

attraction perfectly balance, so that the earth stays in its orbit the same way a marble

所以地球才能像彈珠在碗內運動一樣，

stays at the bottom of a bowl even if it gets knocked around a little bit.

在受到外力作用下還能待在碗裡般運行於軌道上。

This balance is very special indeed - it's highly dependent on the strength of the gravitational

這個均衡的確十分特別 - 因為這個現象高度受到地心引力的強度變化、和我們所處的空間維度而改變

force and the number of dimensions we live in, and in fact, these stable orbits only

而事實上，這些穩定軌道只存在於

exist in a three dimensional universe.

三度空間所構成的宇宙。

The details are a bit subtle, but if gravity were just slightly steeper, as it would be

這其中的細節有些隱晦，但是如果重力比現在更強，就會好像

if we lived in four spatial dimensions, you could never orbit the sun because you'd get

我們處在四維度空間中一般，永遠無法以繞著太陽方式的軌道運行

pulled in without picking up enough speed to escape and you WOULD spiral in to your

因為地球將會由於無法獲得足夠的速度以逃離太陽引力，而最終以螺旋方式撞上太陽而至末日。

doom. And if we lived in fewer dimensions so that gravity were a bit tamer, then you

另一方面，如果我們處在較少維度空間中，將會受到比較微弱的重力吸引，

could ALSO never orbit the sun, because as you approached it, you wouldn't be pulled

結果也就是同樣永遠無法繞著太陽運行，因為，當地球靠近太陽時，

enough and would merely pass by with your path slightly bent.

將沒有足夠的引力將地球拉回，而就只是沿著切線方向離去。

So we're incredibly lucky to live in a three dimensional universe where there ARE stable

所以，我們存在這個三維空間宇宙，

orbits that allow planets, solar systems, and galaxies to exist at all! Thank you, stable

具備著能夠讓行星、太陽系和銀河系穩定存在的軌道，是何等不可思議的幸運呀！感謝你！

orbits, for without you, life as we know it, and especially cheese, would be impossible.

穩定的軌道！因為沒有你，生命就會像我們所知道的，特別是瑞士起司，不可能發生！

ps An awesome down-to-earth example of stable orbits are the hyperbolic funnels that you

備註：一個非常棒且實際關於穩定軌道的例子是我們經常能夠在博物館或是購物中心看見的大型，

often see at museums or in shopping malls: the physics is almost identical to the stable

"漏斗"，其中的物理作用和星球、人造衛星以及月亮所運行的穩定軌道相似程度極高。

orbits of planets, satellites, and moons, and the only reason the coins in the funnels

而且，這些漏斗中的錢幣（或者類似地球周圍的人造衛星），最終....

(or satellites around the earth) eventually DO spiral in to their doom is because they

將進入"螺旋宿命"的唯一原因

lose energy to friction and thus shift down from one stable orbit to another, until eventually,

就是由於摩擦力造成動能損失，不斷地從一個穩定的軌道移轉到另一個趨向中心的軌道，

their orbit coincides with the ground. Which is called crashing.

最終，它們的軌道與中心相互重疊，然後發生也就是我們所謂的"墜毀"。