[{"data":1,"prerenderedAt":1082},["ShallowReactive",2],{"layer:eclipses:understand":3},{"layer":4,"contentHash":1062,"dependencyHashes":1063,"approval":1076,"releaseId":1081},{"schemaVersion":5,"conceptId":6,"locale":7,"depth":8,"revision":5,"title":9,"subtitle":10,"summary":11,"objectives":12,"estimatedMinutes":18,"plate":19,"blocks":43,"sourceIds":1057,"reviewStatus":1058,"authoring":1059},1,"eclipses","en","understand","The geometry of a shadow in space","Umbra and penumbra, apparent sizes, nodes and seasons — and the reasons behind every safety rule","Work out the actual geometry: how long each shadow cone is, why the Moon's only just reaches us, why the discs match to 3%, how far from a node an eclipse can happen, why the Moon turns red, and the physics behind every solar viewing rule.",[13,14,15,16,17],"Calculate the length and width of a shadow cone using similar triangles, for the Moon and for Earth.","Predict whether a solar eclipse will be total, annular or partial from the Moon's and Sun's apparent sizes.","Explain why lunar eclipses last hours and are seen from half the planet, while solar totality lasts minutes in a 160 km strip.","Explain the red colour of an eclipsed Moon using refraction and scattering, and read the Danjon scale.","State every solar viewing rule with the physical reason behind it, and set up a projection with a known image size.",40,{"title":20,"rows":21},"Lesson plate",[22,25,28,31,34,37,40],{"label":23,"value":24},"Depth","Understand",{"label":26,"value":27},"Reading time","≈ 40 minutes",{"label":29,"value":30},"Prior knowledge","Eclipses = shadows (Discover); shadows (Light)",{"label":32,"value":33},"Chapters","9",{"label":35,"value":36},"Labs","Shadow lab, eclipse lab ×3, safety sort",{"label":38,"value":39},"Maths used","Similar triangles, ratios, sine (explained)",{"label":41,"value":42},"Safety","Full solar viewing rules with reasons",[44,50,56,62,65,81,101,126,131,167,172,175,208,222,227,241,246,249,279,292,307,312,330,335,338,375,389,393,404,409,415,419,447,452,465,470,473,488,528,543,548,554,559,562,594,611,614,627,631,636,641,681,685,699,763,768,832,890,1024,1028,1045],{"id":45,"type":46,"markdown":47,"help":48},"u-intro","prose","In Discover you met the idea: an eclipse is a shadow falling somewhere that somebody can see it. That is true, and it is enough to tell solar from lunar and to watch one safely.\n\nBut it leaves a pile of sharper questions unanswered.\n\n- Why does a shadow have a dark middle and a grey edge at all?\n- The Moon's shadow cone is about 374,000 km long and the Moon is about 384,400 km away. Those numbers do not fit. So how do we ever get a total eclipse?\n- Why is the path of totality so absurdly narrow — 160 km on a planet 12,742 km across?\n- Why is the eclipsed Moon **red** rather than simply dark, and why is it never the same red twice?\n- How tilted is \"tilted\", exactly, and how tilted would be too tilted?\n\nThis layer answers all of them with numbers you can check. Nothing here needs more than multiplication, division and the idea of similar triangles.",{"simplerExplanation":49},"Discover told you what an eclipse is. This layer shows you the geometry that decides which kind you get, where, and for how long.",{"id":51,"type":52,"variant":53,"title":54,"markdown":55},"u-how-to-read","callout","observation","How to use this lesson","Chapters build on each other, so read in order the first time. Every number in this lesson was calculated rather than copied, and the working is shown where it matters, so you can check it.\n\nWherever you see a **prediction**, decide your answer before reading on. And wherever you see a **safety** box, read it even if you think you already know — the rules are not obvious, and one of them catches almost everybody.",{"id":57,"type":58,"title":59,"eyebrow":60,"navLabel":61},"u-ch1","chapter","Why a shadow has two parts","Chapter 01","1 Two-part shadow",{"id":63,"type":46,"markdown":64},"u-two-parts","If the Sun were a single glowing point, every shadow in the world would have a knife-sharp edge. Light would either reach a place or it would not, and there would be nothing in between.\n\nThe Sun is not a point. It is a disc about half a degree wide. That single fact is responsible for the whole structure of an eclipse.\n\nStand somewhere behind a blocking object and ask: **how much of the Sun's disc can I see from here?**\n\n- **None of it.** You are in the **umbra**. The blocker covers the whole disc. This is total darkness as far as that source is concerned.\n- **Some of it.** You are in the **penumbra**. Part of the disc peeps past one edge of the blocker. There is real light here, just less of it.\n- **All of it.** You are outside the shadow entirely.\n\nThat is the entire definition, and it works for a hand in front of a lamp, for the Moon in front of the Sun, and for Earth in front of the Sun.",{"id":66,"type":67,"items":68},"u-formula-cone","formulas",[69,72,75,78],{"expression":70,"caption":71},"L = r × D ÷ (R − r)","Length of the umbra cone behind a body of radius r, lit by a source of radius R at distance D.",{"expression":73,"caption":74},"L(Moon) = 374,180 km","r = 1,737 km, R = 696,350 km, D = 149,597,871 km.",{"expression":76,"caption":77},"L(Earth) = 1,381,300 km","r = 6,371 km, same Sun. Earth is bigger, so its shadow reaches much further.",{"expression":79,"caption":80},"w = 2r × (1 − d ÷ L)","Width of the umbra at distance d along the cone. At d = L it has shrunk to nothing.",{"id":82,"type":83,"title":84,"problem":85,"steps":86,"help":96},"u-we-umbra-length","worked_example","How long is the Moon's shadow?","The Moon has a radius of 1,737 km. The Sun has a radius of 696,350 km and sits 149,597,871 km away. How far behind the Moon does its full-dark umbra cone reach before it tapers to a point?",[87,88,89,90,91,92,93,94,95],"Draw the two outer rays: one from the **top** of the Sun past the **bottom** of the Moon, the other from the bottom of the Sun past the top of the Moon. They cross at the tip of the umbra.","This gives two similar triangles. The big one has half-height (R − r) over the length D; the small one has half-height r over the length L.","So r ÷ L = (R − r) ÷ D, which rearranges to L = r × D ÷ (R − r).","Put the numbers in: R − r = 696,350 − 1,737 = **694,613 km**.","L = 1,737 × 149,597,871 ÷ 694,613.","149,597,871 ÷ 694,613 = 215.4, and 1,737 × 215.4 = **374,180 km**.","Now compare that with the Moon's average distance from Earth: **384,400 km**. The cone is about 10,000 km **too short**.","Subtract Earth's radius, because an observer stands on the surface, 6,371 km nearer: the gap is still about **3,850 km**.","**Conclusion:** at the Moon's average distance, the umbra does not reach the ground at all. An average eclipse is annular, not total.",{"simplerExplanation":97,"hints":98},"The Moon's full shadow is a cone about 374,000 km long. The Moon is on average 384,400 km away. The cone runs out before it gets here — unless the Moon happens to be closer than usual.",[99,100],"Sketch the two crossing rays first. The similar triangles jump out.","Check the subtraction: 696,350 − 1,737, not 696,350 − 3,475.",{"id":102,"type":103,"caption":104,"columns":105,"rows":109},"u-table-two-cones","table","The two shadow cones, side by side",[106,107,108],"Property","Moon's umbra","Earth's umbra",[110,114,118,122],[111,112,113],"Length","374,180 km","1,381,300 km",[115,116,117],"Casts onto","Earth (sometimes)","The Moon (sometimes)",[119,120,121],"Reaches the target?","Only just, and only near perigee","Easily — 3.6× the Moon's own distance",[123,124,125],"Footprint width there","≈160 km","≈9,196 km (2.6 Moon-widths)",{"id":127,"type":52,"variant":128,"title":129,"markdown":130},"u-aha-just-barely","aha","Totality is a near miss, every single time","Look at those two numbers again:\n\n- Length of the Moon's umbra cone: **374,180 km**\n- Distance from the Moon to Earth's surface, on average: **378,029 km**\n\nThe shadow falls short by about **3,850 km** — less than 1% of the distance. The Moon's orbit is not a circle, though: it swings between about 363,300 km and 405,500 km. So when an eclipse catches the Moon near its closest point, the cone overshoots the surface by about **17,250 km** and a real black shadow lands on us.\n\nEvery total solar eclipse in history has depended on that 1% margin. It is the tightest coincidence in the visible sky.",{"id":132,"type":133,"component":134,"componentVersion":5,"config":135,"objective":161,"textAlternative":162,"help":163},"u-lab-shadow","interactive","shadow-lab",{"objects":136,"source":149,"maxDistanceCm":150,"challenges":151},[137,141,145],{"id":138,"label":139,"heightCm":140},"moon","2 cm ball (Moon)",2,{"id":142,"label":143,"heightCm":144},"earth","7 cm ball (Earth)",7,{"id":146,"label":147,"heightCm":148},"big","15 cm disc",15,"both",400,[152,155,158],{"prompt":153,"targetRatio":154},"Find the distance where the umbra just vanishes to a point.",0.05,{"prompt":156,"targetRatio":157},"Make the umbra exactly half as wide as the ball.",0.5,{"prompt":159,"targetRatio":160},"Make the penumbra three times the ball's width.",3,"Measure a real umbra and penumbra, find where the umbra tapers to nothing, and check the similar-triangles rule.","A lamp, a movable ball and a screen, with a ruler along the base and a readout of the umbra and penumbra widths.\n\nSwitch the source to **extended** so there is a real penumbra. Now slide the ball away from the lamp and watch two things happen at once: the **umbra shrinks** and the **penumbra grows**.\n\nKeep sliding and the umbra reaches zero width — its cone has ended exactly at the screen. Push the ball a little further and the umbra does not come back; instead a small bright patch appears in the middle of the shadow, because the lamp is now peeping past the ball on *every* side at once. That bright-centred shadow is the model of an **annular** eclipse, and the region beyond the cone's tip has its own name: the **antumbra**.\n\nCheck the arithmetic with the point source, where the shadow is a simple projection: a 2 cm ball 20 cm from the lamp, screen at 60 cm, gives 2 × 60 ÷ 20 = **6 cm**. At 30 cm it gives **4 cm**. At 40 cm, **3 cm**.",{"hints":164},[165,166],"Push the ball past the point where the umbra vanishes and look at the middle of the shadow.","That bright middle is what an annular eclipse is: you are standing beyond the tip of the cone.",{"id":168,"type":58,"title":169,"eyebrow":170,"navLabel":171},"u-ch2","Solar eclipse: the exact conditions","Chapter 02","2 Solar geometry",{"id":173,"type":46,"markdown":174},"u-solar-conditions","A solar eclipse needs **three** things to be true at the same moment. Miss any one and nothing happens.\n\n**1. It must be new moon.** The Moon has to be on the Sun's side of Earth. This is not a coincidence you hope for; it happens every 29.53 days like clockwork.\n\n**2. The Moon must be near a node.** Its tilted orbit must be crossing the plane of Earth's orbit right now, so that \"between Earth and the Sun\" really means *in front of the Sun* and not 34,000 km above it. This is the condition that fails most months.\n\n**3. You must be standing where the shadow lands.** Even when conditions 1 and 2 are met, the umbra's footprint is a spot roughly 160 km across on a planet 12,742 km across. Almost everybody is outside it.\n\nThe third condition is the one people forget. A total solar eclipse is happening somewhere on Earth about every 18 months. A total solar eclipse is happening *over your house* about once in 375 years.",{"id":176,"type":177,"tone":178,"items":179},"u-spec-solar","spec","amber",[180,184,188,192,196,200,204],{"label":181,"big":182,"value":183},"Must be","New moon","Every 29.53 days — the synodic month.",{"label":185,"big":186,"value":187},"Must be near","A node","Within about 16.6° of longitude from the node for any solar eclipse at all.",{"label":189,"big":190,"value":191},"Umbra footprint","≈ 160 km","Typical width of the path of totality. Maximum possible: 267 km.",{"label":193,"big":194,"value":195},"Penumbra footprint","1000s of km","Thousands of kilometres across — this is why partial eclipses are common.",{"label":197,"big":198,"value":199},"Shadow ground speed","≥ 2,000 km\u002Fh","The Moon's shadow moves at 3,679 km\u002Fh; Earth's surface chases it at up to 1,674 km\u002Fh at the equator.",{"label":201,"big":202,"value":203},"Longest totality","7 min 32 s","The theoretical maximum. Two to three minutes is typical.",{"label":205,"big":206,"value":207},"Chance for one spot","≈ 375 years","The average wait for totality to pass over any particular place.",{"id":209,"type":83,"title":210,"problem":211,"steps":212,"help":220},"u-we-shadow-speed","How fast does the Moon's shadow race across India?","The Moon travels along its orbit at about 1.022 km per second. Earth spins eastwards, carrying the ground at the equator right round its 40,075 km circumference in one sidereal day of 23.934 hours. Both move the same way — eastwards. Estimate the slowest the shadow can sweep across the ground.",[213,214,215,216,217,218,219],"The shadow follows the Moon, so through space it moves at about 1.022 km\u002Fs.","Turn that into km\u002Fh: 1.022 × 3,600 = **3,679 km\u002Fh**.","Now the ground. Equatorial speed = 40,075 ÷ 23.934 = **1,674 km\u002Fh**, also eastwards.","Because both move east, the ground is *running after* the shadow, so the shadow's speed **relative to you** is the difference.","3,679 − 1,674 = **about 2,005 km\u002Fh**, say 2,000 km\u002Fh.","That is the best case: standing on the equator, with the Sun overhead. Away from the equator the ground moves slower, and the shadow strikes at an angle and stretches out, so it can exceed 8,000 km\u002Fh near the poles.","**Sense check:** a 160 km path crossed at 2,000 km\u002Fh takes 160 ÷ 2,000 hours = 0.08 h = **4.8 minutes**. Totality is shorter still, because you are only in the very middle for part of that, and the real maximum is 7 min 32 s under the most favourable geometry.",{"simplerExplanation":221},"The shadow flies east at about 3,700 km\u002Fh. You are already running east at up to 1,674 km\u002Fh. The difference, about 2,000 km\u002Fh, is how fast it overtakes you — which is why totality is measured in minutes, not hours.",{"id":223,"type":52,"variant":224,"title":225,"markdown":226},"u-misconception-close","misconception","\"The Moon must be very close for a total eclipse\"","Half right, and the half that is wrong matters.\n\nThe Moon does have to be **nearer than usual** — inside about 379,500 km rather than its average 384,400 km. But \"nearer\" here means about **1% nearer**, not dramatically closer. The Moon does not swoop in. It simply happens to be at the near end of a slightly oval orbit.\n\nA second version of the same mistake: \"the Moon must be directly overhead\". It need not be. It must be in front of the **Sun** as seen from where you stand, and that can be anywhere from the zenith to low in the sky. Eclipses at sunrise and sunset are real, and rather beautiful.",{"id":228,"type":133,"component":229,"componentVersion":5,"config":230,"objective":235,"textAlternative":236,"help":237},"u-lab-solar","eclipse-lab",{"modes":231,"showShadowCones":233,"tiltDegrees":234},[232],"solar",true,5.1,"Change the Moon's distance and alignment, and watch the umbra reach the ground, fall short, or miss Earth entirely.","The Sun, the Moon and Earth drawn from the side, with both shadow cones marked behind the Moon and a distance slider for the Moon.\n\nSet the Moon to **perigee, 363,300 km**. The umbra cone's tip now lies about 17,250 km *beyond* Earth's surface, so a black spot around 160 km wide lands on the globe. The view panel shows a black disc with a corona: **total**.\n\nSet the Moon to its **mean distance, 384,400 km**. The cone's tip now falls about 3,850 km *short* of the surface. No black spot lands. Instead the region past the tip — the **antumbra** — reaches us, and the panel shows a black disc inside a bright ring: **annular**.\n\nSet the Moon to **apogee, 405,500 km**. The cone falls short by over 35,000 km and the ring is at its widest, with about 18% of the Sun's face still shining.\n\nNow move the Moon off the Sun–Earth line. Within a small range the black spot slides off the globe while the grey penumbra still clips it: everyone there sees a **partial** eclipse. Further still and both cones miss Earth and nothing happens at all.",{"hints":238},[239,240],"Watch where the umbra's tip is compared with Earth's surface. That single fact decides total versus annular.","Count how wide the range of 'nothing happens' is compared with the range that gives an eclipse.",{"id":242,"type":58,"title":243,"eyebrow":244,"navLabel":245},"u-ch3","The three kinds of solar eclipse","Chapter 03","3 Total, annular…",{"id":247,"type":46,"markdown":248},"u-three-kinds","Everything about which kind of solar eclipse you get comes down to a single comparison: **is the Moon's disc bigger or smaller than the Sun's disc, as seen from where you stand?**\n\nBoth discs change size, because both orbits are slightly oval.\n\nThe Sun's apparent width ranges from **31.5 arcminutes** (early July, when Earth is furthest out) to **32.5 arcminutes** (early January, when Earth is closest). An arcminute is one sixtieth of a degree.\n\nThe Moon's apparent width ranges much more: from **29.5 arcminutes** at apogee to **32.9 arcminutes** at perigee.\n\nThose two ranges overlap. So:\n\n- **Moon bigger than the Sun** → the disc is fully covered → **total**.\n- **Moon smaller than the Sun** → a ring of Sun is left → **annular**.\n- **Only the penumbra reaches you** → **partial**, whatever the distances.\n\nAnd there is a fourth, rare case. Earth is round, so someone standing directly beneath the shadow is about 6,371 km closer to the Moon than someone near the edge of the illuminated face. If the cone's tip falls in between, the same eclipse is **total** in the middle of its track and **annular** at both ends. That is a **hybrid** eclipse, and only a few per century happen.",{"id":250,"type":103,"caption":251,"columns":252,"rows":257},"u-table-sizes","Apparent widths in arcminutes: which disc wins",[253,254,255,256],"Situation","Moon","Sun","Result",[258,263,267,272,276],[259,260,261,262],"Moon at perigee, Sun in July","32.9′","31.5′","Moon wins by 4.5% — deep **total**, longest totality",[264,260,265,266],"Moon at perigee, Sun in January","32.5′","Moon just wins — **total**, but brief",[268,269,270,271],"Moon at mean distance","31.1′","32.0′","Sun wins narrowly — a thin **annular** ring",[273,274,261,275],"Moon at apogee, Sun in July","29.5′","Sun wins — **annular**, a clear ring",[277,274,265,278],"Moon at apogee, Sun in January","Sun wins by 9.5% — widest ring; about **18%** of the Sun's face still showing",{"id":280,"type":83,"title":281,"problem":282,"steps":283,"help":289},"u-we-ring","How much Sun is left in the widest ring of fire?","In the deepest annular eclipse, the Moon looks 29.5 arcminutes across and the Sun 32.5 arcminutes across. What fraction of the **area** of the Sun's face is still shining?",[284,285,286,287,288],"Width tells you about diameters. Brightness depends on **area**, and area goes as the square of the diameter.","Fraction of the Sun's diameter that the Moon covers: 29.5 ÷ 32.5 = **0.905**, or 90.5%.","Fraction of the Sun's **area** covered: 0.905 × 0.905 = 0.819, or **81.9%**.","So the fraction still shining is 100 − 81.9 = **18.1%**.","**Why this matters for your eyes:** nearly a fifth of the Sun's blazing surface is visible the whole time. The sky barely darkens. There is no safe moment in an annular eclipse, ever. Certified filters or projection from beginning to end.",{"simplerExplanation":290,"anotherExample":291},"The Moon covers about 90% of the Sun's width, which is only about 82% of its area. Roughly 18% of the Sun is left shining — far too much to look at.","Even at 99% coverage by width, about 2% of the Sun's area is still shining. Two per cent of the Sun is still thousands of times brighter than anything else you ever look at.",{"id":293,"type":294,"itemId":295,"prompt":296,"check":297,"hints":301,"feedback":304},"u-practice-ring","practice","eclipses.understand-p-ring","The Moon looks 30 arcminutes across and the Sun 32 arcminutes across. What percentage of the Sun's diameter does the Moon cover? Round to the nearest whole per cent.",{"kind":298,"answer":299,"tolerance":5,"unit":300},"number",94,"%",[302,303],"Divide the Moon's width by the Sun's width, then convert to a percentage.","30 ÷ 32 × 100 = ?",{"correct":305,"incorrect":306},"Right: 30 ÷ 32 × 100 ≈ 94%. Remember this is diameter coverage, not area — the area covered is smaller still (about 88%).","30 ÷ 32 = 0.9375, or about 94% of the diameter. Squaring that gives the area covered, roughly 88%, leaving about 12% of the Sun's area as a ring.",{"id":308,"type":52,"variant":309,"title":310,"markdown":311},"u-safety-annular","careful","Eye safety: annular and partial eclipses have no safe moment","This is the rule that catches people out, so it gets its own box.\n\nDuring a **total** eclipse there are a few minutes when the Sun's bright surface is entirely hidden. That, and only that, is when bare eyes are allowed.\n\nDuring an **annular** eclipse, a blazing ring of the Sun's surface is showing the **entire time** — about 18% of its face in the deepest case. During a **partial** eclipse, part of the surface is showing the entire time.\n\nSo: **for annular and partial eclipses, certified ISO 12312-2 filters or projection, from first contact to last. No exceptions, no quick glances.**\n\nThe deceptive part is that the sky looks dimmer and your eyes feel comfortable, so it *seems* safe. Your comfort is not the test. The Sun's surface is at about 5,500 °C whether 1% or 100% of it is showing, and the retina cannot tell the difference until the damage is done.",{"id":313,"type":314,"prompt":315,"options":316,"explanation":329},"u-predict-99","prediction","At maximum, a partial eclipse covers 99% of the Sun's **diameter** as seen from your town. Is it safe to take a quick look with bare eyes?",[317,320,323,326],{"id":318,"label":319},"a","Yes — only 1% is left, that is nothing",{"id":321,"label":322},"b","Yes, as long as it is under two seconds",{"id":324,"label":325},"c","No — about 2% of the Sun's area is still shining, thousands of times too bright",{"id":327,"label":328},"d","Yes, if you squint","**No (c).** Two separate reasons, and either one is enough.\n\nFirst the arithmetic. 99% of the diameter covered means 0.99 × 0.99 = 0.980 of the **area** covered, so **2%** of the Sun's face is still shining. The Sun is about 400,000 times brighter than a full moon; 2% of it is still around 8,000 times brighter than a full moon.\n\nSecond, and worse: at 99% coverage your pupils have **opened wide** because the surroundings are dim. A wide pupil lets far more of that remaining light onto the retina than a normal daytime pupil would. The dimmed sky actively makes it more dangerous, not less.\n\nAnd squinting does nothing at all: eyelids are not filters.\n\nThe only correct action is filters or projection.",{"id":331,"type":58,"title":332,"eyebrow":333,"navLabel":334},"u-ch4","Lunar eclipse: a much bigger target","Chapter 04","4 Lunar geometry",{"id":336,"type":46,"markdown":337},"u-lunar-geometry","Turn around and look at the other shadow.\n\nEarth is 3.67 times wider than the Moon, so its shadow cone is far longer and far fatter. Its umbra runs **1,381,300 km** into space — about **3.6 times** the Moon's distance from us. So where the Moon crosses it, the cone is nowhere near tapering out. It is still enormous.\n\nHow enormous? Use the taper formula. At 384,400 km along a 1,381,300 km cone, the umbra's radius has shrunk from Earth's own 6,371 km to:\n\n6,371 × (1 − 384,400 ÷ 1,381,300) = 6,371 × 0.7217 = **4,598 km**\n\nThat is a circle **9,196 km across** — about **2.6 Moon-widths**. The Moon, only 3,475 km wide, drops into it with room on either side.\n\nAround that sits the penumbra, about **4.7 Moon-widths** across.\n\nThis single fact explains everything that is different about lunar eclipses: they last hours instead of minutes, they can be total for a long stretch, the Moon can even pass through slightly off-centre and still be entirely swallowed — and because it is the **Moon** that changes rather than a small patch of Earth, everyone on the night side sees the same thing at the same instant.",{"id":339,"type":340,"title":341,"items":342},"u-steps-lunar","steps","The stages of a total lunar eclipse, and how long each takes",[343,347,351,355,359,363,367,371],{"title":344,"tag":345,"text":346},"P1 — penumbra begins","0:00","The Moon's edge enters the grey penumbra. Almost nothing is visible. Most people looking up would say the Moon is normal.",{"title":348,"tag":349,"text":350},"Subtle shading","~0:45","One side of the Moon looks faintly grubby. Photographs show it better than eyes do.",{"title":352,"tag":353,"text":354},"U1 — partial begins","1:05","The Moon's edge touches the dark umbra. Now it is unmistakable: a sharp, curved bite.",{"title":356,"tag":357,"text":358},"The bite grows","~1 hour","The curve of the shadow creeps across. Its edge is always the same curve — the round shadow of a round Earth.",{"title":360,"tag":361,"text":362},"U2 — totality begins","2:10","The last bright sliver goes. The whole Moon is inside the umbra and turns copper-red.",{"title":364,"tag":365,"text":366},"Greatest eclipse","middle","Deepest colour. If the Moon passes centrally, this is the darkest moment.",{"title":368,"tag":369,"text":370},"U3 — totality ends","up to 1 h 40 m later","A brilliant white edge reappears, and your eyes, now dark-adapted, find it startlingly bright.",{"title":372,"tag":373,"text":374},"U4 and P4","the reverse","Partial phase unwinds, then the penumbral phase. The whole event runs about 5 to 6 hours from P1 to P4.",{"id":376,"type":83,"title":377,"problem":378,"steps":379,"help":387},"u-we-lunar-duration","Why totality lasts so much longer for the Moon","Earth's umbra where the Moon crosses it is 9,196 km across. The Moon is 3,475 km across, and it moves relative to the shadow at about 3,408 km per hour. Roughly how long can the Moon stay completely inside the umbra?",[380,381,382,383,384,385,386],"Totality starts when the Moon's **trailing** edge enters the shadow and ends when its **leading** edge leaves.","So the centre of the Moon has to travel the width of the umbra **minus** one Moon-width.","Distance = 9,196 − 3,475 = **5,721 km**.","Speed relative to the shadow: the Moon goes right round its 384,400 km orbit in 29.53 days, and it is the shadow-relative (synodic) motion that matters here. Circumference = 2 × π × 384,400 = 2,415,000 km; time = 29.53 × 24 = 708.7 hours; speed = **3,408 km\u002Fh**.","Time = 5,721 ÷ 3,408 = **1.68 hours**, which is about **1 hour 41 minutes**.","The published maximum is about 1 h 47 min, a little longer than this estimate because the real umbra is enlarged by roughly 2% by Earth's atmosphere, and because the Moon can be further away and so moving more slowly across the shadow.","**Compare with a solar eclipse:** there the shadow is 160 km wide and crosses you at 2,000 km\u002Fh, giving minutes. Here the shadow is 9,196 km wide and is crossed at 3,408 km\u002Fh, giving hours. Same physics; wildly different scale.",{"simplerExplanation":388},"Earth's shadow at the Moon is 2.6 Moon-widths across, so the Moon takes ages to get through it. The Moon's shadow at Earth is a 160 km dot, so it is over in minutes.",{"id":390,"type":52,"variant":128,"title":391,"markdown":392},"u-aha-round-earth","Every lunar eclipse re-proves the Earth is round","Watch the umbra's edge creep across the Moon during a partial lunar eclipse and notice something: **it is always an arc of a circle**, and always the same size of circle, whether the Moon enters at the top, the bottom or the side.\n\nOnly one shape casts a circular shadow from every direction: a **sphere**. A disc would cast an ellipse or a line, depending on how it was turned.\n\nAristotle used exactly this argument around 350 BCE, and it remains one of the cleanest pieces of evidence any person can check for themselves. You do not need a telescope, a satellite or a trip to space. You need a partial lunar eclipse and a pair of eyes.\n\nA bonus: the shadow's arc is clearly **wider** than the Moon — about 2.6 times — which tells you Earth is several times bigger than the Moon. Aristarchus used that to estimate their relative sizes in the third century BCE.",{"id":394,"type":133,"component":229,"componentVersion":5,"config":395,"objective":398,"textAlternative":399,"help":400},"u-lab-lunar",{"modes":396,"showShadowCones":233,"tiltDegrees":234},[397],"lunar","Slide the Moon's path across Earth's shadow and compare penumbral, partial and total lunar eclipses with a timer running.","Earth's umbra and penumbra drawn to scale at the Moon's distance: the umbra a black circle **2.6 Moon-widths** across, the penumbra a grey circle **4.7 Moon-widths** across, with the Moon crossing from left to right.\n\nDrag the crossing height and watch the timer:\n\n- **Right through the middle.** Totality lasts the longest — about 1 hour 40 minutes in the model. The Moon panel goes deep copper-red.\n- **Off-centre but still inside.** Totality is shorter, and the limb nearest the shadow's edge stays noticeably brighter and more orange.\n- **Just clipping the black circle.** A *partial* eclipse: a dark curved bite whose edge is always the same circular arc.\n- **Only in the grey.** A *penumbral* eclipse: a slight shading you would probably miss.\n\nA second readout shows the whole event from first penumbral contact to last: typically about 5 to 6 hours. A globe inset shades the night side of Earth to show that the entire hemisphere sees the same thing at the same instant.",{"hints":401},[402,403],"Compare the timer for a central pass and an off-centre pass.","Look at the shape of the bite during the partial phase. It is always the same arc.",{"id":405,"type":58,"title":406,"eyebrow":407,"navLabel":408},"u-ch5","Why the eclipsed Moon turns red","Chapter 05","5 The red Moon",{"id":410,"type":46,"markdown":411,"help":412},"u-red-explained","If Earth had no atmosphere, a totally eclipsed Moon would simply go out — a black gap among the stars. It does not, and the reason is a two-step process. Both steps happen every day, right over your head.\n\n**Step 1: refraction bends sunlight into the shadow.** Air is denser at the bottom than the top, and light slows down slightly in denser air, so a ray grazing Earth's edge is **bent inwards** — by up to about half a degree. That bending is enough to curl sunlight around the rim of Earth and pour it into the shadow behind. So the umbra is not truly empty; it is filled with a dim, bent light.\n\n**Step 2: scattering strips out the blue.** That light has travelled a very long, slanting path through the whole depth of the atmosphere. Along the way, the air molecules scatter short-wavelength light — blue and violet — sideways, far more strongly than long-wavelength red. This is the same effect that makes our sky blue and our sunsets red. By the time the beam emerges on the far side, most of the blue has been thrown away and what is left is red and orange.\n\nPut those together and you get the real explanation:\n\n**The red light landing on an eclipsed Moon is the light of every sunrise and every sunset happening on Earth at that moment, gathered into one beam.**\n\nIf you were standing on the Moon during a lunar eclipse and looked back, you would not see a bright Earth. You would see a black disc, four times wider than the Sun looks to us, ringed by a thin band of blazing orange — the whole world's terminator, all at once.",{"simplerExplanation":413,"anotherExample":414},"Earth's air bends sunlight into the shadow, and along the way the blue gets scattered out. What arrives is sunset-coloured, and it lands on the Moon.","Hold a glass of water with a drop of milk in it up to a torch. Light coming straight through looks orange; light scattered sideways looks bluish. Earth's atmosphere does the same thing on a planetary scale.",{"id":416,"type":52,"variant":224,"title":417,"markdown":418},"u-misconception-red","\"Red from reflecting Mars, the Sun's edge, or its own heat\"","All three explanations turn up, and none is right.\n\n**Mars** is far too faint and often nowhere near the Moon. A planet lights nothing.\n\n**\"The Sun's edge\"** is closer but confused. It is not that we see a red part of the Sun; it is that **Earth's atmosphere** turns ordinary white sunlight red on the way past, exactly as it does at sunset.\n\n**The Moon's own heat** is nowhere near enough. During totality the lunar surface cools rapidly — measurements show it dropping by well over 100 °C in a couple of hours — and it glows nothing you could see.\n\nThe test that settles it: if the colour came from the Moon or from Mars, every lunar eclipse would look the same. They do not. After a big volcanic eruption loads the stratosphere with dust, eclipses come out almost black. The colour is made in **our** air, so it changes when **our** air changes.",{"id":420,"type":103,"caption":421,"columns":422,"rows":426},"u-table-danjon","The Danjon scale: astronomers score the colour of every total lunar eclipse",[423,424,425],"L","What it looks like","Usually because",[427,431,435,439,443],[428,429,430],"**0**","Very dark. The Moon almost invisible at mid-eclipse.","A stratosphere loaded with volcanic dust that blocks the bent light.",[432,433,434],"**1**","Dark grey or brown; surface details hard to make out.","Heavy high-altitude aerosols.",[436,437,438],"**2**","Deep red or rust-coloured, with a dark centre to the shadow.","A fairly dusty atmosphere.",[440,441,442],"**3**","Brick-red, often with a bright grey or yellow rim to the shadow.","A typical, clear-ish atmosphere.",[444,445,446],"**4**","Very bright copper-red or orange, with a bluish, very bright rim.","An unusually clean, clear stratosphere.",{"id":448,"type":52,"variant":449,"title":450,"markdown":451},"u-example-pinatubo","example","The eclipse that went out","In June 1991 Mount Pinatubo in the Philippines erupted and threw an enormous quantity of sulphur dioxide high into the stratosphere, where it formed a global haze that stayed for years.\n\nAt the total lunar eclipse of **9 December 1992**, observers reported the Moon almost vanishing — a Danjon **L = 0**. Some could not find it with the naked eye at mid-eclipse.\n\nNothing had changed about the Moon, Earth's shadow or the Sun. What had changed was the thin layer of air around the rim of Earth, thousands of kilometres from any of the observers. An eclipsed Moon is a screen on which the state of our whole atmosphere is projected.",{"id":453,"type":314,"prompt":454,"options":455,"explanation":464},"u-predict-from-moon","You are an astronaut standing on the Moon during a **total lunar eclipse**. You look up at Earth. What do you see?",[456,458,460,462],{"id":318,"label":457},"A brightly lit Earth, as usual",{"id":321,"label":459},"A total solar eclipse: a black Earth with a thin ring of orange fire around it",{"id":324,"label":461},"Nothing at all — the sky is completely black",{"id":327,"label":463},"Earth half lit, like a half moon","**(b).** A lunar eclipse seen from Earth is a **solar eclipse seen from the Moon**. The same three bodies are in the same line; only your viewpoint has moved.\n\nEarth is directly between you and the Sun, so it blocks the Sun's disc completely — and Earth looks about **four times wider** than the Sun does, so there is no chance of a ring or a corona peeping past the edge the way the Moon manages from Earth.\n\nBut Earth has air, and that air is lit from behind. So the black disc is rimmed by a continuous band of red-orange light: every sunrise and sunset on the planet, seen at once as a ring of fire.\n\nThat ring is the source of the red light falling on the ground around you. Astronauts have never seen this; no crewed mission has been on the Moon during a lunar eclipse. Spacecraft cameras have.",{"id":466,"type":58,"title":467,"eyebrow":468,"navLabel":469},"u-ch6","Half a degree: the coincidence measured","Chapter 06","6 Angular size",{"id":471,"type":46,"markdown":472},"u-angular-size","\"How big does it look?\" is a different question from \"how big is it?\", and astronomy runs on the first one.\n\nThe answer is an **angle**: the angle between the two edges of an object as seen from your eye. It is called the **angular size** or apparent size, and it depends on both the real size and the distance.\n\nUseful units:\n\n- **1 degree (°)** — about the width of your little finger held at arm's length.\n- **1 arcminute (′)** — one sixtieth of a degree.\n- **1 arcsecond (″)** — one sixtieth of an arcminute, one 3,600th of a degree.\n\nNow the numbers that make eclipses possible. The Sun's average angular width is **0.533°**, or **32.0′**. The Moon's is **0.518°**, or **31.1′**.\n\nThey differ by less than one part in thirty. Out of everything in the sky, the two brightest objects happen to be almost exactly the same apparent size — and there is no physical reason at all. The Moon is not tuned to the Sun; it is simply where it is.",{"id":474,"type":67,"items":475},"u-formula-angular",[476,479,482,485],{"expression":477,"caption":478},"angle ≈ 57.3 × size ÷ distance","Angular size in degrees, for anything small and far away. 57.3 is the number of degrees in a radian.",{"expression":480,"caption":481},"Sun: 57.3 × 1,392,700 ÷ 149.6M","= 0.533°, or 32.0 arcminutes.",{"expression":483,"caption":484},"Moon: 57.3 × 3,475 ÷ 384,400","= 0.518°, or 31.1 arcminutes.",{"expression":486,"caption":487},"Ratio: 400.8 vs 389.2","Sun ÷ Moon in size, and Sun ÷ Moon in distance. Both are 'about 400'.",{"id":489,"type":490,"title":491,"note":492,"scale":493,"rungs":494},"u-ladder-angular","ladder","Angular sizes, from a full Moon to a fingernail","Log scale in arcminutes. Everything from about 29 to 33 arcminutes is 'the same size as the Sun'.","log",[495,498,502,505,508,511,514,517,520,524],{"label":496,"value":5,"display":497},"Venus at its widest (a dot)","1.0′",{"label":499,"value":500,"display":501},"Jupiter through binoculars",0.75,"0.75′ (45″)",{"label":503,"value":504,"display":274},"Moon at apogee — too small, gives a ring",29.5,{"label":506,"value":507,"display":261},"Sun in early July — smallest",31.5,{"label":509,"value":510,"display":269},"Moon, average",31.1,{"label":512,"value":513,"display":270},"Sun, average",32,{"label":515,"value":516,"display":265},"Sun in early January — largest",32.5,{"label":518,"value":519,"display":260},"Moon at perigee — big enough for totality",32.9,{"label":521,"value":522,"display":523},"Your little fingernail at arm's length",57.3,"≈ 57′ (about 1°)",{"label":525,"value":526,"display":527},"Your fist at arm's length",600,"≈ 10°",{"id":529,"type":83,"title":530,"problem":531,"steps":532,"help":541},"u-we-coincidence","Check the 400-and-400 coincidence yourself","The Sun is 1,392,700 km across and 149,597,871 km away. The Moon is 3,475 km across and 384,400 km away. Show that both discs come out at about half a degree, and say how close the match is.",[533,534,535,536,537,538,539,540],"Sun ÷ Moon by **size**: 1,392,700 ÷ 3,475 = **400.8**. The Sun is about 401 times wider.","Sun ÷ Moon by **distance**: 149,597,871 ÷ 384,400 = **389.2**. The Sun is about 389 times further.","If those two ratios were equal, the discs would look exactly the same size.","Angular size of the Sun: 57.3 × 1,392,700 ÷ 149,597,871 = 57.3 × 0.00931 = **0.533°**.","Angular size of the Moon: 57.3 × 3,475 ÷ 384,400 = 57.3 × 0.00904 = **0.518°**.","How close? 0.533 ÷ 0.518 = **1.03**. The Sun looks about **3% wider** than the average Moon.","That 3% is smaller than the Moon's own range as its distance changes (29.5′ to 32.9′, a swing of 11%), which is exactly why we get **both** total and annular eclipses.","**And note what this is not:** a law, a design, or anything caused. It is a coincidence of the present era, and the next chapter shows it is slowly ending.",{"simplerExplanation":542},"Sun ÷ Moon is about 400 both ways — 401 in size, 389 in distance. The two 400s cancel, so both discs look about half a degree wide.",{"id":544,"type":52,"variant":545,"title":546,"markdown":547},"u-nuance-ending","nuance","A coincidence with an expiry date","The Moon is moving away from Earth at about **3.8 centimetres a year**, measured by bouncing laser pulses off reflectors left on the surface by the Apollo missions and by the Soviet Lunokhod rovers. Tides are doing it: they drag on Earth's spin and hand the energy to the Moon's orbit.\n\n3.8 cm a year is **38 km every million years**. Slow, but relentless.\n\nHere is the arithmetic for when totality runs out. For a total eclipse you need the Moon's perigee disc to beat the Sun's smallest disc, 31.5 arcminutes. That fails once perigee passes about **379,500 km**. Today's perigee is 363,300 km, so it must grow by about **16,200 km**, which at 3.8 cm a year takes roughly **430 million years**.\n\nTreat that as an order of magnitude, not a date: the recession rate itself changes as the continents and oceans rearrange, and published estimates run from about 400 to 600 million years. Either way, **totality is a temporary feature of our era**. Dinosaurs saw longer, deeper total eclipses than we do. In a few hundred million years there will be nothing but rings of fire.",{"id":549,"type":550,"conceptId":551,"relation":552,"explanation":553},"u-conn-gravity","connection","gravity","helps_understand","The Moon's orbit, its slightly oval shape and its slow retreat from Earth are all gravity at work.",{"id":555,"type":58,"title":556,"eyebrow":557,"navLabel":558},"u-ch7","The tilt, the nodes and the eclipse seasons","Chapter 07","7 Nodes and seasons",{"id":560,"type":46,"markdown":561},"u-tilt-detail","Now the central question: why not every month?\n\nThe Moon's orbit is tilted by **5.145°** to the plane of Earth's orbit around the Sun (the **ecliptic**). Compare that with what it is trying to hit — a Sun only **0.53°** wide. The tilt is **nearly ten times** the target's own width.\n\nPut it in kilometres and it is starker. At the Moon's distance, a 5.145° offset is:\n\n384,400 × tan(5.145°) = **34,600 km**\n\nThat is **2.7 Earth-diameters**. At most new moons the Moon is tens of thousands of kilometres above or below the Sun–Earth line, and the shadow cone flies past Earth into empty space.\n\nBut a tilted circle must cut a flat plane in exactly **two** points, on opposite sides. Those are the **nodes**: the **ascending node**, where the Moon crosses from south to north, and the **descending node**, where it crosses the other way. Near a node, and only near a node, the Moon is back in the plane where eclipses can happen.\n\nIn classical Indian astronomy those two points are called **Rahu** and **Ketu**. They are treated as the two halves of a severed body that chases and swallows the Sun and Moon — which is a rather good description of what geometry says actually goes on there.",{"id":563,"type":177,"tone":564,"items":565},"u-spec-limits","neutral",[566,570,574,578,582,586,590],{"label":567,"big":568,"value":569},"Orbit tilt","5.145°","Mean inclination of the Moon's orbit to the ecliptic.",{"label":571,"big":572,"value":573},"Sun's width","0.53°","The tilt is 9.6 times the Sun's own apparent width.",{"label":575,"big":576,"value":577},"Miss distance","34,600 km","How far the Moon can be from the Sun–Earth line — about 2.7 Earth-diameters.",{"label":579,"big":580,"value":581},"Solar eclipse limit","≈ 16.6°","How far in longitude the Moon may be from a node and still give some kind of solar eclipse.",{"label":583,"big":584,"value":585},"Lunar eclipse limit","≈ 10.6°","The same for a lunar eclipse. Smaller, because Earth's shadow is a smaller target than the Sun.",{"label":587,"big":588,"value":589},"Eclipse season","≈ 32 days","Long enough that at least one new moon — 29.53 days apart — must fall inside. So every season has a solar eclipse.",{"label":591,"big":592,"value":593},"Seasons per year","2","About 173.3 days apart, not 182.6 — because the nodes slide backwards.",{"id":595,"type":83,"title":596,"problem":597,"steps":598,"help":606},"u-we-node-limit","How near a node does the Moon have to be?","The Moon's height above or below the ecliptic swings smoothly from +5.145° at one quarter-point to −5.145° at the other, passing through zero at each node. For any solar eclipse at all, the Moon's centre must come within about 1.47° of the Sun's centre. How far from a node, measured along its orbit, can the Moon be?",[599,600,601,602,603,604,605],"The Moon's angular distance from the ecliptic behaves like tilt × sin(angle from node). Call the angle from the node x.","So we need 5.145 × sin(x) ≤ 1.47.","sin(x) ≤ 1.47 ÷ 5.145 = **0.286**.","x ≤ the angle whose sine is 0.286, which is **16.6°**.","So the Moon has a window of 16.6° on each side of a node — a total of **33.3°** out of 360°.","As a fraction of the orbit that is 33.3 ÷ 360 = **9.2%**. For a lunar eclipse the required separation is smaller (about 0.94°), giving a window of only ±10.6°, or **5.9%** of the orbit.","**Why this makes eclipses come in bunches:** it is not the Moon that has to be in the window twice a year, it is the **Sun**, moving along the ecliptic, that has to pass through it. That passage takes about a month, and that month is an **eclipse season**.",{"simplerExplanation":607,"hints":608},"The Moon is only close enough to the plane for about 9% of each orbit near a node, and the Sun has to be lined up with that node at the same time.",[609,610],"The 1.47° comes from adding the Sun's and Moon's half-widths plus a correction for the Moon being near enough that your position on Earth matters.","If you have not met sine yet, read 5.145 × sin(x) as 'how far off the plane the Moon is when it is x degrees past a node'.",{"id":612,"type":46,"markdown":613},"u-seasons","So an eclipse needs the **Sun** to be near a node, and the **Moon** to arrive there at the right phase on the same trip.\n\nHere is the crucial piece of arithmetic. The Sun's window around a node is about 33.3° wide, and the Sun creeps along the ecliptic at 0.986° a day. But the nodes themselves are not fixed — they slide **backwards** around the ecliptic at 19.34° a year, or 0.053° a day, completing one full circuit in **18.6 years**. (This slow wobble is caused by the Sun's pull on the tilted orbit, and it is the same physics that makes a spinning top's axis circle around.)\n\nBecause the Sun and the nodes move in opposite directions, they close on each other at 0.986 + 0.053 = **1.039° a day**. So:\n\n- **Eclipse season length** = 33.3 ÷ 1.039 = about **32 days**.\n- That is **longer than one synodic month** (29.53 days), so at least one new moon *must* fall inside every eclipse season. **There is always at least one solar eclipse per season, and so at least two a year.**\n- **Time from one node to the next** = 180 ÷ 1.039 = **173.3 days**, so seasons come about every 5.7 months, not every 6.\n- One full circuit — an **eclipse year** — is 360 ÷ 1.039 = **346.6 days**, which is **18.6 days shorter** than an ordinary year. That is why eclipse seasons drift steadily earlier through the calendar.\n\nBecause a season is only just longer than a month, most seasons contain two eclipses (one solar, one lunar) and some squeeze in three. Add them up and the total across a year comes to between **4 and 7**, of which **2 to 5** are solar.",{"id":615,"type":133,"component":229,"componentVersion":5,"config":616,"objective":620,"textAlternative":621,"help":622},"u-lab-whynot",{"modes":617,"showShadowCones":233,"tiltDegrees":619},[618],"why-not-monthly",5.145,"Watch the nodes rotate through the year, find the eclipse seasons, and see the whole year's eclipse count change as you alter the tilt.","Earth's year drawn as a circle around the Sun, with the Moon's tilted orbit shown as a ring around Earth and the **line of nodes** drawn straight through it.\n\nStep through the months with the tilt set to the real **5.145°**. For most of the year the line of nodes points sideways — off at right angles to the Sun — and new moons pass above or below, giving nothing. Twice a year the line of nodes swings round to point **at the Sun**, and the lab highlights a window about 32 days wide: an **eclipse season**. Inside it, eclipses appear.\n\nTwo extra controls make the point:\n\n- **Tilt slider.** At 0° the counter reads 24 eclipses a year. At 1° it reads far more than now. At the real 5.145° it settles between 4 and 7. Past about 10° eclipses would stop happening altogether.\n- **Node drift.** Switch it on and the line of nodes rotates slowly backwards, completing a circuit in 18.6 years, so the eclipse seasons creep about 19 days earlier each year.",{"simplerExplanation":623,"hints":624},"Eclipses need the line where the Moon's tilted orbit crosses ours to be pointing at the Sun. That happens twice a year, for about a month each time.",[625,626],"Find the two months in which the line of nodes points at the Sun. Those are the eclipse seasons.","Set the tilt to 10° and see whether any eclipses are left.",{"id":628,"type":52,"variant":224,"title":629,"markdown":630},"u-misconception-syzygy","\"The three bodies line up exactly\"","You will often read that an eclipse happens when the Sun, Earth and Moon are \"perfectly aligned\". That word does a lot of damage.\n\nA **perfect** line-up almost never happens. Eclipses occur across a whole range of near-alignments, and the range is what produces the variety:\n\n- Nearly perfect → a long central total eclipse, or a deep dark total lunar eclipse.\n- Slightly off → a short total eclipse near the edge of the path, or a partial lunar eclipse.\n- Further off → only a partial solar eclipse, seen from a corner of the globe.\n- A little further still → a penumbral lunar eclipse most people cannot see.\n- Further than about 16.6° from the node → nothing at all.\n\nThe proper word for the three bodies lying roughly in a line is **syzygy** (say it \"SIZZ-i-jee\"). It is a useful word, and it wins arguments at Scrabble.",{"id":632,"type":58,"title":633,"eyebrow":634,"navLabel":635},"u-ch8","Eye safety, and why the rules are what they are","Chapter 08","8 Eye safety",{"id":637,"type":46,"markdown":638,"help":639},"u-safety-why","Every rule below has a reason. Knowing the reasons is what makes you keep the rules under pressure, when the sky is doing something amazing and there is a strong temptation to take one quick look.\n\n**Reason 1: the retina has no pain nerves.** The back of your eye can detect light beautifully and cannot feel anything at all. Sunlight focused on it cooks the light-sensing cells silently. You get no warning, no flinch, no ouch. The symptoms — a blurred or blank patch in the middle of your vision — usually turn up **hours later**, often the next morning. This condition is called **solar retinopathy**, and it can be permanent.\n\n**Reason 2: your pupil opens as the eclipse deepens.** As more of the Sun is covered, the world dims, and your pupils widen to let more light in. The Sun's remaining sliver has lost none of its brightness per square millimetre — but now a wider pupil is aiming more of it at your retina. A deep partial eclipse is genuinely **more** dangerous than an ordinary sunny day, not less.\n\n**Reason 3: the eye is a lens.** Your eye's whole job is to gather light over the area of your pupil and focus it to a tiny point on the retina. That is a concentration of hundreds of times. Put a camera lens, binoculars or a telescope in front of it and the concentration multiplies again, by thousands. This is why the telescope rule is absolute.\n\n**Reason 4: filters are not about comfort.** The Sun also emits infrared and ultraviolet that you cannot see. A dark piece of glass or plastic that makes the Sun *look* comfortable may pass plenty of both. Comfort is not the test. Certification is.",{"simplerExplanation":640},"You cannot feel your retina burning, the danger goes up as the eclipse deepens, your eye focuses light like a lens, and looking comfortable is no proof of being safe.",{"id":642,"type":103,"caption":643,"columns":644,"rows":648},"u-table-filters","Filters and fakes: what passes, and what that means",[645,646,647],"Method","Roughly how much light it passes","Safe?",[649,653,657,661,665,669,673,677],[650,651,652],"**ISO 12312-2 eclipse glasses**","About 0.003% — roughly one part in 31,000","**Yes**, if undamaged and uncreased. Inspect before every use.",[654,655,656],"**Welding glass, shade 12 or higher**","Similar order to eclipse glasses","**Yes** at shade 12+. Shades below 12 are **not** safe.",[658,659,660],"**Pinhole or colander projection**","Nothing reaches your eye; you look at paper","**Yes** — the safest method of all, and it costs nothing.",[662,663,664],"**Sunglasses**","About 10% — over 3,000 times too much","**No.** Stacking pairs does not fix it.",[666,667,668],"**Smoked or candle-blackened glass**","Unpredictable; often passes plenty of infrared","**No.** A traditional method that caused a great many injuries.",[670,671,672],"**Exposed film, X-ray film, CDs**","Unpredictable, usually far too much, uneven","**No.** Modern colour film contains no silver layer at all.",[674,675,676],"**Camera, phone, binoculars, telescope**","Concentrates light hundreds or thousands of times","**No** — not even with eclipse glasses on. The filter melts.",[678,679,680],"**Reflection in water or ink**","Still roughly a tenth of full sunlight","**No.** A reflection is dimmer, not safe.",{"id":682,"type":52,"variant":309,"title":683,"markdown":684},"u-safety-master","The eight rules, in full","1. **Never look at the Sun with unprotected eyes**, at any stage of a partial or annular eclipse, no matter how thin the crescent or how brief the glance.\n2. **Use only ISO 12312-2 certified eclipse filters**, or welding glass of shade 12 or above. Inspect for scratches, holes and creases before every use, and discard damaged ones.\n3. **Sunglasses are never safe** — not one pair, not several, not the darkest ones you own.\n4. **Never use smoked glass, candle-blackened glass, exposed photographic or X-ray film, CDs, DVDs, coloured plastic, or the Sun's reflection in water or ink.**\n5. **Never look through a camera, phone camera, binoculars, telescope or spotting scope**, even while wearing eclipse glasses. The optics concentrate the light and injure you in an instant. Such instruments need a purpose-built filter fitted at the **front**.\n6. **Projection is always safe**: a pinhole in card, a kitchen colander, the gaps between leaves, or a covered mirror bouncing the image onto a shaded wall. Your back stays to the Sun.\n7. **Bare eyes are allowed only during totality of a total eclipse**, inside the path, and filters go back on the instant the first bright bead appears. No safe moment exists in an annular or partial eclipse.\n8. **Retinal damage is painless and can be permanent.** If someone gets a blurred patch in their vision after an eclipse, see an eye doctor promptly.\n\n**Lunar eclipses need none of this.** Watch with eyes, binoculars, telescopes and cameras.",{"id":686,"type":83,"title":687,"problem":688,"steps":689,"help":697},"u-we-pinhole","How big is the Sun's image from a pinhole?","You make one clean pinhole in a card and hold it so sunlight falls on a second card held 1 metre behind. How big is the bright disc, and what happens if you move the second card to 5 metres?",[690,691,692,693,694,695,696],"A pinhole makes an image whose angular size is the same as the Sun's: **0.533°**.","The size of the image = distance × tan(0.533°). tan(0.533°) = **0.00931**.","At 1 metre: 1,000 mm × 0.00931 = **9.3 mm**. About the size of a shirt button.","At 5 metres: 5,000 mm × 0.00931 = **46.5 mm**. Nearly 5 cm across.","So a longer projection distance gives a **bigger** image — but the same amount of light is now spread over 25 times the area, so it is also **25 times fainter**. Shade the screen and you can go further.","**Rule of thumb to remember:** the Sun's image from a pinhole is about **1 cm across for every metre** of projection distance. Handy for planning a set-up before an eclipse.","Make the hole itself small and clean: a big or ragged hole makes a brighter but blurrier patch, and the crescent shape gets lost.",{"simplerExplanation":698},"About 1 cm of image for every metre of distance. Longer means bigger but dimmer, so shade the screen.",{"id":700,"type":133,"component":701,"componentVersion":5,"config":702,"objective":761,"textAlternative":762},"u-lab-sort-safety","sort-game",{"prompt":703,"bins":704,"items":711,"seconds":760},"Safe or unsafe for watching a partial solar eclipse? Sort each one.",[705,708],{"id":706,"label":707},"safe","Safe",{"id":709,"label":710},"unsafe","Unsafe",[712,716,720,724,728,732,736,740,744,748,752,756],{"id":713,"label":714,"bin":706,"why":715},"s1","ISO 12312-2 eclipse glasses, undamaged","Certified filters pass about 0.003% of the light and block infrared and ultraviolet too.",{"id":717,"label":718,"bin":706,"why":719},"s2","A pinhole in card, projected onto paper","Nothing reaches your eye but the paper. The safest method there is.",{"id":721,"label":722,"bin":706,"why":723},"s3","A kitchen colander held in the sunlight","Every hole makes its own image of the Sun on the ground. Projection, so safe.",{"id":725,"label":726,"bin":706,"why":727},"s4","Crescent shadows under a leafy tree","Gaps between leaves act as natural pinholes. You are looking at the ground.",{"id":729,"label":730,"bin":706,"why":731},"s5","Welding glass, shade 14","Shade 12 and above is dark enough. Below shade 12 is not.",{"id":733,"label":734,"bin":709,"why":735},"s6","Two pairs of dark sunglasses together","Sunglasses pass about 10% of the light. Even stacked, they are thousands of times too bright.",{"id":737,"label":738,"bin":709,"why":739},"s7","A piece of glass blackened over a candle","The soot layer is uneven and passes a lot of invisible infrared. A traditional method that caused many injuries.",{"id":741,"label":742,"bin":709,"why":743},"s8","Looking through binoculars while wearing eclipse glasses","The binoculars concentrate the light, melt the filter and injure you in an instant. Filters must go on the FRONT of any optics.",{"id":745,"label":746,"bin":709,"why":747},"s9","An old exposed X-ray film","It passes an unpredictable amount of light and plenty of infrared. Never use it.",{"id":749,"label":750,"bin":709,"why":751},"s10","The Sun's reflection in a bucket of water","A reflection is dimmer but nowhere near dim enough — still about a tenth of full sunlight.",{"id":753,"label":754,"bin":709,"why":755},"s11","A quick one-second glance when 99% is covered","About 2% of the Sun's area is still blazing, and your pupil is wide open because the sky is dim.",{"id":757,"label":758,"bin":706,"why":759},"s12","A mirror covered with card, with a 5 mm hole, aimed at a shaded wall","Projection again — you look at the wall, never at the mirror. Do not aim it at anyone's face.",0,"Sort twelve viewing methods into safe and unsafe, and read the reason for each.","A sorting game with two boxes, **Safe** and **Unsafe**, and twelve cards describing ways people try to watch a partial solar eclipse: certified filters and projection methods go in Safe; sunglasses, blackened glass, film, optics and quick glances go in Unsafe, each with its reason.\n\nThe pattern worth noticing: every safe method either carries a **certification mark** or works by **projection**. Nothing qualifies just because it looks dark or feels comfortable.",{"id":764,"type":58,"title":765,"eyebrow":766,"navLabel":767},"u-ch9","Putting it together","Chapter 09","9 Putting it together",{"id":769,"type":770,"title":771,"prompt":772,"options":773},"u-explorer-five","explorer","Five eclipses, five geometries","Pick a scenario and follow the chain from the geometry to what you would see.",[774,787,798,809,821],{"id":775,"label":776,"chain":777,"badge":783,"note":786},"t","Total solar",[778,779,780,781,782],"New moon at a node","Moon near perigee","Umbra reaches the ground","160 km path","Corona, 360° sunset",{"text":784,"tone":785},"Filters off only during totality","yes","The Moon is within about 16.6° of a node at new moon, and near enough (inside about 379,500 km) that its umbra cone overshoots Earth's surface. A black spot roughly 160 km across lands and races east at 2,000 km\u002Fh or more. Inside it the disc is fully covered for seconds up to a maximum of 7 min 32 s: the corona appears, planets come out, temperature falls around 5 °C, and the horizon glows orange all round. Outside the path, the same eclipse is merely partial.",{"id":318,"label":788,"chain":789,"badge":794,"note":797},"Annular solar",[778,790,791,792,793],"Moon near apogee","Umbra tip falls short","Antumbra lands","Ring of fire, 18% left",{"text":795,"tone":796},"Filters on the whole time","no","Same alignment, but the Moon is too far away — its disc is only 29.5 to 31 arcminutes against a Sun of 31.5 to 32.5. The umbra cone ends in space before reaching us, and the antumbra beyond its tip lands instead. A bright ring stays visible throughout, up to about 18% of the Sun's area. The sky dims a little, but there is no corona, no stars and no safe moment.",{"id":799,"label":800,"chain":801,"badge":807,"note":808},"p","Partial solar",[802,803,804,805,806],"New moon near a node","But not central","Only penumbra lands","Crescent Sun","Very common",{"text":795,"tone":796},"The Moon passes in front of the Sun but not squarely, so only the wide grey penumbra sweeps over you. A bite grows then shrinks. Unless over about 90% is covered, daylight looks nearly normal, because our eyes compensate so well — which has fooled many people into a dangerous glance. Every total and annular eclipse is also partial for the huge region around the central path, which is why most people's eclipse memories are a crescent through a colander.",{"id":810,"label":811,"chain":812,"badge":818,"note":820},"tl","Total lunar",[813,814,815,816,817],"Full moon at a node","Moon fully in umbra","Refracted red light","Copper Moon","Whole night side sees it",{"text":819,"tone":785},"Completely safe to watch","At full moon within about 10.6° of a node, the Moon slides entirely inside Earth's umbra, about 2.6 Moon-widths across there. The whole event runs 5 to 6 hours, with totality lasting up to about 1 h 40 min. The Moon turns copper-red because refracted sunset light is the only light reaching it, and the exact shade — the 0-to-4 Danjon scale — reports how dusty Earth's stratosphere is. Everyone on the night side sees the same thing at once.",{"id":822,"label":823,"chain":824,"badge":830,"note":831},"pl","Penumbral lunar",[825,826,827,828,829],"Full moon near a node","Misses the umbra","Only the grey zone","Slight shading","Easy to miss",{"text":819,"tone":785},"The Moon's path clips only Earth's penumbra, where part of the Sun is still visible from the Moon, so it is merely lit a little less brightly on one side. The dimming is gradual with no sharp edge, and unless the Moon goes deep in, most people looking up notice nothing. Photographs pick it up better than eyes. These still count in the official tallies, which is why 'four to seven a year' sounds higher than people's experience.",{"id":833,"type":834,"title":835,"terms":836},"u-glossary","glossary","Words for the geometry",[837,841,845,848,852,856,858,861,865,869,873,876,880,883,887],{"term":838,"meaning":839,"example":840},"Angular size","How wide something looks, measured as an angle rather than in kilometres.","The Sun and the Moon are both about 0.5° wide from Earth.",{"term":842,"meaning":843,"example":844},"Arcminute (′)","One sixtieth of a degree. Sixty arcminutes make one degree.","The Sun averages 32.0 arcminutes across.",{"term":846,"meaning":847},"Ecliptic","The plane of Earth's orbit around the Sun, and the line the Sun appears to trace across our sky.",{"term":849,"meaning":850,"example":851},"Node","Either of the two points where the Moon's tilted orbit crosses the ecliptic plane.","Called the ascending and descending nodes; Rahu and Ketu in Indian astronomy.",{"term":853,"meaning":854,"example":855},"Line of nodes","The straight line joining the two nodes. Eclipses need it to point roughly at the Sun.","It rotates backwards once every 18.6 years.",{"term":587,"meaning":857},"The window of about 32 days, twice a year, in which eclipses are possible.",{"term":859,"meaning":860},"Eclipse year","346.6 days — the time for the Sun to return to the same node. 18.6 days shorter than a normal year.",{"term":862,"meaning":863,"example":864},"Perigee","The Moon's closest point to Earth, about 363,300 km.","Eclipses near perigee are total and long.",{"term":866,"meaning":867,"example":868},"Apogee","The Moon's furthest point, about 405,500 km.","Eclipses near apogee are annular.",{"term":870,"meaning":871,"example":872},"Antumbra","The region beyond the tip of an umbra cone, where the blocker looks too small to cover the source.","Standing in the antumbra gives you a ring of fire.",{"term":874,"meaning":875},"Syzygy","Three bodies roughly in a straight line. Every eclipse is a syzygy.",{"term":877,"meaning":878,"example":879},"Danjon scale","A 0-to-4 scale for how dark and what colour a totally eclipsed Moon looks.","0 is almost invisible; 4 is bright copper-orange.",{"term":881,"meaning":882},"Solar retinopathy","Damage to the retina caused by looking at the Sun. Painless, and often permanent.",{"term":884,"meaning":885,"example":886},"Refraction","The bending of light as it passes into a denser or thinner material, such as air.","Refraction is what curls sunlight into Earth's shadow.",{"term":888,"meaning":889},"Hybrid eclipse","A rare eclipse that is total along the middle of its track and annular at the ends, because Earth is round.",{"id":891,"type":892,"title":893,"questions":894},"u-quiz","quiz","Check your geometry",[895,908,921,934,947,960,973,986,999,1011],{"itemId":896,"prompt":897,"options":898,"correct":321,"why":907},"eclipses.understand-q-cone-length","The Moon's umbra cone is about 374,000 km long and the Moon is on average 384,400 km away. What does this tell you about an average solar eclipse?",[899,901,903,905],{"id":318,"label":900},"It will be total",{"id":321,"label":902},"The umbra falls short, so an average eclipse is annular",{"id":324,"label":904},"There can be no eclipse at all",{"id":327,"label":906},"The eclipse will last longer than usual","The cone runs out before reaching us; only inside about 379,500 km does the umbra reach the ground.",{"itemId":909,"prompt":910,"options":911,"correct":321,"why":920},"eclipses.understand-q-umbra-size","Earth's umbra at the Moon's distance is about 2.6 Moon-widths across. What follows?",[912,914,916,918],{"id":318,"label":913},"Lunar eclipses can never be total",{"id":321,"label":915},"The Moon fits inside with room to spare, so totality can last well over an hour",{"id":324,"label":917},"Only half the Moon is ever covered",{"id":327,"label":919},"The Moon must pass exactly through the centre","The Moon crosses the umbra's width minus its own width: 9,196 − 3,475 = 5,721 km at ≈3,408 km\u002Fh ≈ 1 h 41 min.",{"itemId":922,"prompt":923,"options":924,"correct":321,"why":933},"eclipses.understand-q-arcmin","The Moon at apogee looks 29.5′ across; the Sun in January looks 32.5′. What kind of central solar eclipse is possible?",[925,927,929,931],{"id":318,"label":926},"Total",{"id":321,"label":928},"Annular",{"id":324,"label":930},"Hybrid",{"id":327,"label":932},"None","The Moon looks smaller, so it cannot cover the Sun. A ring is left showing — about 18% of the Sun's area.",{"itemId":935,"prompt":936,"options":937,"correct":321,"why":946},"eclipses.understand-q-node-limit","Why must the Moon be within about 16.6° of a node for a solar eclipse?",[938,940,942,944],{"id":318,"label":939},"Beyond that the Moon is too far from Earth",{"id":321,"label":941},"Beyond that its 5.145° tilt puts it more than 1.47° from the Sun, so the shadow misses",{"id":324,"label":943},"Beyond that it is a different phase",{"id":327,"label":945},"Beyond that Earth's shadow gets in the way","5.145 × sin(16.6°) = 1.47°, which is the largest separation that still allows some part of the Moon's shadow to reach Earth.",{"itemId":948,"prompt":949,"options":950,"correct":321,"why":959},"eclipses.understand-q-season","An eclipse season lasts about 32 days and a synodic month is 29.53 days. What must follow?",[951,953,955,957],{"id":318,"label":952},"There may be no solar eclipse in some seasons",{"id":321,"label":954},"At least one new moon must fall inside every season, so there are at least two solar eclipses a year",{"id":324,"label":956},"There are exactly two eclipses a year",{"id":327,"label":958},"Eclipse seasons happen every month","Because the season is longer than one month, a new moon cannot skip over it. That is why the minimum is two solar eclipses a year.",{"itemId":961,"prompt":962,"options":963,"correct":321,"why":972},"eclipses.understand-q-red","What two processes together make the eclipsed Moon red?",[964,966,968,970],{"id":318,"label":965},"Reflection off Mars and absorption by dust",{"id":321,"label":967},"Refraction bending sunlight into the shadow, and scattering removing the blue",{"id":324,"label":969},"The Moon's own heat and Earth's magnetic field",{"id":327,"label":971},"Ozone and moonlight","Earth's air bends light into the umbra; along that long slanting path the blue is scattered away, leaving sunset colours to land on the Moon.",{"itemId":974,"prompt":975,"options":976,"correct":321,"why":985},"eclipses.understand-q-danjon","A total lunar eclipse is scored Danjon L = 0: the Moon nearly vanishes. What is the most likely cause?",[977,979,981,983],{"id":318,"label":978},"The Moon was at apogee",{"id":321,"label":980},"Volcanic dust high in Earth's stratosphere blocked the refracted light",{"id":324,"label":982},"There was a solar eclipse at the same time",{"id":327,"label":984},"The Moon passed through the penumbra only","After Mount Pinatubo erupted in 1991, the December 1992 eclipse was scored L = 0. The colour is made in our atmosphere, so it changes when our atmosphere changes.",{"itemId":987,"prompt":988,"options":989,"correct":318,"why":998},"eclipses.understand-q-shadow-speed","Why is the Moon's shadow never slower than roughly 2,000 km\u002Fh across the ground?",[990,992,994,996],{"id":318,"label":991},"Because the Moon orbits at 3,679 km\u002Fh and the equator spins east at only 1,674 km\u002Fh",{"id":321,"label":993},"Because Earth orbits the Sun at 107,000 km\u002Fh",{"id":324,"label":995},"Because light travels fast",{"id":327,"label":997},"Because the umbra is only 160 km wide","Both move east, so the ground chases the shadow and the difference is what you feel: 3,679 − 1,674 ≈ 2,005 km\u002Fh at best, and much faster away from the equator.",{"itemId":1000,"prompt":1001,"options":1002,"correct":321,"why":1010},"eclipses.understand-q-99pc","At 99% coverage of the Sun's **diameter**, how much of its **area** is still shining?",[1003,1005,1007,1009],{"id":318,"label":1004},"1%",{"id":321,"label":1006},"About 2%",{"id":324,"label":1008},"About 10%",{"id":327,"label":932},"Area goes as the square of the diameter: 1 − 0.99 × 0.99 = 0.0199, so about 2%. Still thousands of times too bright to look at, and your pupil is wide open.",{"itemId":1012,"prompt":1013,"options":1014,"correct":324,"why":1023},"eclipses.understand-q-future","The Moon recedes about 3.8 cm a year. What does that mean for total solar eclipses?",[1015,1017,1019,1021],{"id":318,"label":1016},"They will get longer",{"id":321,"label":1018},"Nothing — the Sun grows at the same rate",{"id":324,"label":1020},"They will eventually stop, in a few hundred million years, leaving only annular ones",{"id":327,"label":1022},"They will stop within a thousand years","Perigee must grow by about 16,200 km before the Moon can no longer cover the Sun, which at 3.8 cm a year takes on the order of 400 to 600 million years.",{"id":1025,"type":1026,"prompt":1027},"u-reflect","reflection","A friend argues: \"Total solar eclipses prove the Moon was designed to fit the Sun exactly — the odds of a 400-to-400 match are too small to be chance.\"\n\nUsing what you now know about how the Moon's apparent size changes through its orbit, and about the Moon's steady recession, write a reply. What evidence would you point to, and what would you say about the difference between a coincidence and a design?",{"id":1029,"type":1030,"title":1031,"points":1032},"u-cheat","summary","Cheat sheet",[1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044],"**Umbra** = no part of the source visible. **Penumbra** = part visible. A shadow has both only because the Sun is a **disc**, not a point.","**Cone lengths:** Moon's umbra 374,180 km; Earth's umbra 1,381,300 km (3.6 × the Moon's distance). Formula: L = r × D ÷ (R − r).","**The Moon's shadow only just reaches us.** At mean distance it falls about 3,850 km short — so an average eclipse is annular. At perigee it overshoots by about 17,250 km and gives totality.","**Apparent sizes:** Sun 31.5′ to 32.5′; Moon 29.5′ to 32.9′. The ranges overlap, which is why both total and annular eclipses exist.","**Area, not width:** covering 99% of the Sun's diameter leaves about **2%** of its area shining. The deepest annular ring leaves about **18%**.","**Earth's umbra at the Moon** is 2.6 Moon-widths across, so lunar totality can run about **1 h 40 min**, and the whole event 5 to 6 hours, seen from the entire night side.","**The red Moon = refraction + scattering.** Air bends sunlight into the shadow; the blue is scattered out on the way. Scored 0 to 4 on the **Danjon scale**, and volcanic dust can push it to 0.","**Tilt 5.145°** is 9.6 times the Sun's apparent width, and puts the Moon up to 34,600 km — 2.7 Earth-diameters — off the line. Eclipses need the Moon within about **16.6°** of a node (10.6° for lunar).","**Eclipse seasons** last about **32 days** and come every **173.3 days**, because the nodes slide backwards at 19.34° a year. A season is longer than a month, so there are **always at least two solar eclipses a year**; 4 to 7 of all kinds.","**Shadow speed** across the ground: at least about **2,000 km\u002Fh** (3,679 − 1,674). Totality: seconds to **7 min 32 s**.","**SAFETY:** ISO 12312-2 filters or projection only, for any partial or annular eclipse. Never sunglasses, smoked glass, film or reflections, never through a camera or binoculars. Bare eyes only during **totality of a total** eclipse; filters back on at the first bead.","**Lunar eclipses are entirely safe** to watch by any means.",{"id":1046,"type":1047,"sourceIds":1048},"u-sources","sources",[1049,1050,1051,1052,1053,1054,1055,1056],"eclipses-nasa-eclipses","eclipses-nasa-safety","eclipses-nasa-gsfc-catalog","eclipses-wiki-solar","eclipses-wiki-lunar","eclipses-britannica-kids","eclipses-timeanddate","eclipses-ncert-curiosity",[1049,1050,1051,1052,1053,1054,1055,1056],"needs_review",{"generatedBy":1060,"notes":1061},"claude-code","Draft generated locally; pending owner review. Every number computed in scratchpad\u002Feclipses\u002Fnumbers.py.","e25935053d3475de78e32faa0013ccdf92a19aa3547648fb9f8404aa362113db",{"component:shadow-lab@1":1064,"component:eclipse-lab@1":1065,"logic:practice":1066,"component:sort-game@1":1067,"source:eclipses-britannica-kids":1068,"source:eclipses-nasa-eclipses":1069,"source:eclipses-nasa-gsfc-catalog":1070,"source:eclipses-nasa-safety":1071,"source:eclipses-ncert-curiosity":1072,"source:eclipses-timeanddate":1073,"source:eclipses-wiki-lunar":1074,"source:eclipses-wiki-solar":1075},"7476ef546fdb1f398a07393483e549c923f9568dc1bb1c2561191bf47862c475","284cb1682e3994af706a6cf907dd7747c9c141577245765bceff3a44fc81cf10","3d6b0fe1b15255975a32b0fcd94e8019bc959ad45cbf12e136e86149549c6878","b164f45a2c8ca08f26c450768ff0231e113e9fe45381eddb34dc6d0548596c38","b10d074ebe9d86c884d3f9aab5d21f1e9ba85495f2d6add6a9263b96a9eb0a6a","c0bbcfd69fe06099e49c296bba2b105973ec1a794b69292fb65b4d81e9a2d672","6d5419b315b3a5ac0fa1e59e6867819029a60d74510dcb96fecec0d8b1f98fbe","f585b6bff2c52e5ed1c593b6222bc1e2805b7024b64f26d49271a5f19aa6dff7","c8e27588447f45548af86f4ac4ceb632dd451d78252b13c94d725b85ce34a24d","1508f2bc1fe7211250c3bc94beb9fff17e79cf0168bd0bd30264ee1e68d0086a","a72372b1c84fe7003a52eaf5654f6b88dabc645b405b6df7578cea1bae5d55e2","e32e7e8bfd7f8db32db243544cfc60cb96c0c7f050e964450ae3fc99bb21d344",{"state":1077,"reviewer":1078,"selfReview":233,"reviewedAt":1079,"method":1080},"approved","The library owner","2026-09-20T10:18:37.581Z","owner_bulk","preview-7e1cbbcc4f",1789899597689]