2d:null 2e:["$","title",null,{"children":"Solar Eclipses | Christophe Yamahata | Observable"}] 33:T9ab, nextEclipseBanner = { const now = new Date(); const todayUTC = new Date(Date.UTC(now.getUTCFullYear(), now.getUTCMonth(), now.getUTCDate())); const next = eclipses.find(e => e.date >= todayUTC); const daysUntilNext = Math.round((next.date - todayUTC) / (1000 * 60 * 60 * 24)); const { resolveType } = eclipseFormatters; const dateLabel = next.date.toLocaleDateString("en-US", { year: "numeric", month: "long", day: "numeric", timeZone: "UTC" }); const isoDate = next.date.toISOString().split("T")[0]; const eclipseLink = `?eclipse=${isoDate}`; const type = resolveType(next.type); const nextEclipseText = `${dateLabel} (${type})`; const primaryType = next.type ? next.type.charAt(0) : "T"; const imageMap = { "P": await FileAttachment("partial_eclipse.jpg").url(), "T": await FileAttachment("total_eclipse.jpg").url(), "A": await FileAttachment("annular_eclipse.jpg").url(), "H": await FileAttachment("total_eclipse.jpg").url(), }; const imageFile = imageMap[primaryType] ?? await FileAttachment("total_eclipse.jpg").url(); return html`

The next solar eclipse ${daysUntilNext === 0 ? "takes place" : "will take place"} ${daysUntilNext === 0 || daysUntilNext === 1 ? "" : "in"} ${ daysUntilNext === 0 ? "TODAY" : daysUntilNext === 1 ? "tomorrow" : `${daysUntilNext} days` }, on ${nextEclipseText}.

`; }34:T4c8,Predicting the path, duration, and local circumstances of a solar eclipse requires precise knowledge of the relative positions of the Sun, Moon, and Earth. Rather than continuously recomputing these positions for a given eclipse, astronomers use a compact set of parameters known as the **Besselian elements**. Once known, these elements allow the computation of the umbral and penumbral paths across Earth’s surface, global and local contact times, magnitude, and local circumstances (such as duration and solar altitude) for any location. This notebook visualizes solar eclipses using Besselian elements from NASA’s *Five Millennium Catalog of Solar Eclipses* (−1999 to +3000), compiled by Fred Espenak and Jean Meeus. ✦︎ This notebook was built with the assistance of Gemini AI.35:Tc51,viewof controls = { const time = Inputs.range( [eclipseTimeRange.min, eclipseTimeRange.max], { value: 0, step: 0.001, label: html`Time Offset, t (Hours from ${tex`t_0`})` } ); const timeExplanation = html` ${tex`t_0`} is the instant of greatest eclipse (maximum magnitude) `; const timeRow = html`

${time} ${timeExplanation}

`; const speedControl = Inputs.range([200, 2000], { label: html`Sequence
Speed (ms)`, value: eclipsePlaySpeed, step: 100 }); speedControl.addEventListener("input", () => { mutable eclipsePlaySpeed = speedControl.value; }); const speedHint = html` Delay between eclipses
(press button ▶ to play) `; const speedRow = html`

${speedControl} ${speedHint}

`; const prev = this?.value; const size = Inputs.range([480, 800], { value: prev?.mapWidth ?? 540, step: 20, label: "Globe Size (px):" }); const sizeLabel = size.querySelector("label"); sizeLabel.style.marginRight = "-5px"; const allowLatDrag = Inputs.toggle({ label: "Allow Latitude Tilt", value: prev?.allowLatDrag ?? true }); const firstColumn = html`

${speedRow} ${timeRow}

`; const secondColumn = html`

${size} ${allowLatDrag}

`; const form = html`

${firstColumn} ${secondColumn}

`; const update = () => { form.value = { timeOffset: time.value, mapWidth: size.value, allowLatDrag: allowLatDrag.value, playSpeed: speedControl.value }; form.dispatchEvent(new Event("input", { bubbles:true })); }; form.value = { timeOffset: time.value, mapWidth: size.value, allowLatDrag: allowLatDrag.value, playSpeed: speedControl.value }; time.addEventListener("input", update); speedControl.addEventListener("input", update); size.addEventListener("input", update); allowLatDrag.addEventListener("input", update); return form; }36:T2772,viewof selection = { const { resolveType, formatDateLabel } = eclipseFormatters; const params = new URLSearchParams(window.location.search); const urlEclipseParam = params.get("eclipse"); let targetEclipse = null; if (urlEclipseParam) { targetEclipse = eclipses.find(e => e.dateString === urlEclipseParam); } const centuries = Array.from( new Set(eclipses.map(e => Math.floor(e.year / 100) * 100)) ).sort((a, b) => a - b); const defaultCentury = targetEclipse ? Math.floor(targetEclipse.year / 100) * 100 : centuries.includes(2000) ? 2000 : centuries[0]; const centuryInput = Inputs.select(centuries, { label: html`Century:`, value: defaultCentury, format: c => formatCenturyLabel(c) }); const centuryLabel = centuryInput.querySelector("label") || centuryInput.querySelector("div > label"); if (centuryLabel) { centuryLabel.style.marginRight = "-50px"; centuryLabel.style.marginLeft = "72px"; } const selectCenturyInput = centuryInput.querySelector("select"); if (selectCenturyInput) { selectCenturyInput.style.width = "260px"; } let currentCentury = defaultCentury; let currentEclipse = null; const items = new Map(); const prevButton = html``; const nextButton = html``; const playButton = html``; let isPlaying = false; let playTimer = null; const button = html`

You can save the displayed map in either SVG or PNG format.
For PNG, the original SVG map is first converted to a canvas format before being downloaded.

`; container.querySelector("#save-svg").onclick = () => { const blob = new Blob([serialize(eclipseMap)], {type: "image/svg+xml"}); const url = URL.createObjectURL(blob); const a = document.createElement("a"); a.href = url; a.download = "Solar_Eclipse_" + selectedEclipse.dateString + ".svg"; a.click(); URL.revokeObjectURL(url); }; container.querySelector("#save-png").onclick = async () => { const result = await rasterize(eclipseMap); const blob = result; const url = URL.createObjectURL(blob); const a = document.createElement("a"); a.href = url; a.download = "Solar_Eclipse_" + selectedEclipse.dateString + ".png"; a.click(); URL.revokeObjectURL(url); }; return container; }3a:T72c,--- ## Noticeable Eclipses * [May 28, 585 BC](?eclipse=-0584-05-28) — According to the ancient Greek historian Herodotus (c. 484 BC – c. 425 BC), this solar eclipse was accurately predicted by the Greek philosopher **Thales** of Miletus (c. 626/623 BC – c. 548/545 BC) * [November 24, 29 AD](?eclipse=0029-11-24) — Known as the Eclipse of Phlegon after Greek historian Phlegon of Tralles (2nd century AD) wrote an account of it, this eclipse is allegedly associated by some with the **darkness at Christ’s crucifixion**. * [August 21, 1560](?collection=@christophe-yamahata/astronomy&eclipse=1560-08-21) — Although it was only seen as a partial eclipse from Denmark, a 13-year-old boy named **Tycho Brahe** (1546 – 1601) witnessed it and was deeply struck by the fact that it had been accurately predicted in advance, sparking his lifelong devotion to astronomy. * [August 18, 1868](?eclipse=1868-08-18) — Sent by the *Bureau des Longitudes* to Guntur, India, to observe the solar eclipse, Jules Janssen used spectroscopy to analyze the light coming from the solar atmosphere. During this observation, he noticed a previously unknown yellow spectral line (Fraunhofer line D₃, 587.562 nm). It was the signature of **helium** (He), an atom then unknown on Earth. The term “helium” was coined by Norman Lockyer, in reference to Helios, the Greek god of the Sun. * [May 29, 1919](?eclipse=1919-05-29) — Arthur Eddington led an expedition to the island of Príncipe (Gulf of Guinea, west coast of Africa) and another team traveled to Sobral, Brazil, to photograph the stars visible around the darkened Sun. Their goal was to test Albert Einstein’s **General Theory of Relativity**, and they successfully confirmed that the Sun's massive gravity bends starlight passing close to it.3b:T717,--- ### Notes on Time and Calendar The timestamps are given in **Terrestrial Dynamical Time (TD)**, a uniform astronomical time scale that does not follow the irregularities of Earth’s rotation. To obtain civil time (**UTC**), subtract ${tex`\Delta T`}: > ${tex`\text{UTC} = \text{TD} - \Delta T`} ${tex`\Delta T`} is a measure of the accumulated clock error due to the variable rotation period of Earth. For modern 21st-century eclipses, ${tex`\Delta T \approx 70`} seconds. #### Calendar convention Dates follow the convention used by NASA’s *Five Millennium Catalog of Solar Eclipses*: - **Gregorian calendar** from 15 October 1582 onward, - **Julian calendar** for all earlier dates. ***Note.*** Tycho Brahe continued to use the Julian calendar for his observations long after the Gregorian reform of 1582. Therefore, dates in the *Tychonis Brahe Dani Opera Omnia* are 10 days earlier than the corresponding dates listed here. Readers comparing this catalog with Brahe's original solar eclipse observations should keep this calendar difference in mind.
***Example:*** Brahe's observations recorded in Tomus X on April 30, 1584 (Julian calendar) corresponds to the partial eclipse of [May 10, 1584](?eclipse=1584-05-10) in the modern calendar). **Year 0** Julian and Gregorian calendars do not include a year 0 (jumping straight from 1 BC to 1 AD), which is awkward for arithmetic calculations. Years in NASA's catalog are *numbered astronomically* and include the year 0: The astronomical year 0 BCE corresponds to 1 BC. As a result, the eclipse of Thales (may 28, 585 BC) is found at date [-0584-05-28](?eclipse=-0584-05-28) in NASA's *Five Millennium Catalog of Solar Eclipses*. 3c:Ta88,tychonis_XIII_p196 = { const container = html`

Solar eclipse of July 10, 1600: Tycho Brahe's recording of the solar eclipse as observed at Benátky Castle (Central Bohemia, Czech Republic), noting dual dating (Julian June 30 / Gregorian July 10).

— “Obſeruatio Eclipſis ☉^lis quæ viſa eſt anno 1600 […] Die 30 Junij veteri ſtilo: 10 Julij nouo.”
(“Observation of the solar eclipse seen in the year 1600 […] June 30 Old Style : July 10 New [Style].”)

First diagram (beginning of obscuration):
— “Innotuit nobis primo initium huius Eclipſis hora 12 poſt M. & 46'. Eratque tunc Altitudo centri Solis 60° 35' […] propterea initium eße poterat iuxta horologium circa minutum 43, vel circiter […] Fuit igitur verum initium Eclipſis H. 0.43 P. M.”
(“The beginning of this eclipse first came to our notice at 12:46 PM, at which time the altitude of the Sun’s center was 60° 35' […] estimating from this, the initial contact likely occurred around minute 43 according to the clock […] Thus, the true beginning of the eclipse was determined to be 12:43 PM.”)

Reference: Tychonis Brahe Dani Opera Omnia, Tomus XIII, p. 196.

👆🏻 Click to resize the illustration

`; container.onclick = (e) => { if (e.target.closest("a")) return; const currentWidth = container.style.width; container.style.width = currentWidth === "630px" ? "800px" : "630px"; }; return container; } 3d:T41e,viewof display_inspect = { const el = htl.html`

Variables & Functions

⇣ Check to inspect the notebook script

`; const checkbox = el.querySelector("input"); const spacer = el.querySelector("div"); function update() { const show = checkbox.checked; document.querySelectorAll(".observablehq--inspect").forEach(node => { if (el.contains(node)) return; node.style.display = show ? "" : "none"; }); spacer.style.height = show ? "0" : "20vh"; } checkbox.addEventListener("change", update); const observer = new MutationObserver(update); observer.observe(document.body, { childList: true, subtree: true }); update(); invalidation.then(() => observer.disconnect()); return el; }3e:T59a,eclipses = besselianRaw.map(d => { const y = +d.year; const m = +d.month - 1; // 0-indexed month const day = +d.day; // Construct UTC date object safely for BCE/CE years const dateObj = new Date(Date.UTC(2000, m, day)); dateObj.setUTCFullYear(y); // Format human-readable date string (e.g., "2026-08-12") const absYear = Math.abs(y); const formattedYear = y < 0 ? `-${String(absYear).padStart(4, '0')}` : String(y).padStart(4, '0'); const formattedMonth = String(m + 1).padStart(2, '0'); const formattedDay = String(day).padStart(2, '0'); const dateString = `${formattedYear}-${formattedMonth}-${formattedDay}`; return { catNo: +d.cat_no, year: y, month: +d.month, day: day, date: dateObj, dateString: dateString, timeGE: d.td_ge, dt: +d.dt, type: d.eclipse_type, saros: +d.saros, gamma: +d.gamma, magnitude: +d.magnitude, latGE: +d.lat_dd_ge, lngGE: +d.lng_dd_ge, durationSecs: +d.duration_secs, pathWidthKm: +d.path_width, t0: +d.t0, tMin: +d.tmin, tMax: +d.tmax, // Polynomial coefficients x: [+d.x0, +d.x1, +d.x2, +d.x3 || 0], y: [+d.y0, +d.y1, +d.y2, +d.y3 || 0], d: [+d.d0, +d.d1, +d.d2, +d.d3 || 0], mu: [+d.mu0, +d.mu1, +d.mu2, +d.mu3 || 0], l1: [+d.l10, +d.l11, +d.l12, +d.l13 || 0], l2: [+d.l20, +d.l21, +d.l22, +d.l23 || 0], tanF1: +d.tan_f1, tanF2: +d.tan_f2 }; })3f:T679,eclipseFormatters = { const typeMap = { "T": "Total", "Tn": "Total (Central, No Northern Limit)", "Ts": "Total (Central, No Southern Limit)", "T+": "Total (Non-Central, No Northern Limit)", "T-": "Total (Non-Central, No Southern Limit)", "Tm": "Total (Middle of Saros Series)", "A": "Annular", "An": "Annular (Central, No Northern Limit)", "As": "Annular (Central, No Southern Limit)", "A+": "Annular (Non-Central, No Northern Limit)", "A-": "Annular (Non-Central, No Southern Limit)", "Am": "Annular (Middle of Saros Series)", "H": "Hybrid", "H2": "Hybrid (Total → Annular)", "H3": "Hybrid (Annular → Total)", "P": "Partial", "Pb": "Partial (Beginning of Saros Series)", "Pe": "Partial (End of Saros Series)" }; const monthNames = [ "January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December" ]; return { resolveType(code) { if (!code) return "Unknown"; const trimmed = code.trim(); if (typeMap[trimmed]) return typeMap[trimmed]; const baseChar = trimmed.charAt(0); const baseNames = { "T": "Total", "A": "Annular", "H": "Hybrid", "P": "Partial" }; return baseNames[baseChar] ? `${baseNames[baseChar]} (${trimmed})` : trimmed; }, formatDateLabel(e) { const monthName = monthNames[e.month - 1]; const yearDisplay = e.year < 0 ? `${Math.abs(e.year)} BCE` : `${e.year}`; return `[${e.dateString}] ${monthName} ${e.day}, ${yearDisplay}`; } }; }40:T43d,function formatCenturyLabel(startYear) { const endYear = startYear + 99; const superscripts = { "th": "ᵗʰ", "st": "ˢᵗ", "nd": "ⁿᵈ", "rd": "ʳᵈ" }; const getSuffix = (n) => { const v = n % 100; const key = ["th", "st", "nd", "rd"][(v - 20) % 10] || ["th", "st", "nd", "rd"][v] || "th"; return superscripts[key]; }; if (startYear >= 0) { const centuryNum = Math.floor(startYear / 100) + 1; const sup = getSuffix(centuryNum); const rangeStr = `${String(startYear).padStart(4, '0')}–${String(endYear).padStart(4, '0')}`; return `${centuryNum}${sup} Century (${startYear == 3000 ? startYear: rangeStr})`; } else { // BCE centuries (-1999 to -0001) const centuryNum = Math.abs(startYear / 100); const sup = getSuffix(centuryNum); const startStr = `-${String(Math.abs(startYear)).padStart(4, '0')}`; const endStr = endYear === 0 ? "0000" : `-${String(Math.abs(endYear)).padStart(4, '0')}`; return `${centuryNum}${sup} Century BCE (${centuryNum == 20 ? -1999 : startStr} to ${endStr})`; } }41:T646,eclipsePathGeoJSON = { if (!selectedEclipse) return null; const dt = selectedEclipse?.dt ?? defaultDeltaT; const centerCoords = []; const upperL1 = []; const lowerL1 = []; for (let t = -4.0; t <= 4.0; t += 0.02) { const bessel = evaluateBesselian(selectedEclipse, t); if (!bessel) continue; // Central line point (if axis hits Earth) const center = shadowEdgeToLatLon(bessel.x, bessel.y, bessel.dec, bessel.mu, 0, 0, dt); if (center) centerCoords.push(center); // Penumbra L1 limits const l1 = bessel.l1 || 0.53; // Penumbra radius const upper = shadowEdgeToLatLon(bessel.x, bessel.y, bessel.dec, bessel.mu, l1, Math.PI / 2, dt); const lower = shadowEdgeToLatLon(bessel.x, bessel.y, bessel.dec, bessel.mu, l1, -Math.PI / 2, dt); if (upper) upperL1.push(upper); if (lower) lowerL1.push(lower); } const features = [] // Central Path Feature if (centerCoords.length > 0) { features.push({ type: "Feature", properties: { pathType: "central" }, geometry: { type: "LineString", coordinates: centerCoords } }); } // Penumbra Boundaries (Dashed Lines) if (upperL1.length > 0) { features.push({ type: "Feature", properties: { pathType: "limit" }, geometry: { type: "LineString", coordinates: upperL1 } }); } if (lowerL1.length > 0) { features.push({ type: "Feature", properties: { pathType: "limit" }, geometry: { type: "LineString", coordinates: lowerL1 } }); } return features.length > 0 ? { type: "FeatureCollection", features: features } : null; }42:T430,eclipseTimeRange = { if (!selectedEclipse) return { min: -3.5, max: 3.5 }; const dt = selectedEclipse?.dt ?? defaultDeltaT; const shadowDist = (t) => { const bessel = evaluateBesselian(selectedEclipse, t); if (!bessel) return 999; const l1 = bessel.l1 || 0.53; return Math.sqrt(bessel.x * bessel.x + bessel.y * bessel.y) - (1.0 + l1); }; let t1 = -4.0; for (let t = -4.0; t <= 0; t += 0.05) { if (shadowDist(t) <= 0) { t1 = t; break; } } let t4 = 4.0; for (let t = 4.0; t >= 0; t -= 0.05) { if (shadowDist(t) <= 0) { t4 = t; break; } } const bisect = (a, b) => { for (let i = 0; i < 10; i++) { const mid = (a + b) / 2; if (shadowDist(mid) <= 0) { if (a < b) b = mid; else a = mid; } else { if (a < b) a = mid; else b = mid; } } return (a + b) / 2; }; const exactT1 = bisect(t1 - 0.1, t1); const exactT4 = bisect(t4, t4 + 0.1); return { min: Math.floor(exactT1 * 100) / 100, max: Math.ceil(exactT4 * 100) / 100 }; }43:T66a,formatAstronomicalDate = { if (!selectedEclipse) return "No eclipse selected"; const year = selectedEclipse.year ?? 2026; const month = (selectedEclipse.month ?? 1) - 1; const day = selectedEclipse.day ?? 1; const t0 = selectedEclipse.t0 ?? 12.0; const baseDate = new Date(Date.UTC(2000, month, day, 0, 0, 0)); baseDate.setUTCFullYear(year); baseDate.setUTCMilliseconds((t0 + timeOffset) * 3600 * 1000); const h = String(baseDate.getUTCHours()).padStart(2, "0"); const min = String(baseDate.getUTCMinutes()).padStart(2, "0"); const s = String(baseDate.getUTCSeconds()).padStart(2, "0"); let dateLabel; if (year < 0) { const y = `-${String(Math.abs(year)).padStart(4, "0")}`; const m = String(baseDate.getUTCMonth() + 1).padStart(2, "0"); const d = String(baseDate.getUTCDate()).padStart(2, "0"); dateLabel = `${y}-${m}-${d}`; } else if (year === 0) { const m = String(baseDate.getUTCMonth() + 1).padStart(2, "0"); const d = String(baseDate.getUTCDate()).padStart(2, "0"); dateLabel = `0000-${m}-${d}`; } else { const monthName = baseDate.toLocaleString("en-US", { month: "long", timeZone: "UTC" }); const displayYear = String(year).padStart(4, "0"); if (year >= 1900 && year <= 2100) { const weekday = baseDate.toLocaleString("en-US", { weekday: "short", timeZone: "UTC" }); dateLabel = `${weekday}, ${monthName} ${baseDate.getUTCDate()}, ${displayYear}`; } else { dateLabel = `${monthName} ${baseDate.getUTCDate()}, ${displayYear}`; } } return ` ${dateLabel} \u00A0 ${h}:${min}:${s} UTC`; }44:T6f6,function analyzeEclipseEdges(eclipse, evaluateBesselian, timeRange, steps = 50) { let hasNorthLimit = false; let hasSouthLimit = false; const tMin = timeRange.min; const tMax = timeRange.max; for (let i = 0; i <= steps; i++) { const t = tMin + (i / steps) * (tMax - tMin); const b = evaluateBesselian(eclipse, t); if (!b) continue; const x = b.x; const y = b.y; const l1 = b.l1 || 0.53; const northDistSq = x * x + (y + l1) * (y + l1); if (northDistSq <= 1.0) { hasNorthLimit = true; } const southDistSq = x * x + (y - l1) * (y - l1); if (southDistSq <= 1.0) { hasSouthLimit = true; } } if (hasNorthLimit && hasSouthLimit) { return { limitCount: 2, hasNorthLimit: true, hasSouthLimit: true, shadowDirection: "BETWEEN", description: "Standard eclipse with both Northern and Southern limit lines." }; } else if (hasNorthLimit && !hasSouthLimit) { return { limitCount: 1, hasNorthLimit: true, hasSouthLimit: false, shadowDirection: "SOUTH_OF_NORTH_LIMIT", description: "Non-central eclipse. Shadow axis passes South of Earth; shadow lies SOUTH of Northern limit." }; } else if (!hasNorthLimit && hasSouthLimit) { return { limitCount: 1, hasNorthLimit: false, hasSouthLimit: true, shadowDirection: "NORTH_OF_SOUTH_LIMIT", description: "Non-central eclipse. Shadow axis passes North of Earth; shadow lies NORTH of Southern limit." }; } else { return { limitCount: 0, hasNorthLimit: false, hasSouthLimit: false, shadowDirection: "HORIZON_ONLY", description: "Partial eclipse where penumbra grazes the Earth without full limit line coverage." }; } }45:T6b2,staticEclipseBounds = { if (!selectedEclipse || !eclipseEdgeAnalysis) return null; const { limitCount, hasNorthLimit, hasSouthLimit, shadowDirection } = eclipseEdgeAnalysis; const dt = selectedEclipse?.dt ?? defaultDeltaT; const tMin = eclipseTimeRange.min; const tMax = eclipseTimeRange.max; const steps = 60; const features = []; const northEdge = []; if (hasNorthLimit) { for (let i = 0; i <= steps; i++) { const t = tMin + (i / steps) * (tMax - tMin); const b = evaluateBesselian(selectedEclipse, t); if (!b) continue; const l1 = b.l1 || 0.53; const pt = shadowEdgeToLatLon(b.x, b.y, b.dec, b.mu, l1, Math.PI / 2, dt); if (pt && !isNaN(pt[0]) && !isNaN(pt[1])) northEdge.push(pt); } if (northEdge.length > 1) { features.push({ type: "Feature", properties: { layer: "northLimit", side: "NORTH" }, geometry: { type: "LineString", coordinates: northEdge } }); } } const southEdge = []; if (hasSouthLimit) { for (let i = 0; i <= steps; i++) { const t = tMin + (i / steps) * (tMax - tMin); const b = evaluateBesselian(selectedEclipse, t); if (!b) continue; const l1 = b.l1 || 0.53; const pt = shadowEdgeToLatLon(b.x, b.y, b.dec, b.mu, l1, -Math.PI / 2, dt); if (pt && !isNaN(pt[0]) && !isNaN(pt[1])) southEdge.push(pt); } if (southEdge.length > 1) { features.push({ type: "Feature", properties: { layer: "southLimit", side: "SOUTH" }, geometry: { type: "LineString", coordinates: southEdge } }); } } return { type: "FeatureCollection", analysis: eclipseEdgeAnalysis, features: features }; }46:T86c,penumbralEnvelopeZone = { if (!selectedEclipse || !eclipseTimeRange) return null; const dt = selectedEclipse?.dt ?? defaultDeltaT; const tMin = eclipseTimeRange.min; const tMax = eclipseTimeRange.max; const bandScales = [0.03, 0.03, 0.03, 0.03, 0.12, 0.12, 0.12, 0.25, 0.25, 0.25, 0.5, 0.5, 0.75, 1]; const getPenumbralEdgePoint = (x, y, l1, dec, mu, isNorthernEdge) => { if (Math.abs(x) >= 0.999) return null; const maxY = Math.sqrt(1 - x * x); const rawTargetY = isNorthernEdge ? (y + l1) : (y - l1); const clampedY = Math.max(-maxY * 0.999, Math.min(maxY * 0.999, rawTargetY)); if (Math.abs(clampedY - y) > l1 + 0.05) return null; const pt = shadowAxisToLatLon(x, clampedY, dec, mu, dt); if (pt && !isNaN(pt[0]) && !isNaN(pt[1])) return pt; return null; }; const features = bandScales.map(scale => { const steps = scale <= 0.2 ? 120 : 250; const northBoundary = []; const southBoundary = []; for (let i = 0; i <= steps; i++) { const t = tMin + (i / steps) * (tMax - tMin); const b = evaluateBesselian(selectedEclipse, t); if (!b) continue; const l1 = (b.l1 || 0.53) * scale; const ptN = getPenumbralEdgePoint(b.x, b.y, l1, b.dec, b.mu, true); if (ptN) northBoundary.push(ptN); const ptS = getPenumbralEdgePoint(b.x, b.y, l1, b.dec, b.mu, false); if (ptS) southBoundary.push(ptS); } if (northBoundary.length < 2 || southBoundary.length < 2) return null; const ring = [...northBoundary, ...southBoundary.slice().reverse()]; ring.push(ring[0]); let geometry = { type: "Polygon", coordinates: [ring] }; if (d3.geoArea(geometry) > 2 * Math.PI) { ring.reverse(); geometry = { type: "Polygon", coordinates: [ring] }; } return { type: "Feature", properties: { scale }, geometry: geometry }; }).filter(Boolean); if (features.length === 0) return null; return { type: "FeatureCollection", features: features }; 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Eclipses","cells":[{"id":0,"value":"# Solar Eclipses","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":814,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":647,"value":"$34","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":656,"value":"---\n\n## Eclipse Visualization\n\nSelect a solar eclipse from the catalog. Rotate the 3D globe to follow the Moon’s shadow path across Earth.\n

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1; i >= 0; i--) {\n res = res * t + coeffs[i];\n }\n return res;\n };\n\n return {\n x: evalPoly(eclipseData.x, tHours),\n y: evalPoly(eclipseData.y, tHours),\n dec: evalPoly(eclipseData.d || eclipseData.dec, tHours),\n mu: evalPoly(eclipseData.mu, tHours),\n l1: evalPoly(eclipseData.l1, tHours),\n l2: evalPoly(eclipseData.l2, tHours)\n };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":33,"value":"shadowAxisToLatLon = (x, y, dec, mu, deltaT = selectedEclipse.dt) => {\n if (x == null || y == null || dec == null || mu == null) return null;\n\n const dRad = dec * (Math.PI / 180);\n\n const muCorrected = mu - (deltaT / 240.0);\n const muRad = muCorrected * (Math.PI / 180);\n\n const rho2 = x * x + y * y;\n if (rho2 > 1.0) return null;\n\n const z = Math.sqrt(1.0 - rho2);\n\n const sinD = Math.sin(dRad);\n const cosD = Math.cos(dRad);\n\n const eta = y * cosD + z * sinD;\n const zeta = -y * sinD + z * cosD;\n\n const latGeocentric = Math.asin(Math.max(-1, Math.min(1, eta)));\n const e2 = 0.006694385;\n const latRad = Math.atan(Math.tan(latGeocentric) / (1 - e2));\n const lat = latRad * (180 / Math.PI);\n\n const HRad = Math.atan2(x, zeta);\n\n let lonRad = HRad - muRad;\n let lon = lonRad * (180 / Math.PI);\n\n\n\n // Wrap to range [-180, +180]\n lon = ((lon + 180) % 360 + 360) % 360 - 180;\n\n return [lon, lat];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":238,"value":"shadowEdgeToLatLon = (x, y, dec, mu, radius = 0, angleRad = 0, deltaT = selectedEclipse.dt) => {\n if (x == null || y == null || dec == null || mu == null) return null;\n\n const px = x + radius * Math.cos(angleRad);\n const py = y + radius * Math.sin(angleRad);\n\n const rho2 = px * px + py * py;\n if (rho2 > 1.0) return null;\n\n const z = Math.sqrt(1.0 - rho2);\n const dRad = dec * (Math.PI / 180);\n\n const sinD = Math.sin(dRad);\n const cosD = Math.cos(dRad);\n\n const eta = py * cosD + z * sinD;\n const zeta = -py * sinD + z * cosD;\n\n const latGeocentric = Math.asin(Math.max(-1, Math.min(1, eta)));\n const e2 = 0.006694385;\n const latRad = Math.atan(Math.tan(latGeocentric) / (1 - e2));\n const lat = latRad * (180 / Math.PI);\n\n const HRad = Math.atan2(px, zeta);\n const muCorrected = mu - (deltaT / 240.0);\n const muRad = muCorrected * (Math.PI / 180);\n\n let lonRad = HRad - muRad;\n let lon = lonRad * (180 / Math.PI);\n lon = ((lon + 180) % 360 + 360) % 360 - 180;\n\n return [lon, lat];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":47,"value":"$41","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":253,"value":"mutable globeRotation = [-(selectedEclipse?.lngGE ?? 0), -(selectedEclipse?.latGE ?? 0), 0];","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":670,"value":"timeOffset = controls.timeOffset","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":672,"value":"mapWidth = controls.mapWidth","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2452,"value":"mutable eclipsePlaySpeed = 600","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2490,"value":"mutable hasScrolledToEclipse = false;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":266,"value":"$42","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":272,"value":"$43","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":328,"value":"$44","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":331,"value":"eclipseEdgeAnalysis = {\n if (!selectedEclipse || !eclipseTimeRange) return null;\n return analyzeEclipseEdges(selectedEclipse, evaluateBesselian, eclipseTimeRange);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":335,"value":"$45","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":340,"value":"function getShadowBoundaryPoints(bessel, dt) {\n if (!bessel) return null;\n\n const { x, y, dec, mu, l1 } = bessel;\n const radius = l1 || 0.53;\n\n const xN = x;\n const yN = y + radius;\n let northPt = null;\n\n const distNSq = xN * xN + yN * yN;\n if (distNSq <= 1.0) {\n northPt = shadowAxisToLatLon(xN, yN, dec, mu, dt);\n } else {\n\n const norm = Math.hypot(xN, yN);\n if (norm > 0) {\n const cx = xN / norm;\n const cy = yN / norm;\n\n northPt = shadowAxisToLatLon(cx, cy, dec, mu, dt);\n }\n }\n\n // 2. Evaluate Southern Point (-90°)\n const xS = x;\n const yS = y - radius;\n let southPt = null;\n\n const distSSq = xS * xS + yS * yS;\n if (distSSq <= 1.0) {\n southPt = shadowAxisToLatLon(xS, yS, dec, mu, dt);\n } else {\n\n const norm = Math.hypot(xS, yS);\n if (norm > 0) {\n const cx = xS / norm;\n const cy = yS / norm;\n southPt = shadowAxisToLatLon(cx, cy, dec, mu, dt);\n }\n }\n\n return { northPt, southPt };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":342,"value":"$46","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2678,"value":"// https://observablehq.com/@mbostock/saving-svg\nserialize = {\n const xmlns = \"http://www.w3.org/2000/xmlns/\";\n const xlinkns = \"http://www.w3.org/1999/xlink\";\n const svgns = \"http://www.w3.org/2000/svg\";\n return function serialize(svg) {\n svg = svg.cloneNode(true);\n const fragment = window.location.href + \"#\";\n const walker = document.createTreeWalker(svg, NodeFilter.SHOW_ELEMENT);\n while (walker.nextNode()) {\n for (const attr of walker.currentNode.attributes) {\n if (attr.value.includes(fragment)) {\n attr.value = attr.value.replace(fragment, \"#\");\n }\n }\n }\n svg.setAttributeNS(xmlns, \"xmlns\", svgns);\n svg.setAttributeNS(xmlns, \"xmlns:xlink\", xlinkns);\n const serializer = new window.XMLSerializer;\n const string = serializer.serializeToString(svg);\n return new Blob([string], {type: \"image/svg+xml\"});\n };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2681,"value":"// https://observablehq.com/@mbostock/saving-svg\nfunction rasterize(svg) {\n let resolve, reject;\n const promise = new Promise((y, n) => (resolve = y, reject = n));\n const image = new Image;\n image.onerror = reject;\n image.onload = () => {\n const rect = svg.getBoundingClientRect();\n const context = DOM.context2d(rect.width, rect.height);\n context.drawImage(image, 0, 0, rect.width, rect.height);\n context.canvas.toBlob(resolve);\n };\n image.src = URL.createObjectURL(serialize(svg));\n return promise;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W47","stdlib":"2","titling":"auto"}} 32:"$31:body"