Name: 月球軌道很奇怪 (The Moon's Orbit is WEIRD)
Uploaded: 2025-06-17T18:09:45.000Z
Duration: 5 min 30 s

We think of the moon as orbiting the earth, following a spiraling trajectory as the earth itself orbits the sun.

我們認為月球是繞著地球運行的，就像地球繞著太陽運行一樣，遵循著螺旋形的軌跡。

Not only is the moon's orbit not a spiral, there's an argument that the moon actually orbits the sun, not the earth.

不僅月球軌道不是螺旋形的，還有一種說法認為，月球實際上是圍繞太陽而不是地球運行的。

Sure, from the earth's perspective, the moon appears to orbit the earth, but from the sun's perspective, or from an observer far above the solar system, the moon orbits the earth so slowly and the earth and moon are so far from the sun that the moon's trajectory never actually makes any sort of a loop, and in fact it never even curves outwards towards the earth at all, but always inwards towards the sun.

當然，從地球的角度看，月球似乎是繞著地球運行的，但從太陽的角度看，或者從太陽系上方的觀測者的角度看，月球繞地球運行的速度非常慢，而且地球和月球距離太陽非常遙遠，月球的運行軌跡實際上從來沒有形成任何環形，事實上，它甚至根本就沒有向地球外側彎曲過，而總是向太陽內側彎曲。

The moon's trajectory is more like a 12-sided polygon with curved corners than it is a spiral or even a wiggly line, though the moon's trajectory is so close to being a circle it's kind of hard to see.

月球的軌跡更像是一個帶弧角的 12 邊形多邊形，而不是螺旋形，甚至不是擺動的直線，不過月球的軌跡非常接近於一個圓，有點難看。

Here's a simpler example of an orbit where a planet's moon's trajectory only ever curves towards its sun.

下面是一個更簡單的軌道例子，在這個例子中，行星衛星的軌道永遠只向太陽彎曲。

It looks like this hypothetical moon is actually orbiting the sun, and just getting nudged in and out a little bit by the planet as it orbits.

看起來，這顆假想的衛星實際上是在圍繞太陽運行，只是在運行過程中被行星擠進擠出而已。

This type of curve, where a circle rotates while attached to another rotating circle, is called an epitrochoid, though they're usually generated by rolling a circle around another circle, but the curves are the same.

這種圓與另一個旋轉的圓相連而旋轉的曲線被稱為外接圓，儘管它們通常是由一個圓繞另一個圓滾動產生的，但曲線是一樣的。

It's a fun little bit of geometry, depending on how fast the two circles rotate relative to each other and how big they are relative to each other, you get everything from spirals to wiggles to polygons with rounded corners.

這是一個有趣的幾何圖形，根據兩個圓相對旋轉的速度和大小，你可以得到從螺旋形到扭曲形，再到圓角多邊形的各種圖形。

The faster a moon orbits relative to its planet, or the larger the moon's orbit is relative to the planet's, the more spirally the trajectory.

月球相對於其行星的運行速度越快，或者月球軌道相對於行星的運行速度越大，其運行軌跡就越呈螺旋狀。

The slower the moon moves relative to the planet, or the smaller its orbit, the more wobbly or circular the trajectory.

月球相對於行星的移動速度越慢，或其軌道越小，其軌跡就越搖擺或越圓。

Looking at a whole table of these trajectories, loops are in the upper right half here, and wobbles are in this region.

縱觀這些軌跡的整個表格，環形軌跡位於右上半部分，搖擺軌跡位於這個區域。

Orbits that never curve outwards are in the remaining sliver.

永遠不會向外彎曲的軌道位於剩餘的部分。

In our case, the sun is about 400 times farther away than the moon, and the moon orbits the earth around 13.5 times for each trip around the sun, once every 27 days.

就我們而言，太陽的距離是月球的 400 倍，而月球每繞太陽運行 13.5 圈，每 27 天繞地球運行一圈。

The trajectory looks pretty much like a circle.

Here's a zoomed-in view of what the earth and moon's orbits actually look like, exactly to scale, though the earth and moon are not to scale.

這是地球和月球軌道的放大視圖，完全按照比例，不過地球和月球沒有按照比例。

It does look a lot like the earth and moon are orbiting the sun independently, but side by side, just nudging each other in and out as they go.

看起來，地球和月球確實是在獨立地、並排地繞著太陽運行，只是在運行過程中互相碰撞。

In order to start having a wobble, the moon would need to orbit about twice as fast as it does, but at the same distance, or be twice as far from the earth, and still orbit once per month.

為了開始出現擺動，月球的軌道運行速度必須是現在的兩倍，但距離不變，或者距離地球的距離是現在的兩倍，但仍然每月運行一次。

Or the earth would need to be half as far from the sun, and still orbit once per year.

或者地球需要離太陽一半的距離，但仍然每年運行一次。

In order to start spiraling, the moon would need to orbit about 30 times faster at the same distance, or be 30 times farther from the earth, and still orbit once per month.

為了開始螺旋運動，月球需要在相同距離上以大約 30 倍的速度運行，或者距離地球 30 倍遠，並且仍然每月運行一次。

But in the real universe, orbital speed and distance can't be adjusted independently – the farther out an object is, the longer it takes to complete an orbit.

但在真實的宇宙中，軌道速度和距離是無法單獨調整的--物體越遠，完成一個軌道所需的時間就越長。

It turns out the speed matters more, so the moon would have to come closer to earth where it could orbit faster in order to have a wobbly orbit – one that even curves at all outwards away from the sun.

事實證明，速度更重要，所以月球必須更靠近地球，在那裡它的軌道速度才能更快，才能有一個搖擺不定的軌道--一個甚至完全向外彎曲遠離太陽的軌道。

There's a good reason the moon's orbit never curves outwards away from the sun – due to the distances between the earth, moon, and sun, and their masses, it turns out the sun pulls on the moon with almost twice the force that the earth pulls on the moon.

月球軌道從不向外彎曲遠離太陽是有原因的--由於地球、月球和太陽之間的距離以及它們的品質，太陽對月球的拉力幾乎是地球對月球拉力的兩倍。

Technically speaking, the moon is outside of the earth's Chebotarov radius, where the pull from the earth and sun are equivalent.

從技術上講，月球位於地球的切博塔羅夫半徑之外，在這個半徑內，地球和太陽的拉力是相等的。

That means the net force on the moon is always towards the sun, and that's why the moon's trajectory never curves outwards towards the earth.

這意味著月球所受的淨力始終朝向太陽，這也是月球的軌跡從未向地球外側彎曲的原因。

There's never a net force that would pull it that way.

從來沒有一種淨力量會把它拉向那邊。

The force on the moon is always pointing inwards and just gets stronger or weaker over time, depending on whether the earth is pulling together with the sun, or sideways, or against the sun.

月球所受的力始終是向內的，只是隨著時間的推移而變強或變弱，這取決於地球是與太陽一起拉動，還是側向拉動，或是與太陽對抗。

According to net forces, the moon is primarily orbiting the sun, with perturbations from the earth.

根據淨力，月球主要圍繞太陽運行，並受到地球的擾動。

Except, we shouldn't be using net forces, because the earth and moon are moving in a circle around the sun, so we need to take into account centrifugal effects – those effects weaken the sun's relative pull enough that the earth's pull on the moon is stronger.

只不過，我們不應該使用淨力，因為地球和月球是圍繞太陽做圓周運動的，所以我們需要考慮離心效應--這些效應會削弱太陽的相對拉力，從而使地球對月球的拉力更強。

Technically speaking, we say the moon is inside the earth's hill radius, or hill sphere – the zone where, for practical purposes, for objects orbiting along with the earth, the earth's gravitation dominates the sun's.

從技術上講，我們說月球位於地球的山丘半徑或山丘球內--就實際目的而言，對於與地球一起運行的物體來說，地球的引力在這一區域內主宰著太陽的引力。

According to the hill radius, the moon orbits the earth.

根據山丘半徑，月球繞地球運行。

Though technically speaking, the moon doesn't orbit the earth.

雖然從技術上講，月球並不圍繞地球運行。

The moon and the earth both actually orbit the center of mass of the earth-moon system.

月球和地球實際上都圍繞著地月系統的質心運行。

That center of mass is inside the earth, so it's reasonable to say the moon is orbiting the earth, but not by much.

質心在地球內部，所以說月球在繞地球運行是合理的，但差得不多。

If the moon were exactly the same, but just 40% farther away, or if it was in the same place but just 40% more massive, then the earth-moon center of mass would be outside the earth, and the earth and moon might be better described as a double planet rather than a planet and satellite.

如果月球與地球完全相同，只是距離遠了 40%，或者月球位於同一位置，只是品質大了 40%，那麼地球和月球的質心就會在地球之外，地球和月球最好被描述為雙行星，而不是行星和衛星。

Though this would do basically nothing to change the shape of the moon's trajectory around the sun.

不過，這基本上不會改變月球繞太陽運行的軌道形狀。

Ultimately, defining whether something is a satellite versus independently orbiting the sun is actually a really tricky and possibly even futile endeavor.

歸根結底，界定某物是衛星還是獨立繞太陽運行的物體，實際上是一個非常棘手的問題，甚至可能是徒勞無功的。

The best way to put it is that the earth and moon and sun interact in a complex gravitational dance that defies simple classification.

最好的說法是，地球、月亮和太陽在複雜的引力舞蹈中相互作用，無法進行簡單的分類。

On the one hand, it looks like the earth and moon orbit each other while together orbiting the sun, and on the other it looks like the earth and moon orbit the sun side by side, pulling each other back and forth as they go.

一方面，它看起來像是地球和月球在共同圍繞太陽運行的同時相互繞行；另一方面，它看起來像是地球和月球並排圍繞太陽運行，在運行過程中相互來回拉動。

Both are true, from a certain point of view.

從某種角度看，兩者都是對的。

Oh, and I definitely wouldn't rely too heavily on the shapes of trajectories to think about orbits.

哦，我絕對不會過於依賴軌跡的形狀來思考軌道問題。

Trajectories can easily be used to mislead you.

Like, you might imagine that a point on earth's equator draws out loops as the earth spins along its orbit, but because of how fast the earth is moving around the sun, points on the earth's surface don't trace out loops, but, like the moon, trace out something more like a wobbly circle.

比如，你可能會想象地球赤道上的一個點會隨著地球沿著自己的軌道旋轉而畫出圈，但由於地球圍繞太陽運動的速度非常快，地球表面上的點並不會畫出圈，而是像月球一樣，畫出更像一個搖擺不定的圓。

Should we then say that each part of the earth independently orbits the sun?

那麼，我們是否應該說地球的每一部分都獨立地圍繞太陽運行？

It probably won't surprise you to hear that I needed to do a lot of math and programming in the course of making this video.

在製作這段視頻的過程中，我需要做大量的數學計算和編程工作，你可能不會感到驚訝。

I both love it, and of course regular practice keeps my skills sharp.

我既喜歡它，當然定期練習也能讓我的技能保持鋒利。

That type of problem solving is exactly what you get out of Brilliant, this video's sponsor.

這種解決問題的方式正是本視頻的贊助商 Brilliant 所提供的。

You know the deal, they have thousands of interactive lessons in math, data analysis, programming, and AI.

你知道的，他們有數以千計的數學、數據分析、編程和人工智能互動課程。

Each lesson is filled with hands-on problem solving, a method proven to be more effective than just watching videos.

每節課都有動手解決問題的環節，這種方法被證明比單純觀看視頻更有效。

And Brilliant makes it easy to learn from anywhere, right on your phone.

而且，Brilliant 可以讓您隨時隨地在手機上輕鬆學習。

To sign up for Brilliant for free and get 30 days of full access to all of their courses, go to Brilliant.org slash MinutePhysics, scan the QR code on the screen, or click the link in the description.

要免費註冊 Brilliant 並獲得 30 天的全部課程訪問權限，請訪問 Brilliant.org slash MinutePhysics，掃描螢幕上的二維碼，或點擊描述中的鏈接。

You'll also get 20% off an annual Premium subscription for all of Brilliant's content.

訂閱 Brilliant 所有內容的年度高級版還可享受八折優惠。

Again, that's Brilliant.org slash MinutePhysics, and thanks to Brilliant for their support.

再次感謝 Brilliant.org 對 MinutePhysics 的支持。