太陽の南中高度と影の長さシミュレータNoon Sun Altitude and Shadow Length

1予想しよう（触る前に）Predict (before you touch anything)

1. 同じ場所に立てた高さ1mの棒の正午の影は、夏至の日と冬至の日でどちらが長いと思いますか。For a 1 m pole standing in the same place, do you think its noon shadow is longer on the summer solstice or on the winter solstice?💡 夏と冬で、正午の太陽が空のどのくらいの高さに見えるかを思い出してみましょう。Think about how high in the sky the noon Sun appears in summer and in winter.
2. もっと北の地域(緯度の高い場所)に行くと、同じ日の南中高度はどうなると思いますか。If you go farther north (to a higher latitude), what do you think happens to the noon altitude on the same day?💡 地球は丸いので、北へ行くほど地面の傾きと太陽光の向きの関係が変わります。Earth is round, so as you go north, the angle between the ground and the incoming sunlight changes.

2動かしてみようTry it

1. 「一時停止」ボタンを押してアニメーションを止め、「春分」ボタンを押す(緯度は北緯35.0°のまま)。数値欄の「南中高度 h」と「影の長さ」を記録する。Press the "Pause" button to stop the animation, then press "Spring equinox" (keep Latitude at 35.0°N). Record "Noon altitude h" and "Shadow length" in the readout.
2. 「夏至」ボタン、「冬至」ボタンを順に押し、左図「南中の様子」の光線の傾きと影の長さ、右図「太陽の通り道」の弧の高さを比べながら、南中高度と影の長さを記録する。Press "Summer solstice" and then "Winter solstice". Compare the slant of the rays and the shadow in the left figure "At noon" and the height of the arc in the right figure "Sun's path", and record the noon altitude and shadow length each time.
3. 「緯度」スライダーを北緯45.0°に動かし、もう一度「夏至」と「冬至」を押して南中高度と影の長さを記録する。Move the "Latitude" slider to 45.0°N, press "Summer solstice" and "Winter solstice" again, and record the noon altitude and shadow length.
4. 「再生」ボタンを押し、1年間で日付が進むにつれて光線・影・太陽の通り道がどう連続して変わるかを観察する。Press "Play" and watch how the rays, the shadow, and the Sun's path change continuously as the date advances through one year.

3確かめようCheck

1. 北緯35°で、春分・夏至・冬至の南中高度と影の長さはそれぞれいくらでしたか。At 35°N, what were the noon altitude and shadow length on the spring equinox, summer solstice, and winter solstice?→ 春分は約55.0°で影は約0.70m、夏至は約78.4°で影は約0.21m、冬至は約31.6°で影は約1.63m。南中高度が高いほど影は短い。Spring equinox: about 55.0° with a shadow of about 0.70 m; summer solstice: about 78.4° with about 0.21 m; winter solstice: about 31.6° with about 1.63 m. The higher the noon altitude, the shorter the shadow.
2. 影はどちらの方角に伸びていましたか。それはなぜですか。In which direction did the shadow point, and why?→ 影は北(図の右)に伸びた。日本付近(北緯30°〜60°)では正午の太陽は真南にあり、光が南から差すため。The shadow pointed north (to the right in the figure). At these latitudes (30°N to 60°N) the noon Sun is due south, so the light comes from the south.
3. 北緯45°にすると、夏至と冬至の南中高度はいくらになりましたか。夏至と冬至の差は北緯35°のときと比べてどうでしたか。At 45°N, what were the noon altitudes on the summer and winter solstices? How did the difference between them compare with that at 35°N?→ 夏至は約68.4°、冬至は約21.6°(冬至の影は約2.53m)で、どちらも北緯35°より10°低い。差はどちらの緯度でも約46.8°で変わらない。Summer solstice about 68.4° and winter solstice about 21.6° (winter shadow about 2.53 m), both 10° lower than at 35°N. The difference stays about 46.8° at both latitudes.
4. 右図「太陽の通り道」で、夏至・春分(秋分)・冬至の弧はどのように並んでいましたか。In the right figure "Sun's path", how were the summer solstice, equinox, and winter solstice arcs arranged?→ 夏至の弧が最も高く大きく、冬至の弧が最も低く小さく、春分・秋分はその間にあった。各弧の最も高い点(南中)の角度が、その日の南中高度と一致していた。The summer solstice arc was the highest and longest, the winter solstice arc the lowest and shortest, and the equinox arc in between. The angle of the highest point of each arc (the noon Sun) matched that day's noon altitude.

4考えようThink further

1. 夏至と冬至の南中高度の差が、どの緯度でも約46.8°になるのはなぜですか。Why is the difference in noon altitude between the summer and winter solstices about 46.8° at every latitude?→ 南中高度は h = 90° −(緯度 − δ)で、緯度が同じなら差は赤緯 δ の差だけで決まる。δ は地軸の傾き(約23.4°)により夏至で+23.4°、冬至で−23.4°になるので、差は 2×23.4° = 46.8° になる。The noon altitude is h = 90° − (latitude − δ), so at a fixed latitude the difference depends only on the change in declination δ. Because of the axial tilt (about 23.4°), δ is +23.4° at the summer solstice and −23.4° at the winter solstice, giving 2 × 23.4° = 46.8°.
2. 夏が冬より暑くなる理由を、南中高度と太陽の通り道の両方から説明しましょう。Using both the noon altitude and the Sun's path, explain why summer is hotter than winter.→ 夏は南中高度が高く、同じ面積の地面が受ける光の量が多い(光が垂直に近く当たる)。さらに通り道の弧が長く、昼の時間が長いので、地面があたためられる時間も長い。In summer the noon altitude is high, so each area of ground receives more sunlight (the light strikes closer to perpendicular). The Sun's path is also longer, so daylight lasts longer and the ground is heated for more time.

よくある誤解Common misconceptions

• 「夏に暑いのは地球が太陽に近づくから」という誤解。実際には地軸の傾きで南中高度と昼の長さが変わることが主な原因である。The idea that summer is hot because Earth is closer to the Sun. In fact, the main cause is the axial tilt, which changes the noon altitude and the length of daylight.
• 「正午の太陽は真上(90°)にある」という誤解。日本付近ではどの季節でも南中高度は90°より小さく、太陽は南の空にある。The idea that the noon Sun is directly overhead (90°). At Japan's latitudes the noon altitude is always less than 90°, and the Sun is in the southern sky.

用語（日本語 / English）Key terms (Japanese / English)