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Gravitation"}],"title":"Kepler's Second Law","sceneCode":"<!doctype html>\n<html lang=\"en\">\n<head>\n  <meta charset=\"utf-8\"/>\n  <meta name=\"viewport\" content=\"width=device-width, initial-scale=1\"/>\n  <title>Kepler's Second Law: Equal Areas in Equal Times</title>\n  <style>\n    :root{--bg:#0e121a;--panel:#1c232e;--line:#303449;--accent:#fc884f;--text:#faf9f8;--muted:#9f9ea1;--blue:#627da5;--green:#8decb0;--red:#df8279;}\n    *{box-sizing:border-box;}\n    body{margin:0;font-family:\"Plus Jakarta Sans\",\"Manrope\",\"Inter\",ui-sans-serif,system-ui,sans-serif;background:radial-gradient(120% 90% at 20% -5%,#1c232e 0%,var(--bg) 55%);color:var(--text);}\n    main{min-height:100vh;display:grid;grid-template-columns:minmax(300px,380px) 1fr;}\n    aside{border-right:1px solid var(--line);background:linear-gradient(180deg,rgba(28,35,46,.86),rgba(14,18,26,.94));padding:24px;overflow:auto;backdrop-filter:blur(6px);}\n    section{padding:24px;display:grid;place-items:center;}\n    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</style>\n</head>\n<body>\n<main>\n  <aside>\n    <h1>Kepler's Law II</h1>\n    <p class=\"sub\">Equal areas swept in equal times — but ONLY in central forces.</p>\n    <p class=\"formula\">dA/dt = L/(2m) = const</p>\n    <div class=\"control\">\n      <span>Eccentricity: <strong id=\"v-ecc\">0.6</strong></span>\n      <input id=\"c-ecc\" type=\"range\" min=\"0\" max=\"0.95\" step=\"0.05\" value=\"0.6\"/>\n    </div>\n    <div class=\"control\">\n      <span>Show Sector: <strong id=\"v-show\">1</strong></span>\n      <input id=\"c-show\" type=\"range\" min=\"0\" max=\"1\" step=\"1\" value=\"1\"/>\n    </div>\n    <ul>\n      <li><span class=\"icon-wrong\"></span><strong>Wrong:</strong> Speed is always the same.</li>\n      <li><span class=\"icon-right\"></span><strong>Correct:</strong> Speed varies; area/time is constant.</li>\n      <li><strong>Key:</strong> Equal sectors = equal time intervals (not equal arc length).</li>\n      <li><strong>Constraint:</strong> Only applies with 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