[{"data":1,"prerenderedAt":927},["ShallowReactive",2],{"layer:tides:understand":3},{"layer":4,"contentHash":906,"dependencyHashes":907,"approval":921,"releaseId":926},{"schemaVersion":5,"conceptId":6,"locale":7,"depth":8,"revision":5,"title":9,"subtitle":10,"summary":11,"objectives":12,"estimatedMinutes":18,"plate":19,"blocks":40,"sourceIds":901,"reviewStatus":902,"authoring":903},1,"tides","en","understand","How the Moon builds two bulges","Difference, not strength: the mechanism behind every tide","Work out why a pull towards the Moon makes a bulge away from it, where 24 h 50 min comes from, why the Sun's tide is only 46% of the Moon's, and why the same Moon gives Kochi one metre and Bhavnagar ten.",[13,14,15,16,17],"Explain the two tidal bulges using the difference in the Moon's pull on the near ocean, the solid Earth and the far ocean, and reject the “flung outwards” story.","Derive the lunar day of 24 h 50 min from the month, and use it to predict tide times.","Explain why the Sun raises a smaller tide than the Moon despite its far greater mass, and use that to account for spring and neap tides.","Use the rule of twelfths and a tide table to work out the depth of water at a given time.","Give three reasons why tidal range depends so strongly on place, including resonance.",40,{"title":20,"rows":21},"Lesson plate",[22,25,28,31,34,37],{"label":23,"value":24},"Depth","Understand",{"label":26,"value":27},"Reading time","≈ 40 minutes",{"label":29,"value":30},"Prior knowledge","Discover: tides, range, spring and neap",{"label":32,"value":33},"Chapters","10",{"label":35,"value":36},"Labs","Tide lab, moon phase, sort, match",{"label":38,"value":39},"Maths used","Percentages, ratios, clock arithmetic",[41,45,51,57,63,68,96,101,104,120,125,142,147,153,178,183,188,212,230,235,238,243,248,254,272,286,301,317,327,332,335,368,372,377,380,394,397,402,457,462,465,517,521,527,532,535,566,583,598,603,608,612,616,620,624,629,666,708,868,872,889],{"id":42,"type":43,"markdown":44},"u-intro","prose","In Discover you met the headline: the Moon's gravity stretches Earth's ocean into two bulges, and Earth turns through them. That sentence is true, and it is also doing a great deal of quiet work. This layer opens it up.\n\nBy the end you should be able to answer five questions properly, not just repeat them:\n\n1. What exactly is rising when the tide comes in?\n2. Why does a pull towards the Moon produce a bulge **away** from the Moon?\n3. Where does the strange figure of **24 h 50 min** come from?\n4. Why does the Sun, which is 27 million times more massive than the Moon, raise a tide less than half as big?\n5. Why is the tidal range 1 metre at Kochi and 10 metres at Bhavnagar, when the Moon pulls on both almost exactly the same?",{"id":46,"type":47,"variant":48,"title":49,"markdown":50},"u-how-to","callout","observation","How to use this lesson","Every chapter builds on the one before, so read in order the first time. The three **predictions** are worth committing to before you read on. Two chapters end with a worked example: try the problem yourself first, then check each step.",{"id":52,"type":53,"title":54,"eyebrow":55,"navLabel":56},"u-ch1","chapter","What exactly is going up and down?","Chapter 01","1 What rises",{"id":58,"type":43,"markdown":59,"help":60},"u-what-rises","When the tide comes in, nothing is being poured into the sea. The total amount of water on Earth does not change at all between high and low tide. What changes is **where** the water is — it has slid sideways from one part of the ocean to another.\n\nThat matters for a picture you may be carrying in your head. High tide is not water travelling all the way from another country to your beach. Over each stretch of ocean the water moves only a modest distance, but because the ocean is so wide, a small sideways drift everywhere adds up to a big rise at the edge — at the coast, where the water runs out of room and has to go up.\n\nThat is also why tides are so much bigger at the coast than in the middle of the ocean. Out in the deep mid-Pacific, far from any land, the tide is only about **half a metre**. Ships there do not notice it at all. Bring that same tide to a coast and squeeze it into a bay and it becomes the wall of water that empties the Bay of Fundy.",{"simplerExplanation":61,"anotherExample":62},"The sea does not gain water at high tide. Water slides sideways and heaps up against the land.","Tilt a full tray of water very slightly. The level at one end goes up and at the other end goes down, and the water barely moves — but the edge shows it clearly.",{"id":64,"type":47,"variant":65,"title":66,"markdown":67},"u-def-datum","definition","Heights are measured from a fixed zero","Tide tables give heights in metres, but above what? Every port has an agreed zero line called **chart datum**, set close to the lowest tide that is ever expected there.\n\nSo a tide table entry of *4.3 m* means the water is 4.3 metres above that port's zero — not 4.3 metres deep, and not 4.3 metres above the beach. It is the same idea as measuring everyone's height from the floor rather than from their knees: what matters is that everyone uses the **same** floor.",{"id":69,"type":70,"tone":71,"items":72},"u-spec-scales","spec","neutral",[73,77,81,85,89,93],{"label":74,"big":75,"value":76},"Open ocean tide","≈ 0.5 m","The rise and fall far from any coast: barely noticeable.",{"label":78,"big":79,"value":80},"Kochi","≈ 1 m","An open, straight coast. The tide sweeps past without being squeezed.",{"label":82,"big":83,"value":84},"Mumbai","≈ 4.4 m","A broad shelf and a bay start to build the tide up.",{"label":86,"big":87,"value":88},"Bhavnagar","≈ 10 m","Top of the funnel-shaped Gulf of Khambhat: India's biggest range.",{"label":90,"big":91,"value":92},"Bay of Fundy","≈ 16 m","The world's biggest, because the bay rocks in step with the tide.",{"label":94,"big":75,"value":95},"Solid rock of Earth","The ground itself flexes up and down twice a day too.",{"id":97,"type":53,"title":98,"eyebrow":99,"navLabel":100},"u-ch2","The one rule behind everything: gravity fades with distance","Chapter 02","2 Fading pull",{"id":102,"type":43,"markdown":103},"u-inverse-square","Every tide idea in this lesson comes from a single fact about gravity: **it gets weaker the further away you are**, and it does so quickly.\n\nNewton's rule is that the pull falls off with the **square** of the distance. Double the distance and the pull is not half as strong but a **quarter**. Triple it and the pull is a **ninth**. Ten times further, a hundredth.\n\nNow put Earth in that picture. Earth is 12,742 km wide, and the Moon is about 384,400 km away, measured centre to centre. So the near side of Earth is about 6,371 km closer to the Moon than the centre is, and the far side is about 6,371 km further away. That is only about 1.7% of the distance either way — small, but not zero.\n\nAnd because it is not zero, the Moon does **not** pull on all of Earth equally. It pulls the near side slightly harder than the middle, and the middle slightly harder than the far side. Every single thing about tides follows from that little inequality.",{"id":105,"type":106,"items":107},"u-formulas-gravity","formulas",[108,111,114,117],{"expression":109,"caption":110},"pull ∝ 1 ÷ distance²","Newton's law of gravitation: twice as far away means a quarter of the pull.",{"expression":112,"caption":113},"Earth's radius = 6,371 km","How much nearer the near side is to the Moon than the centre is.",{"expression":115,"caption":116},"Moon's distance ≈ 384,400 km","Centre to centre, on average. It varies through the month.",{"expression":118,"caption":119},"6,371 ÷ 384,400 ≈ 1.7%","The near side is only 1.7% closer — a small difference that is enough.",{"id":121,"type":47,"variant":122,"title":123,"markdown":124},"u-aha-difference","aha","Tides are about difference, not strength","The Moon's total pull on Earth is huge — it is what keeps the Moon in orbit around us and us wobbling around it. But a pull that is the **same everywhere** moves everything together and changes nothing you could see.\n\nWhat raises a tide is only the little bit by which the pull on one part differs from the pull on another. Scientists call that leftover the **tidal force**. It is what is left over after you subtract the average pull that everything shares.\n\nThis is why the Sun, whose total pull on Earth is about 180 times the Moon's, raises a **smaller** tide than the Moon does. A lot of pull, spread very evenly, is no good for tide-making.",{"id":126,"type":127,"title":128,"problem":129,"steps":130,"help":137},"u-we-near-far","worked_example","How much stronger is the Moon's pull on the near side?","The Moon's pull weakens as 1 ÷ distance². Earth's centre is 384,400 km from the Moon; the near side is 6,371 km closer and the far side 6,371 km further. Roughly what percentage stronger is the pull on the near ocean than on the centre?",[131,132,133,134,135,136],"Near-side distance = 384,400 − 6,371 = 378,029 km.","The pull ratio is (384,400 ÷ 378,029)², because a smaller distance means a bigger pull.","384,400 ÷ 378,029 = 1.0169.","1.0169² = 1.0340, so the near-side pull is about **3.4% stronger** than at the centre.","Do the same for the far side: (384,400 ÷ 390,771)² = 0.9677, so it is about **3.2% weaker** than at the centre.","So across Earth the Moon's pull varies by roughly 6.6% from one side to the other. That small unevenness, applied to an ocean that is free to flow, for six hours at a time, is the whole of the tide.",{"simplerExplanation":138,"hints":139},"The near side is 1.7% closer, and because pull goes as 1 ÷ distance², that makes the pull about 3.4% stronger. The far side is 3.2% weaker.",[140,141],"Closer means a bigger pull, so the ratio must be greater than 1.","Square the distance ratio, do not just double it.",{"id":143,"type":53,"title":144,"eyebrow":145,"navLabel":146},"u-ch3","The stretch: why one pull makes two bulges","Chapter 03","3 Two bulges",{"id":148,"type":43,"markdown":149,"help":150},"u-stretch","Now put the three pieces of Earth side by side — near ocean, solid planet, far ocean — and let the Moon pull on each one by the amount it deserves.\n\n- **Near ocean:** pulled hardest, about 3.4% more than average.\n- **Solid Earth:** pulled by the average amount.\n- **Far ocean:** pulled least, about 3.2% less than average.\n\nEverything is moving towards the Moon. Nothing is moving away from it. But they are not moving **equally**, and that is the same as being stretched.\n\nTo see it, stop watching from outside and stand on Earth instead. From here, the average pull that everything shares is invisible — you are moving with it, so it feels like nothing. What is left over is the difference:\n\n- The near ocean seems to creep **towards** the Moon, away from the ground beneath it: it heaps up.\n- The far ocean seems to creep **away** from the Moon, because the solid Earth is being dragged out from under it: it heaps up too.\n\nTwo heaps, at opposite ends of the line pointing at the Moon. That is the whole trick, and it works for any object stretched by any gravity anywhere in the universe.",{"simplerExplanation":151,"anotherExample":152},"Pull three things by different amounts in the same direction and they spread out. Sitting on the middle one, the other two look as if they moved apart.","A stretched rubber band held at both ends looks longer from either end, even though you only pulled outwards on each hand.",{"id":154,"type":155,"title":156,"items":157},"u-steps-subtract","steps","Three steps to the two bulges",[158,162,166,170,174],{"title":159,"tag":160,"text":161},"Pull each part","Unequal","The Moon pulls the near ocean, the solid Earth and the far ocean, each by slightly different amounts, all towards the Moon.",{"title":163,"tag":164,"text":165},"Subtract the average","The shared motion","Earth as a whole accelerates towards the Moon by the average amount. Standing on Earth, you cannot feel that at all.",{"title":167,"tag":168,"text":169},"What is left is the tide","The stretch","The leftovers point outwards at both ends of the Earth–Moon line, and sideways (inwards) around the middle.",{"title":171,"tag":172,"text":173},"Water flows where pushed","Sideways matters most","The leftover force mostly pushes water **along** the surface, towards the two ends. Water slides there and heaps up.",{"title":175,"tag":176,"text":177},"Two bulges, one low band","The result","Deeper water under the Moon and opposite the Moon; shallower water in the ring between them, where low tide is.",{"id":179,"type":47,"variant":180,"title":181,"markdown":182},"u-misc-far-bulge","misconception","“The far bulge is water flung off by Earth's spin”","You will see this claim in books and videos, with words like *centrifugal force flings the water outwards*. It is not how tides work, and you can test it with two questions.\n\n**Does the far bulge follow the Moon?** Yes — always exactly opposite the Moon, moving round as the Moon moves round. Earth's spin points the same way all the time and cannot explain something that tracks the Moon.\n\n**Do slow spinners get tides?** Yes. Earth raises enormous tides on the Moon, and the Moon turns only once a month. Tidal stretching happens even when nothing is spinning at all.\n\nThe honest answer is the one in this chapter: the far ocean is pulled **less** than the solid Earth, so the planet moves out from under it.",{"id":184,"type":47,"variant":185,"title":186,"markdown":187},"u-model-limit-equilibrium","model_limit","What the two-bulge picture leaves out","The two-bulge model is the right explanation of the **cause**. It is a poor predictor of the **details**, and honest scientists say so.\n\nIf the bulges really stood still under the Moon and Earth simply turned through them, high tide everywhere would come when the Moon was overhead, and every coast would get the same half-metre range. Neither is true. Real tides arrive hours after the Moon passes overhead, and ranges differ by a factor of thirty from place to place.\n\nThe reason is that continents are in the way. The bulges cannot travel freely round the planet; the water sloshes around in ocean basins instead, like water in a tray being rocked. What you actually measure at a coast is that sloshing, driven by the Moon. Chapter 8 picks this up, and the Deepen layer builds the real model.",{"id":189,"type":190,"component":191,"componentVersion":5,"config":192,"objective":210,"textAlternative":211},"u-lab-bulges","interactive","tide-lab",{"modes":193,"places":196,"challenges":209},[194,195],"bulges","tide-clock",[197,201,205],{"id":198,"label":199,"rangeM":200},"mumbai","Mumbai (about 4.4 m)",4.4,{"id":202,"label":203,"rangeM":204},"chennai","Chennai (about 1.2 m)",1.2,{"id":206,"label":207,"rangeM":208},"kandla","Kandla, Gulf of Kutch (about 6.5 m)",6.5,5,"Take Earth apart into near ocean, solid planet and far ocean, and watch the difference in the Moon's pull build two bulges.","This lab has two modes.\n\nIn **bulges** mode you see Earth, its ocean and the Moon. Arrows show the Moon's pull on the near ocean, on the solid Earth and on the far ocean: the near arrow is longest, the far arrow shortest, and all three point at the Moon. A switch labelled *subtract the average* removes the shared pull. The three arrows become: one pointing towards the Moon at the near side, one pointing away from the Moon at the far side, and small inward arrows around the middle. The ocean stretches into two bulges. A counter shows the near-side pull is about 3.4% above average and the far-side pull about 3.2% below it.\n\nIn **tide-clock** mode a marker on the coast of Mumbai, Chennai or Kandla is carried round through both bulges, and a graph draws the water level: high, low, high, low in one lunar day, with the range set by the place you chose.\n\nFive challenges ask you to identify the near bulge, the far bulge, the low-tide band, the second high tide of the day, and which place has the biggest range.",{"id":213,"type":214,"prompt":215,"options":216,"explanation":229},"u-predict-no-far-bulge","prediction","Imagine gravity did **not** weaken with distance — the Moon pulled every part of Earth with exactly the same force. What would the tides be like?",[217,220,223,226],{"id":218,"label":219},"a","Twice as big, since the pull is stronger everywhere",{"id":221,"label":222},"b","One bulge only, facing the Moon",{"id":224,"label":225},"c","No tides at all",{"id":227,"label":228},"d","The same as now, but at different times","**No tides at all.** A force that is exactly equal everywhere accelerates the whole planet, ocean and all, in step — and things moving in step do not move relative to each other. The water would sit exactly where it does now.\n\nThis is the cleanest test of whether you have really understood tides: they are made entirely by the **difference** in the pull from one side of Earth to the other, and not by its strength.",{"id":231,"type":53,"title":232,"eyebrow":233,"navLabel":234},"u-ch4","Earth turns through the bulges","Chapter 04","4 Spinning through",{"id":236,"type":43,"markdown":237},"u-spinning-through","The bulges are not water racing round the planet. They are more like two standing heaps, lined up with the Moon, while the planet rotates underneath.\n\nStand on a coast and let Earth carry you round once. You pass through the near bulge — high tide. Six hours later you are in the shallow band between the bulges — low tide. Six hours after that you are in the far bulge — a second high tide, usually about the same size. Six hours later, the other low. Then you are back where you started.\n\nThat gives the pattern most of the world's coasts know: **two highs and two lows a day**, called a **semidiurnal** tide. Kochi, Mumbai, Bhavnagar, Kolkata, Chennai and almost every Indian port work this way.\n\nNotice how the picture flips your intuition. The water is not coming to you. You are being carried into the water, at more than 1,600 kilometres an hour if you live near the equator.",{"id":239,"type":47,"variant":240,"title":241,"markdown":242},"u-nuance-declination","nuance","Why two high tides are sometimes unequal","The Moon is not always directly over the equator. Through the month it swings north and south of it, and the two bulges swing with it — one centred north of the equator, the other south.\n\nIf your coast is well away from the equator, one of the two bulges passes closer to you than the other does, so the two high tides of the day come out **unequal**: a higher high water and a lower high water. Parts of India's east coast show this clearly; the west coast much less so.\n\nHold onto this idea. It is what makes the difference between semidiurnal, mixed and diurnal tides, which you will meet in Investigate.",{"id":244,"type":53,"title":245,"eyebrow":246,"navLabel":247},"u-ch5","The tidal day: where 24 h 50 min comes from","Chapter 05","5 The tidal day",{"id":249,"type":43,"markdown":250,"help":251},"u-tidal-day","If Earth simply spun and the Moon stayed put, tides would repeat every 12 hours exactly and high tide would be at the same clock time every day. It is not, and the reason is that the Moon keeps moving.\n\nIn the time Earth takes one turn, the Moon has gone about **12.2 degrees** further round its orbit as seen against the Sun. Your coast comes back to where it was, but the Moon has left; Earth has to turn that extra bit to bring you back under it.\n\nThere is a very clean way to count this. The Moon goes from one new moon to the next in **29.53 days**. In that same stretch of time, how many times does your coast come back under the **Moon**? Exactly one time fewer than it comes back under the Sun — because the Moon has gone all the way round once in the meantime, in the same direction as Earth's spin.\n\nSo 29.53 solar days contain only **28.53** lunar days. One lunar day must therefore be 29.53 ÷ 28.53 = **1.0351 days**, which is **24 h 50 min**.",{"simplerExplanation":252,"anotherExample":253},"In a month the Moon goes round Earth once, in the same direction Earth spins. So in a month you face the Moon one time fewer than you face the Sun, and each 'Moon day' is a bit longer than a Sun day.","Run 29 laps of a track while a friend walks 1 lap the same way. You pass them only 28 times, so the gap between passes is longer than a lap.",{"id":255,"type":106,"items":256},"u-formulas-day",[257,260,263,266,269],{"expression":258,"caption":259},"29.53 ÷ 28.53 = 1.0351 days","One lunar day, in solar days. Multiply by 24 to get hours.",{"expression":261,"caption":262},"lunar day = 24 h 50 min","Earth's turn relative to the Moon.",{"expression":264,"caption":265},"÷ 2 = 12 h 25 min","From one high tide to the next: half a lunar day.",{"expression":267,"caption":268},"÷ 4 = 6 h 13 min","From high water to the next low water.",{"expression":270,"caption":271},"daily slip = 50 min","Lunar day minus solar day: how much later tides are each day.",{"id":273,"type":127,"title":274,"problem":275,"steps":276,"help":282},"u-we-angle-check","Checking the 50 minutes a second way","Earth turns 360° relative to the Sun in 24 hours, which is 15° per hour. The Moon slips about 12.19° per day further east. Show that the catch-up takes about 50 minutes.",[277,278,279,280,281],"Earth's turning rate relative to the Sun: 360° ÷ 24 h = 15° per hour, which is 0.25° per minute.","In one **lunar day** of 1.0351 days, the Moon moves 12.19 × 1.0351 = **12.62°**.","Time to turn that extra 12.62° at 0.25° per minute: 12.62 ÷ 0.25 = **50.5 minutes**.","That matches the 50 minutes from the month calculation. ✓","Careful with a tempting shortcut: using 24 hours instead of a full lunar day gives 12.19° and about 49 minutes. Close, but the sum only closes properly when you let the Moon move for the whole lunar day, not just 24 hours.",{"hints":283},[284,285],"0.25° per minute is just 15° per hour written differently.","The Moon keeps moving while Earth is catching up, so use the lunar day.",{"id":287,"type":127,"title":288,"problem":289,"steps":290,"help":298},"u-we-week","A week of high tides from one starting time","High water at a port is at **05:10** on Monday. Assuming a regular semidiurnal tide, work out the morning high water for each day up to Friday.",[291,292,293,294,295,296,297],"Each day's tide comes 50 minutes later than the day before.","Monday 05:10. Tuesday: 05:10 + 50 min = **06:00**.","Wednesday: 06:00 + 50 min = **06:50**.","Thursday: 06:50 + 50 min = **07:40**.","Friday: 07:40 + 50 min = **08:30**.","Check it the other way: from Monday to Friday is 4 days, so 4 × 50 = 200 minutes = 3 h 20 min. 05:10 + 3 h 20 min = 08:30. ✓","Over a fortnight the slip is about 14 × 50 = 700 minutes, nearly 12 hours — which is why a tide that is in the morning this week is in the evening a fortnight later.",{"simplerExplanation":299,"anotherExample":300},"Add 50 minutes for each day that passes.","The evening high waters do the same thing: Monday's 17:35 becomes Tuesday's 18:25.",{"id":302,"type":303,"itemId":304,"prompt":305,"check":306,"hints":311,"feedback":314},"u-pr-thursday","practice","tides.understand-thursday","High water is at 11:20 on Sunday. Using the 50-minutes-a-day rule, how many **minutes** after 11:20 will Wednesday's matching high water be?",{"kind":307,"answer":308,"tolerance":309,"unit":310},"number",150,0,"min",[312,313],"Sunday to Wednesday is 3 days.","3 × 50 = ?",{"correct":315,"incorrect":316},"Right: 3 days × 50 min = **150 minutes**, so the tide is at about 13:50 on Wednesday.","Count the days first: Sunday to Wednesday is 3 days. Then 3 × 50 = 150 minutes.",{"id":318,"type":190,"component":319,"componentVersion":5,"config":320,"objective":325,"textAlternative":326},"u-lab-moon-phase","moon-phase",{"startDay":309,"views":321,"showNames":323,"showTithi":323,"quizRounds":324},[322],"both",true,6,"Follow the Moon through a month and read off, from its phase alone, whether tides that day are spring or neap.","This lab shows the Moon in two views at once: what it looks like from Earth, and the whole Sun–Earth–Moon layout from above. A slider moves you through the 29.5 days of a lunar month, with the phase names and the Indian tithi labels shown.\n\nAt day 0, **new moon (amavasya)**, the Moon sits between Earth and the Sun: from Earth it is invisible, and from above the three bodies are in a straight line. Tides that day are **spring** tides.\n\nAt about day 7.4, **first quarter**, you see a half moon, and from above the Moon is at right angles to the Sun: **neap** tides.\n\nAt about day 14.8, **full moon (purnima)**, the Moon is opposite the Sun — a straight line again, so **spring** tides once more.\n\nAt about day 22.1, **last quarter**, another half moon and another neap tide.\n\nSix quiz rounds show you a phase and ask whether that day's tides are spring or neap, and how many days until the next spring tide.",{"id":328,"type":53,"title":329,"eyebrow":330,"navLabel":331},"u-ch6","The Sun's share of the tide","Chapter 06","6 The Sun's tide",{"id":333,"type":43,"markdown":334},"u-sun-share","The Sun raises tides too, and comparing them teaches you something important about how tidal forces work.\n\nStart with the raw numbers. The Sun is about **27 million times** more massive than the Moon. It is also about **390 times** further away. If tides depended on plain gravitational pull, the Sun would win easily: its total pull on Earth really is about 180 times the Moon's.\n\nBut tides do not care about the pull. They care about **how much the pull changes across Earth's width** — and from very far away, a pull barely changes at all over a mere 12,742 km. From the Sun's distance, the near side and the far side of Earth are almost identical places.\n\nWork it out properly and the Moon's tide-raising effect comes to about **2.2 times** the Sun's. In other words the Sun's tide is roughly **46%** of the Moon's: not the main player, but far too big to ignore. That 46% is exactly what makes spring and neap tides.",{"id":336,"type":337,"caption":338,"columns":339,"rows":344},"u-table-sun-moon","table","Moon versus Sun: big pull is not the same as big tide",[340,341,342,343],"Quantity","Moon","Sun","What it means",[345,350,355,359,363],[346,347,348,349],"Mass","1 unit","about 27 million units","The Sun wins by an enormous margin",[351,352,353,354],"Distance from Earth","384,400 km","about 150 million km","The Sun is about 390 times further",[356,347,357,358],"Total pull on Earth","about 180 units","Still the Sun, comfortably",[360,361,347,362],"Tide-raising effect","2.18 units","The Moon wins, because distance counts far more for tides",[364,365,366,367],"Share of a spring tide","about 69%","about 31%","They add when in line",{"id":369,"type":47,"variant":240,"title":370,"markdown":371},"u-nuance-cubed","Why distance matters even more for tides than for gravity","Plain gravity fades as 1 ÷ distance². The **tidal** effect fades faster still: as 1 ÷ distance³, the cube.\n\nThe reason is that the tidal force is a *difference* between two gravity values that are themselves shrinking. Move twice as far away and the pull drops to a quarter — but the difference between the near and far sides drops to an eighth.\n\nThat extra power of distance is the whole story of the Moon beating the Sun. You do not need the cube rule to understand tides, but it is the sentence that explains the 2.2.",{"id":373,"type":53,"title":374,"eyebrow":375,"navLabel":376},"u-ch7","Spring and neap, properly","Chapter 07","7 Spring and neap",{"id":378,"type":43,"markdown":379},"u-spring-neap-detail","Two tides are being raised at every moment: a big one by the Moon and a smaller one, about 46% as strong, by the Sun. Each of them has **two** bulges. What you actually get is the two patterns added together.\n\n**When Sun, Earth and Moon are in a straight line** — at new moon and at full moon — the Sun's bulges sit exactly on top of the Moon's. The heaps add: higher high water, lower low water, the biggest range of the fortnight. This is a **spring tide**. It happens at both new and full moon, because each body makes a pair of bulges at opposite ends; what matters is the straight line, not which end the Sun is at.\n\n**When the Moon is at first or last quarter**, the Sun is off at 90°. The Sun's high water lands where the Moon's low water is and partly fills it in. The range shrinks to its smallest: a **neap tide**.\n\nCompare them with the simplest possible sum. If the Moon's tide is 2.18 units and the Sun's is 1 unit: spring range goes as 2.18 + 1 = **3.18**, neap range as 2.18 − 1 = **1.18**. So a spring range is roughly **2.7 times** a neap range — and that is about what real ports record.",{"id":381,"type":127,"title":382,"problem":383,"steps":384,"help":390},"u-we-spring-neap","Estimating a neap range from a spring range","A port records a spring tidal range of about **4.4 m**. Using the Moon-to-Sun ratio of 2.18 to 1, estimate its neap range.",[385,386,387,388,389],"A spring range is proportional to (Moon + Sun) = 2.18 + 1 = 3.18 units.","A neap range is proportional to (Moon − Sun) = 2.18 − 1 = 1.18 units.","So neap ÷ spring = 1.18 ÷ 3.18 = 0.370.","Neap range ≈ 4.4 × 0.370 = **1.6 m**, a little over a third of the spring range.","Real ports come out close to this but not exactly, because the shape of the coast changes both numbers a little. Mumbai's neaps are around 1.5 to 2 m.",{"simplerExplanation":391,"hints":392},"Spring is Moon plus Sun; neap is Moon minus Sun. Divide one by the other to scale a known range.",[393],"The ratio 1.18 ÷ 3.18 is a bit more than a third.",{"id":395,"type":43,"markdown":396},"u-fortnight","How often do spring tides come round? The Moon takes **29.53 days** from one new moon to the next, and it lines up with the Sun **twice** in that time: once at new moon and once at full moon. So spring tides come every **29.53 ÷ 2 = 14.77 days** — about a fortnight.\n\nThere is a second, lovelier way to get the same answer, and it is the one tide scientists actually use. The Moon's tide repeats every **12 h 25 min** and the Sun's every **12 h exactly**. Two rhythms that are nearly but not quite the same drift in and out of step, the way two clocks ticking at slightly different rates drift from agreeing to disagreeing and back.\n\nWork out how long they take to go from in-step to in-step again and you get **14.77 days** — the same fortnight, arrived at from the clock instead of from the sky.",{"id":398,"type":47,"variant":399,"title":400,"markdown":401},"u-example-lag","example","Spring tides usually arrive a day or two late","Look at a real tide table and you will often find the biggest tides of the fortnight come **one or two days after** the full or new moon, not on the day itself.\n\nThis is called the **age of the tide**. The ocean is enormous and slow: it takes time for all that water to respond to a change in the pull, the way a heavy swing takes a few pushes to reach its biggest arc. The delay is fairly constant for each port, so tide predictions simply build it in.\n\nIt is a good reminder that the sky sets the rhythm, and the ocean plays it a little behind the beat.",{"id":403,"type":190,"component":404,"componentVersion":5,"config":405,"objective":455,"textAlternative":456},"u-lab-sort-springneap","sort-game",{"prompt":406,"bins":407,"items":414,"seconds":309},"Spring tide or neap tide? Sort each description.",[408,411],{"id":409,"label":410},"spring","Spring tide",{"id":412,"label":413},"neap","Neap tide",[415,419,423,427,431,435,439,443,447,451],{"id":416,"label":417,"bin":409,"why":418},"n1","It is full moon tonight","Full moon means Sun, Earth and Moon in a line, so the two tides add.",{"id":420,"label":421,"bin":412,"why":422},"n2","The Moon is a half moon, first quarter","At the quarters the Sun pulls at right angles to the Moon and partly cancels its tide.",{"id":424,"label":425,"bin":409,"why":426},"n3","It is amavasya, new moon","New moon is also a straight-line alignment, so the tides add just as at full moon.",{"id":428,"label":429,"bin":409,"why":430},"n4","The tidal range today is the biggest of the fortnight","Biggest range of the fortnight is the definition of a spring tide.",{"id":432,"label":433,"bin":412,"why":434},"n5","The sea hardly seems to move up or down all day","A small range means the Sun's tide is working against the Moon's.",{"id":436,"label":437,"bin":409,"why":438},"n6","Low water is lower than it has been for a week","Springs give both higher highs and lower lows: the range is stretched at both ends.",{"id":440,"label":441,"bin":412,"why":442},"n7","The Moon is a half moon, last quarter","Last quarter is the other right-angle alignment, so neap tides again.",{"id":444,"label":445,"bin":409,"why":446},"n8","Sun, Earth and Moon are in a straight line","A straight line stacks the Sun's bulges on the Moon's, whichever side the Sun is on.",{"id":448,"label":449,"bin":412,"why":450},"n9","Fishers say the creek will not fill enough to float the boat today","A weak high water is the practical sign of a neap tide.",{"id":452,"label":453,"bin":409,"why":454},"n10","Horseshoe crabs are coming ashore to lay eggs high on the beach","They time egg-laying to the highest tides of the month so the eggs end up above ordinary tides.","Sort ten clues — from moon phases to what fishers say — into spring tides and neap tides.","A sorting game with two bins, spring tide and neap tide, and ten clue cards.\n\nSpring tide clues: it is full moon tonight; it is amavasya (new moon); the range is the biggest of the fortnight; low water is lower than it has been all week; Sun, Earth and Moon are in a straight line; horseshoe crabs are laying eggs high on the beach.\n\nNeap tide clues: the Moon is a half moon at first quarter; the Moon is a half moon at last quarter; the sea hardly moves up or down all day; fishers say the creek will not fill enough to float the boat.",{"id":458,"type":53,"title":459,"eyebrow":460,"navLabel":461},"u-ch8","Why the tide is 1 metre here and 10 metres there","Chapter 08","8 Place matters",{"id":463,"type":43,"markdown":464},"u-place-matters","The Moon pulls on Kochi and on Bhavnagar by the same amount, to within a hair. Yet Kochi's tide is about a metre and Bhavnagar's about ten. Three things about a **place** turn the same sky-driven nudge into wildly different tides.\n\n**1. Funnelling.** When a tide runs into a bay that narrows, the same volume of water is squeezed into a smaller and smaller width. It has nowhere to go but up. The Gulf of Khambhat is a textbook funnel: broad at the mouth, narrow at Bhavnagar.\n\n**2. Shallowing.** A tide entering shallower water slows down, and slowing water piles up behind itself, exactly as a traffic jam builds when cars slow. Wide, shallow shelves — like the one off Gujarat and the one at the head of the Bay of Bengal — grow tides.\n\n**3. Resonance.** This is the big one, and the most beautiful. Every basin of water has a natural rhythm at which it likes to slosh, set by its length and depth. If that natural rhythm happens to be close to **12 h 25 min**, each new tide arrives just as the basin is ready for a push, and the sloshing builds enormously — exactly like pushing a child on a swing at the right moment. The Bay of Fundy's natural rhythm is close to the tidal rhythm, which is why it has the biggest tide on Earth.\n\nTurn all three off and you get an open, straight, deep coastline: Kerala, with its one-metre tide.",{"id":466,"type":467,"title":468,"prompt":469,"options":470},"u-explorer-places","explorer","Four coasts, four very different tides","Pick a coast to see what its shape does to the tide that arrives.",[471,483,494,506],{"id":472,"label":78,"chain":473,"badge":479,"note":482},"kochi",[474,475,476,477,478],"Open Arabian Sea coast","Straight shoreline, no funnel","Deep water close inshore","No squeezing, no resonance","Range about 1 m",{"text":480,"tone":481},"Small tide","no","Kerala's coast runs almost straight and the sea bed drops away quickly. A tide sweeping north along the Arabian Sea passes by without being narrowed or slowed, so what reaches the shore is close to the open-ocean tide. Backwater boats and harbour walls at Kochi show only about a metre of daily movement, which is why the backwaters can be used at almost any hour.",{"id":198,"label":82,"chain":484,"badge":490,"note":493},[485,486,487,488,489],"Wide continental shelf","Tide slows in shallow water","Bay shape gathers it","Range about 4.4 m","Docks need tide planning",{"text":491,"tone":492},"Medium tide","yes","Off Maharashtra the continental shelf is broad and shallow, so the tide slows and builds as it comes in. Mumbai's spring range of about 4.4 m is enough that its old docks were built with gates to hold water in, and enough that the city's low-lying areas flood badly when a spring tide meets heavy monsoon rain: the storm drains simply cannot empty into a sea that is higher than they are.",{"id":495,"label":496,"chain":497,"badge":503,"note":505},"khambhat","Gulf of Khambhat",[498,499,500,501,502],"Broad mouth on the Arabian Sea","Gulf narrows towards the north","Water shallows too","Same water, less room","Range about 10 m",{"text":504,"tone":492},"Huge tide","The Gulf of Khambhat is a funnel about 200 km long, wide at the mouth and narrowing to the river mouths near Bhavnagar. A tide entering the mouth has to fit into less and less width and less and less depth, so it climbs. Spring ranges around Bhavnagar of roughly 10 m are the largest on the Indian coast, and the currents that go with them are fierce. This is why every plan for Indian tidal power has looked at this gulf and at the Gulf of Kutch next door.",{"id":507,"label":90,"chain":508,"badge":514,"note":516},"fundy",[509,510,511,512,513],"Long, narrowing bay","Natural sloshing time ≈ 13 h","Tide arrives every 12 h 25 min","Each tide pushes in step","Range about 16 m",{"text":515,"tone":492},"World's biggest","The Bay of Fundy in Canada is the champion, with a tidal range of about 16 m — roughly the height of a four-storey building, and sixteen times Kochi's. It is a funnel, but the real secret is resonance: the time the bay naturally takes to slosh from end to end and back is close to the 12 h 25 min beat of the tide, so every tide arrives like a perfectly timed push on a swing. About 100 billion tonnes of water move in and out on each tide, more than all the world's rivers carry in the same time.",{"id":518,"type":47,"variant":122,"title":519,"markdown":520},"u-aha-swing","A bay is a swing, and the Moon is the push","You already know resonance from a playground. Push a swing at random moments and it goes nowhere. Push it once per swing, at the right moment, and a child who weighs as much as you goes higher than you could ever throw them.\n\nThe Moon pushes every ocean basin with exactly the same small force every 12 h 25 min. Basins whose natural rhythm is nothing like that barely respond. Basins whose natural rhythm is close to it build up an enormous swing. That single idea explains most of the map of the world's tidal ranges.",{"id":522,"type":523,"conceptId":524,"relation":525,"explanation":526},"u-conn-gravity","connection","gravity","helps_understand","Tides are the clearest everyday proof that gravity weakens with distance: the whole two-bulge picture is nothing but that fading applied across Earth's width.",{"id":528,"type":53,"title":529,"eyebrow":530,"navLabel":531},"u-ch9","Reading a tide table like a sailor","Chapter 09","9 Tide tables",{"id":533,"type":43,"markdown":534},"u-tide-table-read","A tide table gives you, for one port, the **time** and **height** of every high and low water. Everything else is arithmetic.\n\nThree questions a coastal worker asks it every day:\n\n- *When can I get out and back?* Find the high waters and work backwards from the hours when there is enough depth.\n- *How much water will there be at 3 pm?* The tide is not between highs at a steady rate, so there is a rule for this, coming up next.\n- *Is this a big tide or a small one?* Compare today's range with the fortnight around it, or look at the moon symbol.\n\nFor the middle question, sailors use the **rule of twelfths**. Divide the six hours of the rise into six parts. The water does not come in one sixth each hour; it comes in **1, 2, 3, 3, 2, 1 twelfths**, slow at first, fast in the middle two hours, slow at the end. The ebb does exactly the same in reverse.\n\nIt is an approximation, not a law — but it is close enough that it has been used at sea for well over a century.",{"id":536,"type":337,"caption":537,"columns":538,"rows":543},"u-table-twelfths","The rule of twelfths on a 4.4 m range (a Mumbai spring tide)",[539,540,541,542],"Hour of the flood","Twelfths that hour","Water that hour","Total risen",[544,548,553,557,560,563],[545,546,547,547],"1st hour","1 twelfth","0.37 m",[549,550,551,552],"2nd hour","2 twelfths","0.73 m","1.10 m",[554,555,552,556],"3rd hour","3 twelfths","2.2 m (halfway)",[558,555,552,559],"4th hour","3.30 m",[561,550,551,562],"5th hour","4.03 m",[564,546,547,565],"6th hour","4.4 m (high water)",{"id":567,"type":127,"title":568,"problem":569,"steps":570,"help":578},"u-we-twelfths","How much water three hours after low tide?","Low water at a Mumbai jetty is 0.6 m at 08:00 and high water is 5.0 m at about 14:15. A boat needs 3.0 m of water to float off the mud. Can it float at 11:00?",[571,572,573,574,575,576,577],"First the range: 5.0 − 0.6 = **4.4 m**.","From 08:00 to 11:00 is 3 hours, so three of the six hours of the flood have passed.","By the rule of twelfths, after three hours the water has risen 1 + 2 + 3 = 6 twelfths, which is exactly **half** the range.","Half of 4.4 is 2.2 m, so the water level is 0.6 + 2.2 = **2.8 m**.","The boat needs 3.0 m and there is 2.8 m. **Not yet** — it is about 0.2 m short.","How much longer? The fourth hour brings another 3 twelfths, which is 1.1 m, so roughly 11 minutes into that hour the water passes 3.0 m: a little after 11:15.","A cautious skipper waits until 11:30. Tide arithmetic is one place where rounding the wrong way puts a boat on the mud.",{"simplerExplanation":579,"hints":580},"Half the tide comes in during the middle three hours. After three hours of a 4.4 m flood, the water has risen 2.2 m.",[581,582],"1 + 2 + 3 = 6 twelfths = one half.","Add the rise to the low water height, do not use it on its own.",{"id":584,"type":303,"itemId":585,"prompt":586,"check":587,"hints":591,"feedback":595},"u-pr-twelfths","tides.understand-twelfths","A port has low water 1.0 m and high water 7.0 m. Using the rule of twelfths, how high is the water **two hours** after low water, in metres?",{"kind":307,"answer":588,"tolerance":589,"unit":590},3,0.01,"m",[592,593,594],"The range is 7.0 − 1.0 = 6.0 m.","Two hours brings 1 + 2 = 3 twelfths of the range.","Add what has risen to the low water height.",{"correct":596,"incorrect":597},"Right: range 6.0 m, three twelfths of it is 1.5 m, and 1.0 + 1.5 = **3.0 m**.","Range = 7.0 − 1.0 = 6.0 m. After two hours, 1 + 2 = 3 twelfths have come in: 6.0 × 3 ÷ 12 = 1.5 m. Water level = 1.0 + 1.5 = 3.0 m.",{"id":599,"type":523,"conceptId":600,"relation":601,"explanation":602},"u-conn-data","data-handling","applied_in","Tide tables are predictions built from data: years of half-hourly measurements, averaged and analysed until the pattern can be run forwards.",{"id":604,"type":53,"title":605,"eyebrow":606,"navLabel":607},"u-ch10","Five mix-ups worth clearing up","Chapter 10","10 Mix-ups",{"id":609,"type":47,"variant":180,"title":610,"markdown":611},"u-misc-overhead","“High tide is when the Moon is overhead”","If Earth were a smooth ball of water with no continents, that would be roughly true. It is not.\n\nReal high water at a real port can come **hours** after the Moon crosses overhead, and the delay is different at every port — it depends on how long the tide takes to travel round the ocean basin and into that particular bay. Sailors call the port's own delay its **establishment**.\n\nSo the Moon sets the rhythm, and each coast keeps its own steady offset from it. That is exactly why we publish a separate tide table for each port instead of one for the whole world.",{"id":613,"type":47,"variant":180,"title":614,"markdown":615},"u-misc-water-lifted","“The Moon lifts the water straight up”","The straight-up part of the Moon's tidal tug is astonishingly weak: about 1e-07 of Earth's gravity — roughly a ten-millionth. It could never lift a sea.\n\nWhat does the work is the **sideways** part. Around the ring between the bulges, the leftover force points along the surface, towards the sub-lunar point and towards the point opposite. Water slides that way for hours, and piles up at both ends.\n\nLifting water is hard; sliding it downhill along a surface is easy. Tides take the easy route.",{"id":617,"type":47,"variant":180,"title":618,"markdown":619},"u-misc-tidal-wave","“Tsunamis are tidal waves”","They are not, and the old name causes real confusion. A tsunami has nothing to do with the Moon, the Sun or the tide. It is made by an earthquake, a landslide or a volcano shoving the sea bed.\n\nThe differences matter on a coast. Tides are predictable years ahead and printed in a table; a tsunami arrives with at best a few hours of warning. Tides rise and fall twice a day, every day; a tsunami is a rare series of waves that can keep coming for hours.\n\nIndia learned this the hard way on 26 December 2004. Since then INCOIS has run a national tsunami warning centre in Hyderabad — a different service entirely from tide prediction.",{"id":621,"type":47,"variant":180,"title":622,"markdown":623},"u-misc-moon-only","“Only the Moon matters”","The Sun's contribution of about 46% is not a footnote — it is the reason tides have a fortnightly rhythm at all. Without the Sun, every tide would be the same size as every other, there would be no spring or neap tides, and the horseshoe crabs of Odisha would have nothing to set their calendar by.",{"id":625,"type":47,"variant":626,"title":627,"markdown":628},"u-careful-currents","careful","The dangerous part of a tide is the current, not the height","A rising tide of 4 metres sounds like the danger. It is not. The danger is the **tidal stream**: the water moving sideways to make that rise happen.\n\nIn a narrow creek, an estuary or a channel between rocks, tidal currents can run faster than an adult can swim, and they run for hours. Never swim across a tidal creek or channel, never try to walk back across a filling channel, and treat any water that is visibly moving on a beach with great respect.",{"id":630,"type":190,"component":631,"componentVersion":5,"config":632,"objective":664,"textAlternative":665},"u-lab-match","match-pairs",{"prompt":633,"mode":634,"pairs":635},"Match each tide idea to the sentence that explains it.","connect",[636,639,642,645,647,649,652,655,658,661],{"a":637,"b":638},"Tidal force","What is left of the Moon's pull after subtracting the average",{"a":640,"b":641},"Far-side bulge","Water left behind as Earth is pulled out from under it",{"a":643,"b":644},"Lunar day","24 h 50 min: Earth's turn relative to the Moon",{"a":410,"b":646},"Sun and Moon in line, so the two tides add",{"a":413,"b":648},"Sun at right angles to the Moon, so the tides partly cancel",{"a":650,"b":651},"Resonance","A bay whose natural sloshing time matches the tide's beat",{"a":653,"b":654},"Chart datum","The fixed zero level that tide heights are measured from",{"a":656,"b":657},"Rule of twelfths","Water rises 1, 2, 3, 3, 2, 1 twelfths in six hours",{"a":659,"b":660},"Semidiurnal tide","Two high waters and two low waters each day",{"a":662,"b":663},"Age of the tide","Why the biggest tides come a day or two after full moon","Match ten tide ideas from this layer to the sentence that explains each one.","A matching game with ten pairs. Tidal force goes with 'what is left of the Moon's pull after subtracting the average'. Far-side bulge goes with 'water left behind as Earth is pulled out from under it'. Lunar day goes with '24 h 50 min, Earth's turn relative to the Moon'. Spring tide goes with 'Sun and Moon in line, so the two tides add'. Neap tide goes with 'Sun at right angles, so the tides partly cancel'. Resonance goes with 'a bay whose natural sloshing time matches the tide's beat'. Chart datum goes with 'the fixed zero that tide heights are measured from'. Rule of twelfths goes with 'water rises 1, 2, 3, 3, 2, 1 twelfths in six hours'. Semidiurnal tide goes with 'two high waters and two low waters each day'. Age of the tide goes with 'why the biggest tides come a day or two after full moon'.",{"id":667,"type":668,"title":669,"terms":670},"u-glossary","glossary","The vocabulary of tides",[671,673,676,679,681,684,686,688,690,693,695,697,700,702,705],{"term":637,"meaning":672},"The part of the Moon's or Sun's pull that is left over after subtracting the average pull on Earth. It is what stretches the ocean.",{"term":674,"meaning":675},"Tidal bulge","A region of slightly deeper water. There are two, at the ends of the line towards the Moon.",{"term":677,"meaning":678},"Sub-lunar point","The spot on Earth directly under the Moon at a given moment; the near bulge is centred there.",{"term":659,"meaning":680},"A tide with two highs and two lows a day of similar size — the pattern on almost all of India's coast.",{"term":682,"meaning":683},"Lunar day (tidal day)","24 h 50 min: the time Earth takes to turn back under the Moon.",{"term":410,"meaning":685},"The largest range of the fortnight, when Sun, Earth and Moon are in line, at new and full moon.",{"term":413,"meaning":687},"The smallest range of the fortnight, when the Moon is at first or last quarter.",{"term":662,"meaning":689},"The delay of a day or two between a full or new moon and the biggest tides that follow it.",{"term":691,"meaning":692},"Establishment of the port","The steady delay between the Moon passing overhead and high water at a particular port.",{"term":653,"meaning":694},"The fixed zero level at a port from which all tide heights are measured, close to the lowest expected tide.",{"term":656,"meaning":696},"A sailor's estimate: in six hours the tide rises 1, 2, 3, 3, 2 and 1 twelfths of its range.",{"term":698,"meaning":699},"Tidal stream","The sideways flow of water that produces the rise and fall. Often the dangerous part of a tide.",{"term":650,"meaning":701},"The build-up that happens when a bay's natural sloshing rhythm matches the rhythm of the tide pushing it.",{"term":703,"meaning":704},"Continental shelf","The shallow sea floor around a continent. Wide shelves slow tides down and make them bigger.",{"term":706,"meaning":707},"Tide table","The published list of times and heights of high and low water for one port.",{"id":709,"type":710,"title":711,"questions":712},"u-quiz","quiz","Check yourself: how the two bulges really work",[713,726,738,751,764,777,790,803,816,829,842,855],{"itemId":714,"prompt":715,"options":716,"correct":221,"why":725},"tides.understand-q-difference","What actually raises a tide?",[717,719,721,723],{"id":218,"label":718},"The total strength of the Moon's gravity",{"id":221,"label":720},"The difference in the Moon's pull from one side of Earth to the other",{"id":224,"label":722},"The Moon's magnetic field",{"id":227,"label":724},"Earth's spin flinging water outwards","A pull that is the same everywhere moves everything together and changes nothing. Only the **difference** across Earth's width stretches the ocean.",{"itemId":727,"prompt":728,"options":729,"correct":224,"why":737},"tides.understand-q-equal-pull","If the Moon pulled every part of Earth exactly equally, what would happen?",[730,732,734,735],{"id":218,"label":731},"Tides twice as large",{"id":221,"label":733},"One bulge only",{"id":224,"label":225},{"id":227,"label":736},"Tides once a day","No tides. Earth, ocean and all would accelerate in step, so nothing would move relative to anything else.",{"itemId":739,"prompt":740,"options":741,"correct":221,"why":750},"tides.understand-q-nearside","The near side of Earth is about 1.7% closer to the Moon than the centre is. Roughly how much stronger is the pull there?",[742,744,746,748],{"id":218,"label":743},"1.7% stronger",{"id":221,"label":745},"About 3.4% stronger",{"id":224,"label":747},"About 17% stronger",{"id":227,"label":749},"Exactly the same","Gravity goes as 1 ÷ distance², so a 1.7% smaller distance gives about (1.017)² = 1.034, which is about 3.4% more pull.",{"itemId":752,"prompt":753,"options":754,"correct":221,"why":763},"tides.understand-q-lunarday","Where does the lunar day of 24 h 50 min come from?",[755,757,759,761],{"id":218,"label":756},"Earth's spin is slowing down by 50 minutes a day",{"id":221,"label":758},"The Moon moves along its orbit while Earth turns, so Earth must turn further",{"id":224,"label":760},"The Sun drags the tide 50 minutes late",{"id":227,"label":762},"Tides take 50 minutes to cross the ocean","In 29.53 days the Moon goes round once, so a coast faces the Moon one time fewer than it faces the Sun: 29.53 ÷ 28.53 days per lunar day.",{"itemId":765,"prompt":766,"options":767,"correct":221,"why":776},"tides.understand-q-sunshare","The Sun's tide-raising effect is about what fraction of the Moon's?",[768,770,772,774],{"id":218,"label":769},"About 180 times bigger",{"id":221,"label":771},"About 46%",{"id":224,"label":773},"About 5%",{"id":227,"label":775},"Exactly equal","The Sun's total pull is about 180 times the Moon's, but tides depend on how much the pull **changes** across Earth, and from 150 million km away it barely changes at all. Result: about 46% of the Moon's effect.",{"itemId":778,"prompt":779,"options":780,"correct":221,"why":789},"tides.understand-q-springwhen","Spring tides happen at which phases?",[781,783,785,787],{"id":218,"label":782},"First and last quarter",{"id":221,"label":784},"New moon and full moon",{"id":224,"label":786},"Full moon only",{"id":227,"label":788},"Whenever the Moon is closest","Both are straight-line alignments. Each body makes two bulges, so it does not matter which end of the line the Sun is at.",{"itemId":791,"prompt":792,"options":793,"correct":224,"why":802},"tides.understand-q-ratio","A port has a spring range of 6.0 m. Using Moon 2.18 to Sun 1, what is its rough neap range?",[794,796,798,800],{"id":218,"label":795},"About 5 m",{"id":221,"label":797},"About 3 m",{"id":224,"label":799},"About 2.2 m",{"id":227,"label":801},"About 0.5 m","neap ÷ spring = (2.18 − 1) ÷ (2.18 + 1) = 0.370, and 6.0 × 0.370 = **2.2 m**.",{"itemId":804,"prompt":805,"options":806,"correct":221,"why":815},"tides.understand-q-fundy","Why does the Bay of Fundy have the world's biggest tide?",[807,809,811,813],{"id":218,"label":808},"It is closest to the Moon",{"id":221,"label":810},"Its natural sloshing rhythm nearly matches the tide's beat",{"id":224,"label":812},"It is the deepest bay in the world",{"id":227,"label":814},"Two oceans meet there","Resonance. A bay pushed in step with its own rhythm builds an enormous swing, exactly like a child on a swing pushed at the right moment.",{"itemId":817,"prompt":818,"options":819,"correct":221,"why":828},"tides.understand-q-twelfths","Low water 2.0 m, high water 8.0 m. By the rule of twelfths, how high is the water three hours after low water?",[820,822,824,826],{"id":218,"label":821},"3.5 m",{"id":221,"label":823},"5.0 m",{"id":224,"label":825},"6.0 m",{"id":227,"label":827},"8.0 m","Range 6.0 m. After three hours, 1 + 2 + 3 = 6 twelfths = half the range = 3.0 m. So 2.0 + 3.0 = **5.0 m**: exactly halfway up.",{"itemId":830,"prompt":831,"options":832,"correct":221,"why":841},"tides.understand-q-overhead","Why is high water usually **not** at the moment the Moon is overhead?",[833,835,837,839],{"id":218,"label":834},"Tide tables are inaccurate",{"id":221,"label":836},"Continents are in the way, so the tide sloshes around ocean basins and arrives late",{"id":224,"label":838},"The Moon's pull takes hours to travel",{"id":227,"label":840},"Because of the Sun","The bulges cannot sweep freely round a planet covered in continents. Each basin has its own sloshing pattern, so every port has its own steady delay.",{"itemId":843,"prompt":844,"options":845,"correct":221,"why":854},"tides.understand-q-danger","Which part of a tide is usually most dangerous to people?",[846,848,850,852],{"id":218,"label":847},"The height of high water",{"id":221,"label":849},"The sideways tidal stream",{"id":224,"label":851},"Slack water",{"id":227,"label":853},"The moon phase","The current. In creeks and channels a tidal stream can run faster than an adult can swim, and it keeps running for hours.",{"itemId":856,"prompt":857,"options":858,"correct":221,"why":867},"tides.understand-q-fortnight","About how many days pass between one spring tide and the next?",[859,861,863,865],{"id":218,"label":860},"About 7",{"id":221,"label":862},"About 14.8",{"id":224,"label":864},"About 29.5",{"id":227,"label":866},"About 24.8","The Moon lines up with the Sun twice per 29.53-day month, so spring tides come every 14.77 days. The Moon's 12 h 25 min tide and the Sun's 12 h tide drifting in and out of step give the same answer.",{"id":869,"type":870,"prompt":871},"u-reflect","reflection","A friend says: “There are two high tides a day because one is caused by the Moon and the other by the Sun.” Explain, in your own words and in no more than six sentences, exactly what is wrong with this, and what the correct reason is. Then say what evidence you could point to that would settle it.",{"id":873,"type":874,"title":875,"points":876},"u-cheat-sheet","summary","Cheat sheet: the mechanism, in twelve lines",[877,878,879,880,881,882,883,884,885,886,887,888],"Tides move water **sideways** and it piles up at the coast; nothing is added to the sea.","Gravity fades as 1 ÷ distance², so the Moon pulls the near side of Earth about **3.4% harder** than the centre and the far side about **3.2% weaker**.","**Tidal force** is what is left after subtracting the average pull. Tides come from the *difference*, never from the strength.","Two bulges: the near ocean is pulled ahead of the planet, and the planet is pulled ahead of the far ocean. Nothing is flung anywhere.","Earth turns through the bulges, so most coasts get **two highs and two lows** a day — a semidiurnal tide.","29.53 solar days hold only 28.53 lunar days, so a lunar day is **24 h 50 min**, high waters are **12 h 25 min** apart, and tides slip **50 minutes** later daily.","The Sun's tide is about **46%** of the Moon's, because tidal effect falls off as the **cube** of distance.","In line (new and full moon) → **spring tides**, about 2.7 times the range of the **neap** tides at the quarters. Spring tides repeat every 14.77 days.","The two-bulge model explains the **cause**, not the details. Continents make the real ocean slosh in basins, so every port has its own delay and its own range.","Range depends on place: **funnelling**, **shallowing** and above all **resonance**. Kochi 1 m, Mumbai 4.4 m, Bhavnagar 10 m, Bay of Fundy 16 m.","Tide tables give times and heights above **chart datum**; the **rule of twelfths** (1, 2, 3, 3, 2, 1) fills in the hours between.","The dangerous part of a tide is the **tidal stream**, not the height.",{"id":890,"type":891,"sourceIds":892},"u-sources","sources",[893,894,895,896,897,898,899,900],"tides-noaa-tides-tutorial","tides-noaa-tidal-bulge","tides-noaa-lunar-day","tides-nasa-moon-tides","tides-wikipedia-tide","tides-wikipedia-bay-of-fundy","tides-ncert-water-class7","tides-survey-of-india-tidal",[893,894,895,896,897,898,899,900],"needs_review",{"generatedBy":904,"notes":905},"claude-code","Draft generated locally; pending owner review.","366ad4f6d68a94602fe74be277bf37e9fbe603371f46e96c74dcf6d43ff4746e",{"component:tide-lab@1":908,"logic:practice":909,"component:moon-phase@1":910,"component:sort-game@1":911,"component:match-pairs@1":912,"source:tides-nasa-moon-tides":913,"source:tides-ncert-water-class7":914,"source:tides-noaa-lunar-day":915,"source:tides-noaa-tidal-bulge":916,"source:tides-noaa-tides-tutorial":917,"source:tides-survey-of-india-tidal":918,"source:tides-wikipedia-bay-of-fundy":919,"source:tides-wikipedia-tide":920},"5fef8b331bba35d6df96a31b84dd1f98200bcd0242eeed843d22914391057b6c","3d6b0fe1b15255975a32b0fcd94e8019bc959ad45cbf12e136e86149549c6878","39afeb0bba7518b8118317655457b27214a4a2a315d236762bf1d6a6a40e18f3","b164f45a2c8ca08f26c450768ff0231e113e9fe45381eddb34dc6d0548596c38","2a8ee4ac87460b4e1175a4bb13c96b03d577db06dde95670eb7fcfe4ad787899","d71a4932c5e1df6475bdbf45fedc9a0a348ce79ce9d887d3112d5b033fe39998","f50ce71e2c1996d6835461829618cdcc9eb5d21b86a0aba9d75b36e03b20c886","90612e47010c01b42aceceb78286ac6b8cb3123088fe4436ffec59567fa4c7cd","09f2d02f26eb9e83c057dd8b9f786ebfd77b166de366c91b7dfda4074144fa7a","82683db912324c1f40c9e2f4d4cc0312c637b4af2490f13ca404549ec5e414a0","2e99068442e3818ea49964d49796e478ce8718d4e7d9cb9138f2efc27ba39702","a11570fb567503cb357092d9ba5ad5cc3f29fa50d9094d46c5a4b2435e012a92","0c80de822f7941587e525d4a3ae84aabe44b7c2a5d1851e5885d69db0da1e874",{"state":922,"reviewer":923,"selfReview":323,"reviewedAt":924,"method":925},"approved","The library owner","2026-09-20T10:18:37.581Z","owner_bulk","preview-7e1cbbcc4f",1789899597242]