21  Unit 4: Seasons (Optional 3E)

How does the annual cycle of Earth around the Sun create seasonal temperature variations?

22 Engage: Why Do We Have Seasons?

22.0.1 🤔 Initial Question

Many people believe seasons are caused by Earth being closer to or farther from the Sun. Is this correct?

Fact: Earth is actually closest to the Sun (perihelion) in early January during Northern Hemisphere winter!

22.1 Interactive: Earth’s Orbit Distance

Plot = require("@observablehq/plot")

orbitData = [
  {month: "Jan", distance: 147.1, season: "Winter (NH)"},
  {month: "Feb", distance: 147.8, season: "Winter"},
  {month: "Mar", distance: 148.9, season: "Spring"},
  {month: "Apr", distance: 150.0, season: "Spring"},
  {month: "May", distance: 151.0, season: "Spring"},
  {month: "Jun", distance: 151.8, season: "Summer"},
  {month: "Jul", distance: 152.1, season: "Summer (NH)"},
  {month: "Aug", distance: 151.5, season: "Summer"},
  {month: "Sep", distance: 150.5, season: "Fall"},
  {month: "Oct", distance: 149.3, season: "Fall"},
  {month: "Nov", distance: 148.1, season: "Fall"},
  {month: "Dec", distance: 147.3, season: "Winter"}
]

Plot.plot({
  title: "Earth-Sun Distance Throughout the Year",
  subtitle: "Distance in millions of kilometers",
  width: 650,
  height: 350,
  x: {label: "Month", domain: orbitData.map(d => d.month)},
  y: {label: "Distance (million km)", domain: [146, 153]},
  marks: [
    Plot.line(orbitData, {x: "month", y: "distance", stroke: "#e67e22", strokeWidth: 3,
        tip: true}),
    Plot.dot(orbitData, {x: "month", y: "distance", fill: "#e67e22", r: 6,
        tip: true}),
    Plot.text([{month: "Jan", distance: 147.1}], {x: "month", y: "distance", text: d => "Closest!", dy: -15, fill: "red", fontWeight: "bold"}),
    Plot.text([{month: "Jul", distance: 152.1}], {x: "month", y: "distance", text: d => "Farthest!", dy: -15, fill: "blue", fontWeight: "bold"})
  ]
})

// --- Collapsible quiz builder (file-scoped) ---
buildQuiz = function(id, title, questions) {
  const outer = html`<div id="${id}" style="margin:18px 0 24px 0;text-align:center;">
    <button style="
      display:inline-flex;align-items:center;gap:7px;
      background:linear-gradient(135deg,#667eea 0%,#764ba2 100%);
      color:#fff;border:none;padding:9px 22px;border-radius:50px;
      font-size:.95em;font-weight:700;cursor:pointer;
      box-shadow:0 3px 12px rgba(102,126,234,.45);
      transition:transform .15s,box-shadow .15s;"
      onmouseover="this.style.transform='scale(1.04)';this.style.boxShadow='0 5px 18px rgba(102,126,234,.55)'"
      onmouseout="this.style.transform='scale(1)';this.style.boxShadow='0 3px 12px rgba(102,126,234,.45)'"
    >
      <span style="font-size:1.1em;">📝</span> ${title}
      <span class="chevron" style="transition:transform .3s;">▼</span>
    </button>

    <div class="quiz-body" style="
      max-height:0;opacity:0;overflow:hidden;
      transition:max-height .5s cubic-bezier(.4,0,.2,1),opacity .4s ease,margin-top .3s ease;
      margin-top:0;text-align:left;">

      <button class="close-btn" style="
        display:block;margin:0 auto 10px auto;
        background:rgba(102,126,234,.12);color:#667eea;border:none;
        padding:5px 18px;border-radius:50px;font-size:.85em;
        font-weight:600;cursor:pointer;">Hide Quiz</button>
      <p style="text-align:center;color:#718096;font-style:italic;font-size:.9em;margin-bottom:12px;">
        Select an answer for each question.</p>
    </div>
  </div>`;

  const toggle = outer.querySelector("button");
  const chevron = toggle.querySelector(".chevron");
  const body   = outer.querySelector(".quiz-body");
  const closeBtn = body.querySelector(".close-btn");

  function expand(){  body.style.maxHeight="2000px";body.style.opacity="1";body.style.marginTop="14px";chevron.style.transform="rotate(180deg)"; }
  function collapse(){ body.style.maxHeight="0";body.style.opacity="0";body.style.marginTop="0";chevron.style.transform="rotate(0)"; }
  toggle.onclick = () => body.style.maxHeight === "0px" || body.style.maxHeight === "" ? expand() : collapse();
  closeBtn.onclick = collapse;

  questions.forEach((qq, qi) => {
    const card = document.createElement("div");
    card.style.cssText = "background:#fff;border-radius:12px;padding:16px 20px;margin-bottom:14px;box-shadow:0 2px 8px rgba(0,0,0,.08);";
    card.innerHTML = `<p style="font-weight:700;margin:0 0 10px;">${qi+1}. ${qq.q}</p>`;
    qq.options.forEach((opt, oi) => {
      const btn = document.createElement("button");
      btn.textContent = opt;
      btn.style.cssText = "display:block;width:100%;text-align:left;padding:10px 14px;margin:6px 0;border:2px solid #e2e8f0;border-radius:8px;background:#fff;cursor:pointer;font-size:.95em;transition:border-color .2s,background .2s;";
      btn.onmouseover = () => { if(!card.dataset.answered){ btn.style.borderColor="#667eea";btn.style.background="#f0f0ff"; }};
      btn.onmouseout  = () => { if(!card.dataset.answered){ btn.style.borderColor="#e2e8f0";btn.style.background="#fff"; }};
      btn.onclick = () => {
        if(card.dataset.answered) return;
        card.dataset.answered = "true";
        card.querySelectorAll("button").forEach(b => { b.style.cursor="default"; b.onmouseover=null; b.onmouseout=null; });
        if(oi === qq.correct){
          btn.style.borderColor="#48bb78";btn.style.background="#f0fff4";
          fb.innerHTML = "✅ Correct! " + qq.explanation;
          fb.style.color="#276749";fb.style.background="#f0fff4";
        } else {
          btn.style.borderColor="#fc8181";btn.style.background="#fff5f5";
          card.querySelectorAll("button")[qq.correct].style.borderColor="#48bb78";
          card.querySelectorAll("button")[qq.correct].style.background="#f0fff4";
          fb.innerHTML = "❌ " + qq.explanation;
          fb.style.color="#9b2c2c";fb.style.background="#fff5f5";
        }
        fb.style.padding="10px 14px";fb.style.marginTop="8px";
      };
      card.appendChild(btn);
    });
    const fb = document.createElement("div");
    fb.style.cssText = "border-radius:8px;font-size:.9em;transition:all .3s;";
    card.appendChild(fb);
    body.appendChild(card);
  });
  return outer;
}

buildQuiz("orbit-distance-quiz", "Check Your Understanding — Earth-Sun Distance", [
  {
    q: "According to the chart, when is Earth CLOSEST to the Sun?",
    options: [
      "A) June–July (Northern Hemisphere summer)",
      "B) January (Northern Hemisphere winter)",
      "C) March–April (spring equinox)",
      "D) September–October (fall equinox)"
    ],
    correct: 1,
    explanation: "Earth reaches perihelion (closest to the Sun) in early January at ~147.1 million km — during Northern Hemisphere winter! This proves distance isn't the main cause of seasons."
  },
  {
    q: "The difference between Earth's closest and farthest distance from the Sun is only about 5 million km (~3%). What does this tell us about the cause of seasons?",
    options: [
      "A) Distance must be the main cause because 5 million km is a lot",
      "B) The small distance variation means something else must cause seasons",
      "C) Distance only affects the Southern Hemisphere",
      "D) The chart data must be wrong"
    ],
    correct: 1,
    explanation: "A 3% change in distance creates only a ~7% change in solar energy — far too small to explain the large seasonal temperature swings. Earth's 23.5° axial tilt is the real cause."
  }
])

23 Explore: Axial Tilt and Sunlight

23.1 PhET Simulation: Seasons

Explore how Earth’s axial tilt creates seasons:

Note: If the simulation doesn't load, click here to open it in a new tab.

23.1.1 🔬 Exploration Tasks

1. Observe how the angle of sunlight changes throughout the year at different latitudes
2. Compare day length at 45°N during summer vs. winter solstice
3. Notice how the Sun’s rays are more direct in summer and more spread out in winter

23.2 Interactive: Sunlight Angle Simulator

viewof sunAngle = Inputs.range([0, 90], {
  step: 5,
  value: 45,
  label: "Sun Angle (degrees from horizon):"
})

spreadFactor = 1 / Math.sin(sunAngle * Math.PI / 180)
intensityPercent = (Math.sin(sunAngle * Math.PI / 180) * 100).toFixed(1)

html`<div style="display: flex; gap: 30px; align-items: center; margin: 20px 0;">
  <div style="flex: 1;">
    <svg width="300" height="200">
      <!-- Ground -->
      <rect x="0" y="150" width="300" height="50" fill="#8B4513"/>
      <!-- Sun rays -->
      <line x1="50" y1="${150 - 100 * Math.tan(sunAngle * Math.PI / 180)}" x2="50" y2="150" stroke="yellow" stroke-width="3"/>
      <line x1="100" y1="${150 - 100 * Math.tan(sunAngle * Math.PI / 180)}" x2="100" y2="150" stroke="yellow" stroke-width="3"/>
      <line x1="150" y1="${150 - 100 * Math.tan(sunAngle * Math.PI / 180)}" x2="150" y2="150" stroke="yellow" stroke-width="3"/>
      <!-- Angle arc -->
      <path d="M 50 150 L 50 100 A 50 50 0 0 1 ${50 + 50 * Math.cos((90-sunAngle) * Math.PI / 180)} ${150 - 50 * Math.sin((90-sunAngle) * Math.PI / 180)}" fill="none" stroke="red" stroke-width="2"/>
      <text x="70" y="130" fill="red" font-size="14">${sunAngle}°</text>
    </svg>
  </div>
  <div style="flex: 1; padding: 20px; background: #f5f5f5; border-radius: 10px;">
    <h4>Energy Intensity</h4>
    <p><strong>Relative intensity:</strong> ${intensityPercent}%</p>
    <p><strong>Energy spread factor:</strong> ${spreadFactor.toFixed(2)}x</p>
    <div style="background: linear-gradient(to right, #ffeb3b ${intensityPercent}%, #ccc ${intensityPercent}%); height: 30px; border-radius: 5px;"></div>
    <p style="font-size: 12px; margin-top: 10px;">Higher sun angles = more concentrated energy = warmer temperatures</p>
  </div>
</div>`

buildQuiz("sunlight-angle-quiz", "Check Your Understanding — Sunlight Angle & Intensity", [
  {
    q: "Using the simulator, what happens to the relative intensity of sunlight as you decrease the Sun angle from 90° toward 0°?",
    options: [
      "A) Intensity increases because rays travel a shorter path",
      "B) Intensity stays the same regardless of angle",
      "C) Intensity decreases because the same energy is spread over a larger area",
      "D) Intensity decreases only below 30°"
    ],
    correct: 2,
    explanation: "At lower sun angles, the same beam of light is spread over a larger surface area, reducing the energy per unit area. At 90° (directly overhead) intensity is 100%, but at 30° it drops to just 50%."
  },
  {
    q: "How does this sunlight angle effect explain why summers are warmer than winters?",
    options: [
      "A) In summer, Earth is closer to the Sun",
      "B) In summer, the Sun is higher in the sky so sunlight strikes more directly, concentrating energy",
      "C) In summer, the atmosphere is thinner",
      "D) In summer, clouds reflect less sunlight"
    ],
    correct: 1,
    explanation: "During summer, Earth's axial tilt causes the Sun to appear higher in the sky, so sunlight strikes at a steeper angle. This concentrates solar energy over a smaller area, warming the surface more effectively."
  }
])

24 Explain: The Science of Seasons

24.0.1 🌍 Key Concepts

Seasons are caused by Earth’s 23.5° axial tilt, NOT distance from the Sun.

1. Summer: Your hemisphere is tilted TOWARD the Sun
   • Sun appears higher in the sky
   • Sunlight hits more directly (concentrated energy)
   • Longer days = more heating time
2. Winter: Your hemisphere is tilted AWAY from the Sun
   • Sun appears lower in the sky
   • Sunlight hits at an angle (spread out energy)
   • Shorter days = less heating time

24.1 Connection to Climate Change

Understanding seasons helps us understand climate change because:

• Milankovitch Cycles involve changes to Earth’s tilt over thousands of years
• These orbital changes have driven glacial-interglacial cycles
• We’ll explore this in detail in the next lesson!

24.1.1 ✅ Check Your Understanding

1. Why is it WARMER in summer even though Earth is FARTHER from the Sun?
2. How does the angle of sunlight affect heating?
3. Why do the Northern and Southern hemispheres have opposite seasons?

---

buildQuiz("seasons-final-quiz", "📝 Seasons Quiz", [
  {
    q: "Earth is closest to the Sun during which month?",
    options: [
      "A) July",
      "B) January",
      "C) March",
      "D) September"
    ],
    correct: 1,
    explanation: "Earth reaches perihelion (closest approach) in early January at about 147.1 million km, which is during Northern Hemisphere winter."
  },
  {
    q: "What primarily causes Earth's seasons?",
    options: [
      "A) Distance from the Sun",
      "B) Earth's axial tilt of 23.5°",
      "C) Changes in the Sun's output",
      "D) Ocean currents"
    ],
    correct: 1,
    explanation: "Earth's 23.5° axial tilt determines which hemisphere receives more direct sunlight at different times of year, creating the seasons."
  },
  {
    q: "During Northern Hemisphere summer, the North Pole is:",
    options: [
      "A) Tilted away from the Sun",
      "B) Tilted toward the Sun",
      "C) Not tilted at all",
      "D) Experiencing 24 hours of darkness"
    ],
    correct: 1,
    explanation: "During Northern Hemisphere summer, Earth's axial tilt orients the North Pole toward the Sun, resulting in higher sun angles, longer days, and even 24-hour daylight above the Arctic Circle."
  }
])

)