Spring: Handle East春：斗柄東指
The Dipper climbs high in the northeast with its handle to the east. This is the best season to see the whole shape from Taiwan.
北斗七星爬上東北方高空，斗柄朝東。在台灣，這是看清整個北斗的最好季節。
Astronomy · Lesson 6 · 天文教育 第六課
How Do You Find North at Night?夜裡怎麼找北方？
Find the North Star with the Big Dipper, see why it never moves, and measure your latitude with your fist, from Changhua to the North Pole.
用北斗七星找到北極星，看懂它為什麼不動；再用拳頭量出你的緯度，從彰化一路到北極點。
Big idea · 一句話看懂
Earth's axis points almost straight at the North Star, so it stays still while the other stars circle around it. Its height above the horizon equals your latitude.
地軸幾乎正對著北極星，所以它不動，其他星星都繞著它轉；它離地平線的高度，就等於你所在的緯度。
3D Model · 3D 模型
The Axis, the Star, and Your Latitude 地軸、北極星與緯度
From space: Earth's axis points at the North Star. At the chosen place, the gold arc between the ground's north and the line to the North Star is exactly the same as the latitude arc at Earth's center. Switch places and watch both change together. Your sky: the whole dome of stars turns around the North Star; stars inside the teal circle never set. The chart on the right shows the view facing north, with star trails from the past three hours.
從太空看：地軸指向北極星。在所選的地點，「地平線上的北方」和「指向北極星的線」之間的金色角，跟地心的緯度角一模一樣大；換個地點，兩個角一起變。你的天空：整片星空繞著北極星轉，青色圈裡的星永不落下。右邊是面向北方的星圖，附上過去三小時的星軌。
Drag to turn · 拖曳旋轉 Scroll or pinch to zoom · 滾輪／雙指縮放
This 3D model needs WebGL, which this browser does not support. The sky chart and the cards below still work.
這個瀏覽器不支援 WebGL，無法顯示 3D 模型；星空圖與下方的卡片一樣能用。
- White line: Earth's axis, pointing less than one degree from the North Star
白線：地軸，指向離北極星不到一度的地方 - Green disk: the ground at the chosen place. Red line: north along the ground
綠色圓盤：所選地點的地面；紅線：地平線上的北方 - Gold arcs: the North Star's height at the place and the latitude at Earth's center, always the same angle
金色弧：地點上北極星的高度，與地心的緯度角，永遠一樣大 - Your sky: stars inside the teal circle never set; stars inside the red circle never rise
你的天空：青色圈內的星永不落下，紅色圈內的星永不升起
Not to scale. Earth is drawn far too big; the real North Star is more than 400 light-years away, so the lines toward it from anywhere on Earth are parallel. The dates, Earth's spin, and the positions and brightness of the stars are real.
未按比例：地球畫得太大；真實的北極星在 400 多光年外，所以從地球上任何地方看過去的方向都互相平行。日期、地球自轉、星星的位置與亮度都是真實的。
Stars: Yale Bright Star Catalogue, 5th ed. (Hoffleit & Warren, 1991; public domain), 1,634 stars brighter than magnitude 5. Constellation lines drawn by twrses.org. Planets are not shown.
星表：耶魯亮星星表第五版（公有領域），亮於 5 等的 1,634 顆星。星座連線為本站自繪。圖中不含行星。
Reading · 英文閱讀
6
Unit 6: How Do You Find North at Night?
Long before phones and GPS, travelers found their way at night with a single star. On a clear night in Changhua, face north and look about two and a half fists above the horizon. There you will find a star that is not especially bright, yet it does something no other star does: it stays in the same place all night, while the rest of the sky slowly turns around it. This is Polaris, the North Star. Confucius once compared a good ruler to the pole star, which stays in its place while all the other stars turn toward it.
在手機和衛星定位出現之前很久，旅人靠一顆星在夜裡找路。晴朗的晚上在彰化，面向北方，抬頭看地平線上方大約兩個半拳頭高的地方，會找到一顆不怎麼亮的星。它卻做到了別的星星做不到的事：整晚待在同一個位置，其他的星空則慢慢繞著它轉。這就是北極星。孔子曾把好的君王比作北辰：它安居其位，眾星都環繞著它。
Why does it stay still? Earth spins once a day around its axis, an imaginary line through the North and South Poles. Follow that axis out into space from the North Pole, and it lands less than one degree from Polaris. Like the hub of a spinning wheel, Polaris barely moves, while the other stars travel in circles around it: small circles close to it, and big circles farther away. Facing north, you see them turn counterclockwise, about 15 degrees, or one and a half fists, every hour.
它為什麼不動？地球每天繞著地軸自轉一圈，地軸是一條穿過南北極的假想線。從北極沿著地軸往太空延伸，會落在離北極星不到一度的地方。北極星就像旋轉車輪的軸心，幾乎不動；其他星星則繞著它畫圓：離它近的畫小圓，離它遠的畫大圓。面向北方時，會看到它們逆時針轉動，每小時大約 15 度，也就是一個半拳頭。
Here is the most useful fact of all: the height of the North Star above your horizon equals your latitude. At the North Pole, latitude 90 degrees, Polaris is straight overhead. At the equator, latitude 0, it sits right on the horizon. In Changhua, about 24 degrees north, it is about 24 degrees up. The reason is the curve of Earth: as you travel north, your horizon tilts, and the North Star climbs higher. Sailors used this for centuries. The navigators of Zheng He's fleet measured the North Star's height with wooden boards, in units they called "fingers," to know how far north their ships had sailed.
最有用的一件事是：北極星離地平線的高度，等於你所在的緯度。在北極點（緯度 90 度），北極星就在頭頂正上方；在赤道（緯度 0 度），它貼在地平線上；在彰化（北緯約 24 度），它大約高 24 度。原因是地球是圓的：你往北走，你的地平面跟著傾斜，北極星就爬得越高。水手們用這個方法用了好幾百年。鄭和船隊的領航員拿著木板量北極星的高度，單位叫做「指」，藉此知道船往北航行了多遠。
Polaris is not the brightest star in the sky; dozens of stars outshine it. The easy way to find it is with the Big Dipper, seven bright stars shaped like a ladle. The two stars at the end of the bowl are the Pointers: draw a line through them and go about five times the distance between them, and you arrive at Polaris. In Taiwan, the Big Dipper sinks below the northern horizon on autumn and winter evenings. Then use Cassiopeia, a bright W on the other side of Polaris. The North Star sits about halfway between the two.
北極星並不是天上最亮的星，比它亮的星有好幾十顆。要找它，最簡單的方法是用北斗七星——七顆排成長柄勺形狀的亮星。斗杓末端的兩顆星叫「指極星」：把它們連成一線，往外延長大約兩星距離的五倍，就到北極星了。在台灣，秋冬的晚上北斗七星會沉到北方地平線下；這時改用仙后座——北極星另一邊那個明亮的 W。北極星大約就在兩者的中間。
The Big Dipper is also a clock and a calendar. It swings around Polaris once a day, and it sits a little farther around at the same hour each night as the seasons change. An old Chinese saying tells where its handle points in the early evening: east in spring, south in summer, west in autumn, and north in winter. From Changhua, the winter position is below the horizon, because at our latitude the Big Dipper sets for part of each night. The 3D model lets you test the saying on any date.
北斗七星也是時鐘和日曆。它每天繞北極星轉一圈，而且隨著季節推移，每晚同一個時刻都會多轉一點點。中國古話說傍晚時斗柄的方向：春天指東、夏天指南、秋天指西、冬天指北。從彰化看，冬天那個位置在地平線下，因為在我們的緯度，北斗七星每晚都有一段時間會落下。3D 模型可以讓你在任何日期驗證這句話。
The North Star has not always been the North Star. Earth's axis wobbles slowly, like a spinning top, and traces a big circle in the sky every 26,000 years. When the pyramids of Egypt were built, the pole star was Thuban, in the constellation Draco. In Confucius's time, Polaris was about 15 degrees from the pole, so the pole star he admired was a different star. Polaris will come closest to the pole around the year 2100, and in about 12,000 years bright Vega will take its turn. South of the equator, Polaris drops out of sight, and people use the Southern Cross to find south instead.
北極星並不是一直都當北極星。地軸像陀螺一樣緩慢地晃動，每 26,000 年在天上畫一個大圓。埃及建金字塔的時候，北極星是天龍座的右樞（Thuban）。孔子的時代，今天的北極星離天極大約 15 度，所以他讚嘆的北辰是另一顆星。北極星大約在 2100 年最接近天極；再過大約 12,000 年，明亮的織女星就會接班。到了赤道以南，北極星沉到地平線下看不到，人們改用南十字座找南方。
Read aloud · 課文朗讀
Questions · 閱讀理解
Why does the North Star stay in the same place all night?
Earth's axis points almost straight at it, so as Earth spins, the North Star barely moves while the other stars circle around it.
How high is the North Star above the horizon in Changhua, and why?
About 24 degrees, because the North Star's height equals your latitude, and Changhua is about 24 degrees north.
How can you find the North Star when the Big Dipper is below the horizon?
Use Cassiopeia, the W on the other side of the North Star. Polaris sits about halfway between the W and the Big Dipper.
Words & Phrases · 生字及片語
horizon(n.)地平線We watched the sun sink below the horizon.我們看著太陽沉到地平線下。latitude(n.)緯度Taipei and Miami are at almost the same latitude.台北和邁阿密的緯度幾乎一樣。overhead(adv.)在頭頂上A plane flew overhead during recess.下課時間，一架飛機從頭頂飛過。hub(n.)（輪子的）軸心；中心The spokes of a bike wheel meet at the hub.腳踏車輪的輪輻在軸心交會。counterclockwise(adv.)逆時針地Turn the lid counterclockwise to open the jar.把蓋子逆時針轉就能打開罐子。ladle(n.)長柄勺Grandma used a ladle to serve the soup.奶奶用長柄勺盛湯。navigator(n.)領航員The navigator checked the map before the ship left port.船出港前，領航員先看了地圖。wobble(v.)搖晃；晃動The table wobbles because one leg is too short.這張桌子會晃，因為有一隻腳太短。
Quick Check · 小測驗
1. Why do the other stars seem to circle around the North Star?
2. At the equator, where is the North Star?
3. Which stars point to the North Star?
4. Is the North Star the brightest star in the night sky?
5. Why will a different star be the North Star in the future?
The Dipper's Handle · 斗柄指向
A clock and a calendar in the north 北方天空的時鐘與日曆
An old Chinese book, the Heguanzi, says: when the handle points east, it is spring everywhere; south, summer; west, autumn; north, winter. It describes early evening. The cards show 8 p.m. in Changhua.
《鶡冠子》：「斗柄東指，天下皆春；斗柄南指，天下皆夏；斗柄西指，天下皆秋；斗柄北指，天下皆冬。」說的是黃昏時的方向；卡片是彰化晚上八點的樣子。
Summer: Handle South夏：斗柄南指
The Dipper hangs high in the northwest, its handle pointing up toward the south. Follow the curve of the handle to orange Arcturus.
北斗七星高掛西北方，斗柄往上指向南方。順著斗柄的弧線，就能找到橙色的大角星。
Autumn: Handle West秋：斗柄西指
The Dipper lies low in the northwest with its handle to the west, and slips below the horizon soon after. Cassiopeia's W takes over.
北斗七星低低地躺在西北方，斗柄朝西，不久就沉到地平線下；換仙后座的 W 接班。
Winter: Handle North冬：斗柄北指
In Changhua the handle, pointing down toward the north, is below the horizon at this hour. Far to the north, in Tromsø, the Dipper never sets.
在彰化，這個時刻朝下指北的斗柄在地平線下；到了遙遠的特羅姆瑟，北斗七星永遠不會落下。
Around the World · 世界各地
Your Latitude Is Written in the Sky 緯度寫在天上
The North Star's height equals your latitude, so this table is also a list of latitudes. One fist at arm's length is about 10 degrees.
北極星的高度等於緯度，所以這張表同時也是一張緯度表。手臂伸直握拳，一個拳頭大約 10 度。
| Place · 地點 | Latitude · 緯度 | North Star · 北極星 | What you see · 看到什麼 |
|---|---|---|---|
| Changhua彰化 | 24.1°N | 24°, 2½ fists約兩個半拳頭 | Low in the north. The Big Dipper sets for part of every night.低掛北方；北斗七星每晚都有一段時間會落下。 |
| Taipei台北 | 25.0°N | 25°, 2½ fists約兩個半拳頭 | Almost the same as Changhua: all of Taiwan is between 22° and 25°.和彰化幾乎一樣：整個台灣都在北緯 22° 到 25° 之間。 |
| Kenting墾丁 | 21.9°N | 22°, 2 fists約兩個拳頭 | Far enough south that the Southern Cross peeks above the sea on spring nights.夠南，春天夜裡南十字座會從海面上露出來。 |
| Singapore新加坡 | 1.4°N | 1°, on the horizon貼在地平線上 | Almost never seen; haze near the horizon hides it.幾乎看不到，地平線附近的霧氣會把它遮住。 |
| Tokyo東京 | 35.7°N | 36°, 3½ fists約三個半拳頭 | Higher than in Taiwan; the Big Dipper still sets briefly.比台灣高；北斗七星仍會短暫落下。 |
| Boston波士頓 | 42.4°N | 42°, 4 fists約四個拳頭 | The Big Dipper never sets here; it circles the North Star all night.北斗七星在這裡永不落下，整晚繞著北極星轉。 |
| Tromsø, Norway挪威特羅姆瑟 | 69.6°N | 70°, 7 fists約七個拳頭 | High in the sky. Cassiopeia and the Dipper wheel around it without setting.高高在上；仙后座和北斗七星繞著它轉，從不落下。 |
| North Pole北極點 | 90°N | 90°, overhead在頭頂正上方 | Every star circles level with the horizon; nothing rises or sets.每顆星都和地平線平行地繞圈，不升也不落。 |
| Sydney雪梨 | 33.9°S | Below the horizon在地平線下 | No North Star at all. Use the Southern Cross to find south.完全看不到北極星，改用南十字座找南方。 |
Tonight · 今晚
Find North Tonight in Changhua 今晚在彰化找北方
Calculated in your browser for 8 p.m. today. Find a spot with a dark view to the north, away from streetlights, and give your eyes ten minutes to adjust.
依今天晚上八點，在你的瀏覽器裡現算。找一個北方沒有路燈、看得到低空的地方，讓眼睛適應黑暗十分鐘。
Calculating… · 計算中…
East and West · 東西方的星空
Finding North, East and West 東西方怎麼找北方
People everywhere have used the still point of the northern sky to rule, to farm, and to find their way.
世界各地的人，都拿北方天空那個不動的點來治國、務農與認路。
北辰 · The Pole Star
A Ruler Like the Pole Star譬如北辰
為政以德，譬如北辰，居其所而眾星共之。——《論語·為政》"Govern by virtue, like the pole star, which stays in its place while all the other stars turn toward it." (The Analects)
Confucius saw the pole as the still center of the turning sky, the way a good ruler steadies a country. In his day Polaris was about 15 degrees from the pole, so the star he meant was a different one. The idea has outlasted the star.
孔子把天極看成旋轉星空中不動的中心，就像好的君王穩住一個國家。他那個時代，今天的北極星離天極約 15 度，所以他說的北辰是另一顆星——星星換了，這個道理還在。
斗柄 · The Handle
A Calendar in the Sky斗柄指四季
The Heguanzi, a book more than 2,000 years old, tells the seasons by where the Dipper's handle points at dusk. The seven stars have Chinese names too: Tianshu, Tianxuan, Tianji, Tianquan, Yuheng, Kaiyang, and Yaoguang. The first two are the Pointers.
兩千多年前的《鶡冠子》用黃昏時斗柄的方向分辨四季。北斗七星各有名字：天樞、天璇、天璣、天權、玉衡、開陽、搖光；天樞、天璇就是指極星。
牽星 · Star Boards
Zheng He's Star Boards鄭和的牽星板
Six hundred years ago, the navigators of Zheng He's fleet held wooden boards of different sizes at arm's length and measured the North Star's height in "fingers." Their charts noted how many fingers high it stood at each port. Near the equator, where the North Star sank too low, they measured the Southern Cross, which they called the Lantern Frame Stars.
六百年前，鄭和船隊的領航員把大小不同的木板伸直手臂舉起，用「指」量北極星的高度；航海圖上記著每個港口北極星有幾指高。到了赤道附近北極星太低，他們就改量南十字座，當時叫「燈籠骨星」。
Drinking Gourd · 飲水葫蘆
Follow the Drinking Gourd跟著飲水葫蘆走
A well-known American folk song, "Follow the Drinking Gourd," tells of people escaping slavery who followed the Big Dipper north toward freedom. Anywhere in the Northern Hemisphere, the Dipper leads to the North Star.
美國有一首很有名的民謠〈跟著飲水葫蘆走〉，唱的是逃離奴隸制度的人，跟著北斗七星（飲水葫蘆）一路往北走向自由。在北半球任何地方，北斗七星都能帶你找到北極星。
Myth vs. Fact · 常見迷思
Four things people get wrong 四個常見的誤會
✗ Myth · 迷思The North Star is the brightest star in the sky.北極星是天上最亮的星。
✓ Fact · 事實Not even close. Dozens of stars are brighter, and Sirius is the brightest of all. Polaris is special because of where it is, not how bright it is.差得遠。比它亮的星有好幾十顆，最亮的是天狼星。北極星特別，是因為它的位置，不是因為它的亮度。
✗ Myth · 迷思The North Star is high overhead.北極星在頭頂正上方。
✓ Fact · 事實Only at the North Pole. Its height equals your latitude, so in Changhua it is only about 24 degrees up, two and a half fists. Look low in the north, not straight up.只有在北極點才是。它的高度等於緯度，所以在彰化只有大約 24 度高，兩個半拳頭。要往北方低空找，不是往頭頂看。
✗ Myth · 迷思You can see the North Star from anywhere on Earth.地球上任何地方都看得到北極星。
✓ Fact · 事實South of the equator it is below the horizon. People in Australia, South Africa, or Argentina use the Southern Cross to find south instead.赤道以南它在地平線下。澳洲、南非、阿根廷的人改用南十字座找南方。
✗ Myth · 迷思The North Star never moves and has always been the North Star.北極星完全不動，而且永遠都是北極星。
✓ Fact · 事實It circles the pole in a tiny ring about as wide as two and a half full Moons. Over thousands of years, Earth's wobble changes which star is near the pole: Thuban for the pyramid builders, Vega in about 12,000 years.它其實繞著天極畫一個小圈，寬度大約是兩個半滿月。幾千年下來，地軸的晃動會換掉靠近天極的星：建金字塔時是右樞，大約一萬兩千年後是織女星。
Remember It · 記憶口訣
Never lose north 一句話找到北方
Height equals latitude北極星高度＝緯度
Measure the North Star's height and you know how far north you are. Changhua: about 24 degrees, two and a half fists.
量出北極星的高度，就知道自己在北緯幾度。彰化：大約 24 度，兩個半拳頭。
Five times the Pointers指極星延長五倍
From Merak through Dubhe, the two stars at the end of the Dipper's bowl, go about five times their distance to reach Polaris.
從天璇經過天樞（斗杓末端的兩顆星），往外延長約五倍的距離，就到北極星。
Between the Dipper and the W北斗與 W 的正中間
Polaris sits about halfway between the Big Dipper and Cassiopeia. When one is low, the other is high.
北極星大約在北斗七星和仙后座中間；一個低的時候，另一個就高。
Counterclockwise, a fist and a half an hour逆時針，一小時一個半拳頭
Facing north, the stars turn counterclockwise around Polaris, 15 degrees an hour. In six hours the Big Dipper turns a quarter of the way around.
面向北方，星星繞著北極星逆時針轉，一小時 15 度；六小時後，北斗七星就轉了四分之一圈。
Classroom Activity 1 · 課堂活動一
Measure the North Star with a Protractor 用量角器量北極星
You need · 準備材料
- A protractor with a small hole at the center of its straight edge一個直邊中央有小孔的量角器
- A drinking straw and some tape一根吸管和膠帶
- A 30-centimeter string with a small weight, such as an eraser or a washer一條 30 公分的細繩，綁上小重物（橡皮擦或墊圈）
Steps · 步驟
- Tape the straw along the straight edge of the protractor.把吸管貼在量角器的直邊上。
- Tie the string through the hole at the center of the straight edge so the weight hangs freely.把細繩穿過直邊中央的小孔綁好，讓重物自然垂下。
- Look through the straw at the top of a flagpole. Pinch the string against the protractor and read where it crosses. The difference between that number and 90 is the height of the flagpole top in degrees.透過吸管看旗桿頂端，用手指把細繩按在量角器上，讀出細繩經過的刻度；它和 90 的差，就是旗桿頂端的高度（度）。
- On a clear night, sight the North Star the same way. You should get about 24 degrees, Changhua's latitude.晴朗的晚上用同樣的方法瞄準北極星，應該會量到大約 24 度——正是彰化的緯度。
- Check with your fist: two and a half fists should match your number.再用拳頭驗證：兩個半拳頭應該和你量到的數字差不多。
Teaching tip: this is the same idea as Zheng He's star boards and a sailor's sextant. Collect the whole class's numbers and average them; the average usually lands within a few degrees of 24.
教學提示：這和鄭和的牽星板、水手的六分儀是同一個道理。把全班量到的數字平均，通常會落在 24 度上下幾度以內。
Classroom Activity 2 · 課堂活動二
An Umbrella Sky 雨傘星空
You need · 準備材料
- A plain, dark umbrella一把素色的深色雨傘
- White stickers or chalk白色貼紙或粉筆
- The facing-north chart in the 3D model3D 模型旁「面向北方」的星圖
Steps · 步驟
- Open the umbrella. The center, where the tip is, stands for the North Star.打開雨傘，傘尖所在的中心點代表北極星。
- On the inside of the umbrella, stick the seven stars of the Big Dipper on one side of the center and the W of Cassiopeia on the opposite side.在傘的內側，把北斗七星貼在中心的一邊，仙后座的 W 貼在正對面。
- Face north and hold the umbrella over your head so the tip points about 24 degrees above the northern horizon, toward the real North Star.面向北方，把傘舉在頭上，讓傘尖指向北方地平線上方約 24 度，也就是真正的北極星方向。
- Turn the umbrella slowly counterclockwise. The Dipper and the W take turns rising high and dipping toward the ground, and the center never moves.把傘慢慢逆時針轉：北斗和 W 輪流升高、又輪流低到接近地面，只有中心點不動。
- Tip the umbrella straight up: now you are at the North Pole, and nothing sets. Tip it down to the horizon: now you are at the equator.把傘尖轉到正上方：你到了北極點，什麼都不會落下。把傘尖放低到地平線：你到了赤道。
Teaching tip: afterward, open the Your sky view in the 3D model and switch from Changhua to Tromsø and the North Pole. The teal "never sets" circle grows exactly as the umbrella showed.
教學提示：做完後打開 3D 模型的「你的天空」，把地點從彰化切到特羅姆瑟、北極點，會看到青色的「永不落下」圈正像雨傘演示的一樣越變越大。