Your Eyes你的眼睛
0.5°about half a degree · 約半度
Low or high, the Moon is about the size of a pea at arm's length. The gold ring proves it.
不論低或高，月亮都差不多是手臂伸直時一顆豌豆的大小，金色的量月環可以證明。
Astronomy · Lesson 15 · 天文教育 第15課
Why Does the Moon Look Bigger Near the Horizon?月亮在地平線附近為什麼看起來特別大？
The rising Moon looks huge, yet it covers no more sky than a pea at arm's length, and it is actually a tiny bit smaller. Watch tonight's Moon rise over Changhua at its true size and find out where the trick happens.
剛升起的月亮看起來好大，其實它在天上占的範圍不比手臂伸直時的一顆豌豆大，甚至還稍微小一點。照真實大小看今晚的月亮從彰化升起，找出錯覺發生在哪裡。
Big idea · 一句話看懂
The Moon near the horizon is not really bigger. It covers the same tiny angle, about half a degree, whether it is low or high; the big rising Moon is an illusion made by our brain.
地平線附近的月亮並沒有真的變大。不論低或高，它在天上占的角度都一樣，大約半度；剛升起時那顆大月亮，是大腦製造的錯覺。
3D Model · 3D 模型
Watch the Moon Rise at Its True Size 照真實大小看月亮升起
You are standing in Changhua as tonight's Moon rises in the east, drawn at its true size. Press Play and watch it climb. The gold measuring ring never changes size, yet it fits the Moon all night. Switch to Telephoto lens to see how photographers make giant Moons behind towers, and to From space to see why the rising Moon is a little farther from you. On the right, judge two Moons that are exactly the same size.
你站在彰化，今晚的月亮正從東方升起，照真實大小畫出來。按「播放」，看它慢慢爬高。金色的量月環大小從頭到尾不變，卻整晚都剛好套住月亮。切換到「長鏡頭」，看攝影師怎麼拍出塔後面的巨大月亮；切換到「從太空看」，看看為什麼剛升起的月亮離你稍微遠一點。右邊兩個月亮一樣大，你看起來呢？
Drag to look around · 拖曳轉頭看四周
This 3D model needs WebGL, which this browser does not support. The two-Moon picture and tonight's moonrise still work.
這個瀏覽器不支援 WebGL，無法顯示 3D 模型；兩個月亮的圖與今晚的月出一樣能用。
- Gold ring: a fixed-size ring that fits the Moon at moonrise, and still fits it hours later
金色環：大小固定的量月環，月出時剛好套住月亮，幾小時後一樣剛好 - Tower: 42 meters tall and 2 kilometers away, placed where the Moon rises
塔：高 42 公尺、在 2 公里外，放在月亮升起的方向 - From space: gold line from you to the Moon, dashed line from Earth's center
從太空看：金線是你到月亮，虛線是地心到月亮 - The Moon's position and size are real for each night shown; in From space, the distance is squeezed five times
月亮的位置與大小是那一夜的真實數據；「從太空看」的距離壓縮了 5 倍
In the Your eyes view, the screen shows about 66 degrees of sky from side to side, close to what you notice without turning your head, so the Moon looks as small on screen as it really is. The telephoto lens shows only 2.5 degrees. The Moon's distance from you and its size are calculated for Changhua at each moment.
「眼睛」視角的畫面左右約 66 度，接近不轉頭時注意得到的範圍，所以月亮在螢幕上就和真實一樣小。「長鏡頭」只看 2.5 度。月亮離你的距離與大小，都是照彰化當下的位置算的。
Moon position and distance: J. Meeus, Astronomical Algorithms, chapter 47. Earth map: Natural Earth (public domain). Stars: Yale Bright Star Catalogue, 5th ed. (public domain). The houses, hills, and tower are drawn scenery.
月球位置與距離：Meeus《天文演算法》第 47 章。地球地圖：Natural Earth（公有領域）。星表：耶魯亮星星表第五版（公有領域）。房子、山與塔是繪製的布景。
Reading · 英文閱讀
15
Unit 15: Why Does the Moon Look Bigger Near the Horizon?
Have you ever seen a huge, golden full Moon rising behind the rooftops? A few hours later, high in the sky, it looks small and ordinary. Almost everyone sees this, but the Moon has not shrunk. This is the Moon illusion, one of the oldest puzzles about the sky.
你看過一輪又大又金黃的滿月，從屋頂後面升起嗎？幾個小時後，它高掛天上，看起來又小又普通。幾乎每個人都有這種經驗，但月亮並沒有縮小。這叫「月亮錯覺」，是關於天空最古老的謎題之一。
You can test it yourself. Hold a pea or a pencil eraser at arm's length and close one eye. It just covers the Moon, whether the Moon is near the horizon or high overhead. The Moon always takes up about half a degree of the sky. In fact, the rising Moon is a tiny bit smaller, because it is farther from you: when the Moon is overhead, you are closer to it by about 6,400 kilometers, the distance from Earth's surface to its center.
你可以自己測試。把一顆豌豆或鉛筆上的橡皮擦拿在手臂伸直的地方，閉上一隻眼睛：不論月亮在地平線附近還是高掛頭頂，它都剛好遮住月亮。月亮在天上永遠只占大約半度。其實剛升起的月亮還稍微小一點，因為那時它離你比較遠：月亮在頭頂時，你離它近了大約 6,400 公里，也就是從地表到地心的距離。
So the illusion happens in our brain, not in the sky. Scientists still debate exactly how it works. One idea is that the brain treats the sky like a flattened dome, so the horizon seems farther away than the point overhead, and a Moon that seems farther away but covers the same angle must be bigger. Another idea is that trees and buildings near the horizon make the Moon appear large by comparison. Whatever the reason, you can fool the trick: look at the rising Moon through a paper tube, or bend over and look at it upside down between your legs, and it suddenly looks smaller.
所以錯覺發生在大腦裡，不在天上。科學家到現在還在爭論它到底怎麼運作。一種說法是：大腦把天空當成一個壓扁的圓頂，覺得地平線比頭頂遠；一個看起來比較遠、卻占同樣角度的月亮，一定比較大。另一種說法是：地平線附近的樹和房子，讓月亮比較起來顯得很大。不論原因是什麼，你都可以破解這個把戲：用紙筒看剛升起的月亮，或彎下腰從兩腿之間倒著看，它馬上就變小了。
The Moon's true size in the sky does change, just slowly. Its orbit is an oval, so its distance changes from about 356,000 to 407,000 kilometers. A full Moon near its closest point, often called a supermoon, looks about 14 percent wider than one at its farthest, a micromoon. The difference is real but hard to notice, because there is no second Moon in the sky to compare it with.
月亮在天上真正的大小確實會變，只是變得很慢。它的軌道是橢圓，離地球的距離從大約 35.6 萬到 40.7 萬公里不等。最接近時的滿月常被叫做「超級月亮」，看起來比最遠時的「微型月亮」寬約 14%。這個差別是真的，但很難察覺，因為天上沒有第二個月亮可以比。
More than 2,000 years ago, a Chinese story in the Liezi told of two children arguing about the Sun. One said the morning Sun looks as big as a carriage cover but the noon Sun only as big as a plate, so it must be closer in the morning. The other said the noon Sun feels as hot as boiling water, so it must be closer at noon. Even Confucius could not decide who was right. About a thousand years ago, the Arab scientist Ibn al-Haytham explained that the Sun and Moon only seem larger near the horizon because of the way we judge distance.
兩千多年前，《列子》裡有一個故事：兩個小孩在爭論太陽。一個說，早上的太陽大得像車蓋，中午卻只像盤子，所以早上的太陽比較近；另一個說，中午的太陽熱得像滾水，所以中午比較近。連孔子都判斷不了誰對。大約一千年前，阿拉伯科學家海什木解釋：太陽和月亮在地平線附近只是「看起來」比較大，原因在於我們怎麼判斷距離。
What about photos of a giant Moon behind a lighthouse? They are taken from far away with a long telephoto lens, which makes both the Moon and the lighthouse look large. With your own eyes, the Moon is always about the size of a pea at arm's length. Look below for tonight's moonrise over Changhua and this year's biggest and smallest full Moons.
那些燈塔後面巨大月亮的照片呢？它們是從很遠的地方、用長長的望遠鏡頭拍的，月亮和燈塔一起被放大了。用你自己的眼睛看，月亮永遠差不多是手臂伸直時一顆豌豆的大小。看看下面：今晚彰化的月出，以及今年最大、最小的滿月。
Read aloud · 課文朗讀
Questions · 閱讀理解
Is the Moon really bigger when it is near the horizon?
No. It covers the same angle, about half a degree, and the rising Moon is actually a tiny bit smaller because it is farther from you. The big rising Moon is an illusion made by the brain.
How can you test the Moon illusion yourself?
Hold a pea or a pencil eraser at arm's length and see that it covers the Moon whether the Moon is low or high. You can also look through a paper tube, or upside down between your legs.
What is a supermoon, and how much bigger does it look?
A full Moon near its closest point to Earth. It looks about 14 percent wider than a full Moon at its farthest point, a micromoon.
Words & Phrases · 生字及片語
illusion(n.)錯覺；幻覺The magician's trick was only an illusion.魔術師的把戲只是一種錯覺。appear(v.)看起來；出現The road appears wet on hot days, but it is dry.大熱天時路面看起來是濕的，其實是乾的。brain(n.)大腦Your brain needs sleep to stay healthy.你的大腦需要睡眠才能保持健康。fool(v.)愚弄；騙過The fake spider fooled my little brother.那隻假蜘蛛騙過了我弟弟。arm's length(n.)手臂伸直的距離Hold the map at arm's length so you can read it.把地圖拿遠到手臂伸直的地方，你才看得清楚。debate(v.)爭論；辯論The students debated whether school should start later.學生們辯論學校該不該晚一點上課。pea(n.)豌豆There was one pea left on my plate.我的盤子裡還剩一顆豌豆。lens(n.)鏡頭；透鏡She cleaned the camera lens before taking the photo.她拍照前先把相機鏡頭擦乾淨。
Quick Check · 小測驗
1. When the Moon is near the horizon, it really...
2. What can just cover the Moon when held at arm's length?
3. Where does the Moon illusion happen?
4. What is a supermoon?
5. In the old Chinese story, who could not settle the two children's argument about the Sun?
Four Ways to Look · 四種看法
Is the Moon really bigger? 月亮真的變大了嗎？
Press See it in 3D to switch the model's view.
按「在模型中看」，模型就會切換視角。
A Telephoto Lens長鏡頭
2.5°of sky across the picture · 畫面只拍 2.5 度
Photographers stand kilometers away and zoom in, so the Moon and a tower both fill the frame. That is how the famous giant-Moon photos are made.
攝影師站在幾公里外拉近鏡頭，月亮和塔一起塞滿畫面——有名的巨大月亮照片就是這樣拍的。
From Space從太空看
6,400 kmfarther when rising · 剛升起時多遠了
When the Moon rises, you are on the side of Earth, almost one Earth radius farther from it than when it is overhead.
月亮升起時，你在地球的側邊，比月亮在頭頂時遠了將近一個地球半徑。
Super and Micro超級與微型
14%wider at the closest full Moon · 最近的滿月寬了這麼多
The Moon's real size in the sky changes slowly with its distance, from about 356,000 to 407,000 kilometers away.
月亮在天上真正的大小，會隨距離（約 35.6 萬到 40.7 萬公里）慢慢變化。
Tonight · 今晚
Tonight's Moonrise and This Year's Full Moons 今晚的月出與今年的滿月
When the Moon rises over Changhua tonight, how high it climbs, and how its size changes, plus every full Moon in the coming year drawn to scale. Everything is calculated in your browser for today's date.
今晚月亮什麼時候從彰化升起、爬多高、大小怎麼變，以及未來一年每一次滿月（照比例畫）。全部在瀏覽器裡照今天的日期現算。
Calculating… · 計算中…
East and West · 東西方的星空
An Old, Old Puzzle 一個很老很老的謎
People in China, Greece, and the Arab world all noticed that the Sun and Moon look bigger near the horizon, and argued about why.
中國、希臘和阿拉伯世界的人都注意到，太陽和月亮在地平線附近看起來比較大，也都爭論過原因。
列子 · Liezi
Two Children Argue About the Sun兩小兒辯日
日初出大如車蓋，及日中則如盤盂，此不為遠者小而近者大乎？——《列子．湯問》"When the Sun first rises, it is as big as a carriage cover; at noon it is only as big as a plate. Isn't that because far things look small and near things look big?" (Liezi)
The other child answered that the noon Sun feels hotter, so it must be nearer. Confucius could not decide, and the children laughed: "Who says you know so much?" Both were wrong: the Sun is the same size all day, and noon is hotter because sunlight comes down more directly (Lesson 3).
另一個小孩說中午的太陽比較熱，所以比較近。孔子判斷不了，兩個小孩笑他：「孰為汝多知乎？」其實兩人都錯了：太陽一整天一樣大，中午比較熱是因為陽光照得比較直（第三課）。
Ibn al-Haytham
It Is in the Mind錯覺在心裡
About a thousand years ago, Ibn al-Haytham, who studied light and vision in Cairo, wrote that the Moon only seems larger near the horizon because we judge it to be farther away, across the land. Many scientists still build on his idea.
大約一千年前，在開羅研究光與視覺的海什木寫道：月亮在地平線附近只是「看起來」比較大，因為我們隔著大地，判斷它比較遠。今天許多科學家仍延續他的想法。
超級月亮 · Supermoon
A Name from Astrology名字來自占星
The word supermoon was made up in 1979 by an astrologer, not an astronomer. Astronomers call it a full Moon at perigee, the closest point of its orbit. The biggest full Moon of 2026 falls on December 24.
「超級月亮」這個詞是 1979 年一位占星師發明的，不是天文學家。天文學家叫它「近地點滿月」。2026 年最大的滿月在 12 月 24 日。
張九齡 · Zhang Jiuling
A Moon Rising over the Sea海上生明月
海上生明月，天涯共此時。——張九齡〈望月懷遠〉"A bright Moon rises over the sea; at the ends of the earth, we share this moment." (Zhang Jiuling)
Poets often wrote about the Moon rising over the sea or the mountains, just when the illusion is strongest. Everyone sharing that Moon sees it at the same half degree.
詩人常寫月亮從海上、山後升起——正是錯覺最強的時候。天涯海角共看這輪明月，每個人看到的都是同樣的半度。
Myth vs. Fact · 常見迷思
Four things people get wrong 四個常見的誤會
✗ Myth · 迷思The air near the horizon magnifies the Moon like a lens.地平線附近的空氣像透鏡一樣把月亮放大了。
✓ Fact · 事實The air does bend moonlight near the horizon, but it squashes the Moon a little from top to bottom instead of enlarging it.空氣確實會把地平線附近的月光折射，但效果是把月亮上下壓扁一點點，而不是放大。
✗ Myth · 迷思The rising Moon is closer to us.剛升起的月亮離我們比較近。
✓ Fact · 事實It is farther away. When it is overhead, you are about 6,400 kilometers closer to it, so the high Moon is actually about 1.5 percent bigger.其實比較遠。月亮在頭頂時，你離它近了約 6,400 公里，所以高空的月亮反而大了約 1.5%。
✗ Myth · 迷思Photos of a giant Moon behind a building show what your eyes would see.大樓後面巨大月亮的照片，就是眼睛看到的樣子。
✓ Fact · 事實Those photos use a long telephoto lens from far away. To your eyes, the Moon would look about the size of a pea at arm's length.那些照片是在很遠的地方用長鏡頭拍的。用眼睛看，月亮大約只有手臂伸直時一顆豌豆大。
✗ Myth · 迷思A supermoon looks twice as big as a normal full Moon.超級月亮看起來是一般滿月的兩倍大。
✓ Fact · 事實The biggest full Moon is only about 14 percent wider than the smallest. Most people cannot tell the difference without measuring.最大的滿月只比最小的寬約 14%，不測量的話，大多數人看不出差別。
Remember It · 記憶口訣
Don't be fooled 一句話破解月亮錯覺
A pea at arm's length手臂伸直一顆豌豆
That is how big the Moon looks, low or high.
不論低或高，月亮就是這麼大。
In the brain, not in the sky錯覺在腦裡，不在天上
The Moon does not change; our judgment of its size does.
月亮沒變，變的是我們對它大小的判斷。
Tube it紙筒一看就破功
Look through a paper tube, and the giant rising Moon shrinks back to normal.
用紙筒看，剛升起的大月亮馬上變回正常大小。
14% wider, 30% brighter寬 14%、亮 30%
A supermoon compared with a micromoon: real, but small.
超級月亮和微型月亮相比：差別是真的，但很小。
Classroom Activity 1 · 課堂活動一
Measure the Moon with a Card 用卡片量月亮
You need · 準備材料
- A piece of stiff card with holes of 4, 5, 6, and 7 millimeters punched in a row一張硬卡紙，打一排 4、5、6、7 毫米的洞
- A string 60 centimeters long taped to the card, to hold it the same distance every time一條 60 公分的繩子貼在卡紙上，讓每次都拿在一樣遠的地方
- The moonrise time from this page and a worksheet本頁的月出時間和一張學習單
Steps · 步驟
- Soon after moonrise, hold the end of the string to your cheek and the card at the other end. Find the smallest hole that the whole Moon fits inside.月出後不久，把繩子一端貼著臉頰、另一端拿著卡紙，找出能把整個月亮裝進去的最小的洞。
- Write down the hole size and how big the Moon looked to you, from 1 (small) to 5 (huge).記下洞的大小，以及月亮看起來有多大（1 很小到 5 很大）。
- Two or three hours later, measure again when the Moon is high.兩、三小時後，月亮升高了，再量一次。
- Compare: the hole stayed the same, but did your 1-to-5 score change?比較：洞的大小沒變，但你的 1–5 分數變了嗎？
Teaching tip: a 5-millimeter hole at 60 centimeters is about half a degree, the size of the Moon.
教學提示：60 公分外的 5 毫米洞，大約就是半度，和月亮一樣大。
Classroom Activity 2 · 課堂活動二
Fool Your Brain 騙過你的大腦
You need · 準備材料
- A paper tube, such as an empty paper-towel roll一個紙筒，例如用完的廚房紙巾捲軸
- The two-Moon picture next to the 3D model3D 模型旁邊的兩個月亮圖
- A partner and a rising Moon (or the picture, in class)一位夥伴，以及剛升起的月亮（教室裡就用圖）
Steps · 步驟
- In class, look at the two-Moon picture. Which Moon looks bigger? Write down your answer before measuring.在教室先看兩個月亮的圖：哪一個看起來比較大？測量之前先寫下答案。
- Turn on Show the ruler. Were you fooled?按「顯示量尺」：你被騙了嗎？
- At home, look at the rising Moon with both eyes, then through the paper tube. Does it shrink?回家後，先用雙眼看剛升起的月亮，再用紙筒看：它變小了嗎？
- Try the upside-down trick: bend over and look between your legs. Report back to the class.試試倒著看：彎下腰從兩腿之間看月亮，回到班上分享。
Safety tip: watch the rising Moon from a safe place with an adult, away from roads.
安全提示：和大人一起在安全、遠離馬路的地方看月出。