Johannes_Kepler - Wikiparency

# Johannes Kepler ## Microsim ### Live player <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/Y0VWcco23" width="100%" height="620" frameborder="0" sandbox="allow-scripts allow-same-origin"></iframe> </div> <div class="microsim-fallback"> <img src="Microsims/thumbs/Johannes_Kepler.png" alt="Johannes_Kepler microsim poster" style="width:100%;border:1px solid #4445;border-radius:6px;"> <p><em>Live microsim (desktop) · <a href="https://editor.p5js.org/sciencenibber/sketches/Y0VWcco23">open sketch in the p5.js editor</a></em></p> </div> **Editor URL:** https://editor.p5js.org/sciencenibber/sketches/Y0VWcco23 **Description (100 words):** A planet sweeps around the Sun on a true Keplerian ellipse, with the Sun parked at one focus — Kepler's first law. The orbit is sampled at equal time intervals and the sectors swept between samples are shaded alternately; though their shapes differ wildly, every sector encloses the same area, which is Kepler's second law and, equivalently, conservation of angular momentum. Watch the planet race through perihelion and crawl through aphelion. Sliders set the eccentricity e and the sector count N. Live readouts give r and the vis-viva speed v = sqrt(2/r - 1/a), tying the [[Geometry|geometry]] directly to conserved orbital energy. ```js // ===================================================================== // Article : Johannes Kepler — Laws of Planetary Motion // Slug : Johannes_Kepler // Wikitube : en.wikitube.io/wiki/Johannes_Kepler // Room : Energy // // Idea : A planet orbits the Sun on a true Keplerian ellipse with // the Sun at one focus (1st law). The orbit is sampled at // equal TIME intervals; the sectors swept between successive // samples are shaded in alternating tints. They look wildly // different in shape, yet every sector has the SAME area — // that is Kepler's 2nd law (equal areas in equal times), // which is just conservation of angular momentum. The planet // races through perihelion and crawls through aphelion. A // live vis-viva readout ties the geometry to ORBITAL ENERGY: // the specific energy eps = -GM/2a is conserved, trading // kinetic for potential as r changes. // // Equation : 2nd law dA/dt = L/(2m) = const (Unicode OK in comments) // 3rd law T^2 = (4*pi^2 / GM) * a^3 // vis-viva v^2 = GM*(2/r - 1/a) // ===================================================================== // Rule §3 — single source of truth for the slug / URL line / save name. const ARTICLE = "Johannes_Kepler"; // Rule §4 — quiet the Friendly Error System for ship. p5.disableFriendlyErrors = true; // ---------- controls ---------- let eSlider; // orbital eccentricity e (0 = circle, ->1 = needle) let nSlider; // number of equal-TIME sectors used to demonstrate law 2 // ---------- layout constants (computed in setup) ---------- let cx, cy; // ellipse-center pixel position let S; // pixels per world unit (semi-major axis a == 1 world unit) // ---------- accent palette (rule §8, at most three) ---------- let SUN, PLANET, SECTOR; function setup() { // Rule §5 — canvas inside setup, standard size, retina density. createCanvas(720, 520); pixelDensity(2); // Ellipse center sits a little above the slider/readout strip; the Sun // is drawn at a focus, which is offset from this center by c = a*e. cx = width / 2; cy = height / 2 - 8; S = 200; // a = 1 world unit -> 200 px SUN = color(240, 180, 40); // gold PLANET = color(40, 90, 200); // blue SECTOR = color(40, 90, 200, 55);// translucent blue for swept areas // Rule §6 — controls built in setup, positioned explicitly, in a band // separate from the bottom-left readouts (pitfalls: slider/readout overlap). nSlider = createSlider(4, 24, 12, 1); // sectors; default 12 = months-ish nSlider.position(330, height - 56); nSlider.style("width", "150px"); eSlider = createSlider(0, 95, 60, 1); // e*100; default 0.60 eSlider.position(330, height - 30); eSlider.style("width", "150px"); } function draw() { background(248); // ---------- read controls ---------- const e = eSlider.value() / 100; // eccentricity, 0..0.95 const N = nSlider.value(); // equal-time sector count const a = 1; // semi-major axis (world unit) const b = a * Math.sqrt(1 - e * e); // semi-minor axis const c = a * e; // center-to-focus distance // World->screen helpers. World origin = ellipse center; +y is up, so we // subtract in screen space. The Sun sits at the focus (c, 0). const sx = (wx) => cx + wx * S; const sy = (wy) => cy - wy * S; const sunX = sx(c), sunY = sy(0); // ---------- reference geometry (rule §8 layer 1, neutral grey) ---------- // Orbit ellipse, centered at the ellipse center (NOT the Sun). noFill(); stroke(170); strokeWeight(1.5); ellipse(cx, cy, 2 * a * S, 2 * b * S); // Major axis (apse line) and the empty second focus. stroke(210); strokeWeight(1); line(sx(-a), cy, sx(a), cy); fill(150); noStroke(); circle(sx(-c), sy(0), 5); // empty focus noFill(); // ---------- equal-TIME sectors (rule §8 layer 2) ---------- // Sample the orbit at N equally spaced MEAN anomalies M_k = 2*pi*k/N. // Equal mean-anomaly spacing == equal TIME spacing. The triangle from the // Sun to two successive samples approximates the area swept in T/N. All // such sectors have equal area -> Kepler's 2nd law, made visible. noStroke(); for (let k = 0; k < N; k++) { const M0 = TWO_PI * k / N; const M1 = TWO_PI * (k + 1) / N; const E0 = solveKepler(M0, e); const E1 = solveKepler(M1, e); // Ellipse point from eccentric anomaly E: (a*cos E, b*sin E). const p0x = sx(a * Math.cos(E0)), p0y = sy(b * Math.sin(E0)); const p1x = sx(a * Math.cos(E1)), p1y = sy(b * Math.sin(E1)); // Shade alternate sectors so neighbours are distinguishable. fill(k % 2 === 0 ? SECTOR : color(220, 130, 40, 45)); triangle(sunX, sunY, p0x, p0y, p1x, p1y); } // Sample-point dots on the orbit (the equal-time tick marks). fill(90); noStroke(); for (let k = 0; k < N; k++) { const E = solveKepler(TWO_PI * k / N, e); circle(sx(a * Math.cos(E)), sy(b * Math.sin(E)), 3.5); } // ---------- the moving planet ---------- // Animate mean anomaly from the wall clock: one orbit every PERIOD ms. // Because M->E->position is nonlinear, the planet naturally speeds up at // perihelion and slows at aphelion even though M advances uniformly. const PERIOD = 7000; const M = (millis() % PERIOD) / PERIOD * TWO_PI; const E = solveKepler(M, e); const px = a * Math.cos(E), py = b * Math.sin(E); const planetX = sx(px), planetY = sy(py); // Radius line Sun -> planet (the line that "sweeps equal areas"). stroke(PLANET); strokeWeight(1.5); line(sunX, sunY, planetX, planetY); // The Sun at the focus. noStroke(); fill(SUN); circle(sunX, sunY, 18); fill(245, 210, 90); circle(sunX, sunY, 9); // The planet. noStroke(); fill(PLANET); circle(planetX, planetY, 11); // ---------- derived quantities for the readouts ---------- // Distance Sun->planet in world units: r = a*(1 - e*cos E). const r = a * (1 - e * Math.cos(E)); // Vis-viva speed in units where GM = 1 and a = 1: v = sqrt(2/r - 1/a). const v = Math.sqrt(Math.max(0, 2 / r - 1 / a)); // Perihelion / aphelion distances. const rPeri = a * (1 - e); const rApo = a * (1 + e); // ---------- HUD watermark (rule §2) ---------- noStroke(); textFont("system-ui"); // §2a — top-left title block. fill(20); textSize(20); textAlign(LEFT, TOP); text("Johannes Kepler - Laws of Planetary Motion", 16, 14); textSize(12); fill(110); text("Wikitube microsim - en.wikitube.io/wiki/" + ARTICLE, 16, 40); // §2b — top-right control hints. textAlign(RIGHT, TOP); textSize(11); fill(110); text("sliders: e (eccentricity), N (equal-time sectors)", width - 16, 14); text("each shaded sector = equal area = equal time (2nd law)", width - 16, 30); // §2c — bottom-left live readouts in canonical symbols. textAlign(LEFT, BOTTOM); textSize(13); fill(20); text("e = " + e.toFixed(2) + " a = 1.00 (AU) b = " + b.toFixed(3), 16, height - 64); text("r = " + r.toFixed(3) + " v = " + v.toFixed(3) + " (vis-viva, GM=a=1)", 16, height - 46); fill(70); text("perihelion = " + rPeri.toFixed(3) + " aphelion = " + rApo.toFixed(3), 16, height - 28); // Slider labels (rule §7) — left of each slider, right-aligned. textAlign(RIGHT, CENTER); textSize(12); fill(60); text("N (sectors)", 322, height - 56 + 8); text("e (eccentricity)", 322, height - 30 + 8); // §2d — bottom-right equation footer (ASCII only — pitfalls: no Unicode). textAlign(RIGHT, BOTTOM); textSize(11); fill(80); text("dA/dt = L/(2m) = const T^2 = (4*pi^2/GM) a^3", width - 16, height - 8); } // ---------- helpers (rule §10) ---------- // Solve Kepler's equation M = E - e*sin(E) for the eccentric anomaly E, // given mean anomaly M and eccentricity e, via Newton-Raphson. Eight // iterations is ample convergence for e < 0.95. function solveKepler(M, e) { let E = M; // good initial guess for moderate e for (let i = 0; i < 8; i++) { const f = E - e * Math.sin(E) - M; const fp = 1 - e * Math.cos(E); E = E - f / fp; } return E; } ``` ## Links (Wikipedia order)  `1134_Kepler` · `2dF_Galaxy_Redshift_Survey` · `Acceleration` · `Action_at_a_distance` · `Adelberg` · [[Age_of_Enlightenment]] · `Age_of_the_universe` · `Agnes_Mary_Clerke` · `Alan_Guth` · `Albert_Einstein` · `Albrecht_von_Wallenstein` · `Alchemy` · `Alexander_Friedmann` · `Alexander_von_Brill` · `Alexandre_Koyré` · `Alexis_Clairaut` · `Analytical_mechanics` · `Analytical_psychology` · `Angular_acceleration` · `Angular_displacement` · [[Angular_frequency]] · `Angular_momentum` · `Angular_velocity` · `Anima_mundi` · `Apparent_retrograde_motion` · `Appell's_equation_of_motion` · `Applied_mechanics` · `Aristotle` · `Arno_Allan_Penzias` · `Arthur_I._Miller` · `Arthur_Koestler` · `Astrology` · `Astronomer` · `Astronomers_Monument` · `Astronomia_nova` · `Astronomy` · `Atmospheric_refraction` · `Atomism` · `Augustin-Louis_Cauchy` · `BOOMERanG_experiment` · `Baden-Württemberg` · `Baryogenesis` · `Baryon` · `Battle_of_White_Mountain` · `Benoît_Charest` · `Benátky_nad_Jizerou` · `Bernard_Koopman` · `Big_Bang` · `Big_Bang_nucleosynthesis` · `Black_Hole_Initiative` · `Bohemian_Revolt` · `Brian_Schmidt` · `C._Doris_Hellman` · [[Calculus]] · `Cambridge_University_Press` · `Carl_Gustav_Jacob_Jacobi` · `Carl_Sagan` · `Catherine_the_Great` · `Cavalieri's_principle` · `Celestial_mechanics` · `Celestial_spheres` · `Centrifugal_force` · `Centripetal_force` · `Charlemagne` · `Charles_II,_Archduke_of_Austria` · `Charles_Sanders_Peirce` · [[Christiaan_Huygens]] · `Christian_IV_of_Denmark` · `Christopher_Wren` · `Chronology` · `Chronology_of_Jesus` · `Chronology_of_the_universe` · `Circular_motion` · `Classical_field_theory` · `Classical_mechanics` · `Colin_Hardie` · 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Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:JKepler.jpg).* > Johannes Kepler (/ˈkɛplər/;[2] .IPA-label-small{font-size:85%}.references .IPA-label-small,.infobox .IPA-label-small,.navbox .IPA-label-small{font-size:100%}German: [joˈhanəs ˈkɛplɐ, -nɛs -] ⓘ;[3][4] 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music.[5] He is a key figure in the 1 ([Wikipedia](https://en.wikipedia.org/wiki/Johannes_Kepler))   ## From the vault media library !Johannes Kepler thumb.png *Johannes Kepler — from the vault's own media holdings, placed 2026-07-09. MTN / Wikitube.io original · CC BY-SA 4.0.*  > **Room:** [[Energy]] · **Status:** ✅ shipped ## Overview Johannes Kepler (/ˈkɛplər/;2 .mw-parser-output .IPA-label-small{font-size:85%}.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-small{font-size:100%}German: joˈhanəs ˈkɛplɐ, -nɛs - ⓘ;34 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music.5 He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books Astronomia nova, Harmonice Mundi, and Epitome Astronomiae Copernicanae, influencing among others [[Isaac_Newton|Isaac Newton]], providing one of the foundations for his theory of universal gravitation.6 The variety and impact of his work made Kepler one of the founders and fathers of modern astronomy, the scientific method, natural and modern [[Science|science]].789 He has been described as the "father of science fictio _(Overview is shorter than 200 words; the pipeline should expand it from textbook context before publishing.)_ ## See also - Room hub: [[Energy]] - p5.js Editor conventions: P5 JS EDITOR - Wiki root: MAIN --- *Scaffolded by `generative-microsim` from row 11 of the Energy sheet on 2026-06-03T11:28:31Z.* Letters: energy · sampling · conservation · ipa · mined_geometry · mined_science · mined_modern · mined_system   *Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Johannes_Kepler) : [Wikitube](https://en.wikitube.io/wiki/Johannes_Kepler) ## Previous hub tags Tree parent: [[Dynamical_system]]. Legacy hubs: `GENERATIVE`. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*