[{"data":1,"prerenderedAt":1256},["ShallowReactive",2],{"layer:gravity:understand":3},{"layer":4,"contentHash":1236,"dependencyHashes":1237,"approval":1250,"releaseId":1255},{"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":1231,"reviewStatus":1232,"authoring":1233},1,"gravity","en","understand","How gravity works: weight, falling and orbits","Mass against weight, g against speed, drag against gravity — and why an orbit is a permanent miss","Turn the story into rules you can use: weight = mass × g, distance = ½ g t², why mass cancels in free fall, how drag sets terminal velocity, Newton’s universal law in words, and the real reason astronauts float.",[13,14,15,16,17],"Use weight = mass × g in both directions, and keep mass and weight strictly apart.","Read g as both 9.8 N\u002Fkg and 9.8 m\u002Fs², and calculate speeds and distances with v = g t and d = ½ g t².","Explain why mass cancels in free fall, and why a heavier object of the same shape still falls faster in air.","State Newton’s universal law in words and apply the inverse-square rule to distance.","Explain an orbit as falling sideways, and weightlessness as free fall rather than absent gravity.",45,{"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","≈ 45 minutes",{"label":29,"value":30},"Prior knowledge","Discover: what gravity is",{"label":32,"value":33},"Chapters","10",{"label":35,"value":36},"Labs","Drop with air, Newton’s cannon, true\u002Ffalse sort, match",{"label":38,"value":39},"Formulas used","W = m g, v = g t, d = ½ g t²",{"label":41,"value":42},"Big misconception","\"No gravity in space\" — corrected here",[44,48,54,60,63,88,104,109,123,128,131,136,183,188,229,234,237,255,267,282,324,340,354,359,364,367,371,389,402,407,410,414,442,445,494,498,511,516,521,524,569,573,576,620,642,647,650,654,687,698,712,717,720,752,757,761,774,779,782,786,851,854,860,865,870,875,939,974,1035,1195,1216,1220],{"id":45,"type":46,"markdown":47},"u-intro","prose","In **Discover** you met gravity as a story: everything falls, the Moon keeps missing, astronauts float because they are falling. This layer turns that story into **numbers and rules you can use**.\n\nBy the end of it you will be able to work out how long a stone takes to reach the ground, what you would weigh on Mars, why a skydiver stops speeding up, how fast a satellite must travel to stay up, and why \"zero gravity\" is the wrong name for what astronauts feel.\n\nThree ideas do almost all the work:\n\n1. **weight = mass × g** — the pull of a world on a lump of matter.\n2. **Falling speeds up by g every second**, so distance = ½ × g × t².\n3. **Gravity pulls harder between bigger masses and weaker across bigger distances.**\n\nEverything else is a consequence.",{"id":49,"type":50,"variant":51,"title":52,"markdown":53},"u-how-to-read","callout","observation","How to use this lesson","Work the examples with a pencil rather than reading past them — the arithmetic is easy and the habit is what matters.\n\nThroughout, we use **g = 9.8** for Earth. Measured carefully, g is 9.78 N\u002Fkg at the equator and 9.83 at the poles, because the Earth is slightly squashed and spinning. For school work 9.8 is plenty, and 10 is fine for quick estimates.",{"id":55,"type":56,"title":57,"eyebrow":58,"navLabel":59},"u-ch1","chapter","Force, mass and weight, defined properly","Chapter 01","1 The three words",{"id":61,"type":46,"markdown":62},"u-definitions","**Force** is a push or a pull. Its unit is the **newton (N)**.\n\nA newton is defined by what it does to matter: **one newton is the force that makes a mass of one kilogram speed up by one metre per second, every second.** Written compactly, 1 N = 1 kg·m\u002Fs².\n\n**Mass** is the amount of matter in an object, in **kilograms**. Mass does two jobs at once, and it is worth naming both:\n\n- *Gravitational mass*: how strongly gravity pulls on the object.\n- *Inertial mass*: how stubborn the object is — how hard it is to get moving or to stop.\n\nA loaded goods wagon is hard to push on Earth. It would be exactly as hard to push on the Moon, even though it weighs six times less there. Stubbornness does not care about gravity. Keep this in your pocket; it explains the biggest puzzle in Chapter 4.\n\n**Weight** is the gravitational force on a mass, in **newtons**. It is not a property of the object; it is a property of the object *and where it is standing*.",{"id":64,"type":65,"tone":66,"items":67},"u-spec-units","spec","blue",[68,72,76,80,84],{"label":69,"big":70,"value":71},"Mass","kilogram, kg","The amount of matter. Same everywhere in the universe. Measured with a pan balance.",{"label":73,"big":74,"value":75},"Force and weight","newton, N","A push or pull. 1 N = 1 kg·m\u002Fs². Measured with a spring scale or force meter.",{"label":77,"big":78,"value":79},"Strength of gravity","g, in N\u002Fkg","How many newtons pull on each kilogram. On Earth, 9.8 N\u002Fkg.",{"label":81,"big":82,"value":83},"Acceleration","m\u002Fs²","How much the speed changes each second. Free fall on Earth: 9.8 m\u002Fs².",{"label":85,"big":86,"value":87},"Speed","m\u002Fs or km\u002Fh","To convert m\u002Fs into km\u002Fh, multiply by 3.6. So 9.8 m\u002Fs = 35.3 km\u002Fh.",{"id":89,"type":90,"items":91},"u-formulas-core","formulas",[92,95,98,101],{"expression":93,"caption":94},"W = m × g","Weight in newtons = mass in kilograms × the local g in N\u002Fkg.",{"expression":96,"caption":97},"W = 40 × 9.8 = 392 N","A 40 kg child on Earth.",{"expression":99,"caption":100},"m = W ÷ g","Rearranged: a 147 N object on Earth has a mass of 147 ÷ 9.8 = 15 kg.",{"expression":102,"caption":103},"g = W ÷ m","Rearranged: something of mass 5 kg weighing 18.6 N is on a world with g = 3.72.",{"id":105,"type":50,"variant":106,"title":107,"markdown":108},"u-def-newton","definition","What one newton feels like","Hold a **100 gram** object — a small apple, a decent samosa, a bar of soap — in your palm. The downward force on your hand is 0.1 × 9.8 = **0.98 N**, near enough one newton.\n\nThat is why textbooks say \"one newton is about the weight of an apple\". It is a genuinely useful rule of thumb: whenever you calculate a force in newtons, divide by ten to picture how many apples' worth it is.",{"id":110,"type":111,"title":112,"problem":113,"steps":114,"help":121},"u-we-weight-both-ways","worked_example","Reading the weight formula in both directions","A shop's spring balance reads a force of **68.6 N** when a bag of onions hangs from it, in a town where g = 9.8 N\u002Fkg. (a) What is the mass of the onions? (b) What would the same bag read on Mars, where g = 3.72 N\u002Fkg?",[115,116,117,118,119,120],"(a) Start from W = m × g and rearrange to m = W ÷ g.","m = 68.6 ÷ 9.8 = **7 kg**.","(b) The mass does not change on Mars. It is still 7 kg.","W on Mars = 7 × 3.72 = **26.04 N**.","Sense check: Mars pulls about 2.6 times more weakly, and 68.6 ÷ 26.04 ≈ 2.63. ✓","A shopkeeper on Mars using an Earth-calibrated spring balance would see \"2.66 kg\" of onions and be robbed of more than half the bag. A pan balance would still say 7 kg.",{"simplerExplanation":122},"Divide a weight by g to get mass; multiply a mass by g to get weight.",{"id":124,"type":56,"title":125,"eyebrow":126,"navLabel":127},"u-ch2","What g really means","Chapter 02","2 What g means",{"id":129,"type":46,"markdown":130},"u-g-two-readings","The number **9.8** turns up with two different units, and both are correct.\n\n**9.8 newtons per kilogram (N\u002Fkg).** Read this way, g tells you the **pull**: every kilogram of an object is tugged with 9.8 newtons. It is the version you want when you are working out weights.\n\n**9.8 metres per second per second (m\u002Fs²).** Read this way, g tells you the **acceleration**: a freely falling object gains 9.8 metres per second of speed in every second of falling. It is the version you want when you are working out falls.\n\nThese are the same number for a deep reason, which is Chapter 4's business. For now, notice what the second reading actually says. \"Metres per second, per second\" is a rate of change of a speed. After one second of falling the stone is doing 9.8 m\u002Fs; after two, 19.6 m\u002Fs; after three, 29.4 m\u002Fs. The speed is not the thing gravity gives you — the *increase* in speed is.",{"id":132,"type":50,"variant":133,"title":134,"markdown":135},"u-misconception-g-speed","misconception","\"g = 9.8 means things fall at 9.8 metres per second\"","Very nearly the most common slip in this topic.\n\n9.8 is not a speed. It is a **gain in speed each second**. A falling object has no single speed: it has a speed that keeps growing for as long as it falls.\n\nCompare it with a bike. Saying \"I gain 2 km\u002Fh every second\" is completely different from saying \"I travel at 2 km\u002Fh\". A falling stone on Earth gains 9.8 m\u002Fs of speed every second, so after 5 seconds it is doing 49 m\u002Fs — about 176 km\u002Fh.",{"id":137,"type":138,"caption":139,"columns":140,"rows":146},"u-table-g-worlds","table","The strength of gravity at the surface of six worlds, and what it does to a 40 kg child and a 20 m drop",[141,142,143,144,145],"World","g (N\u002Fkg or m\u002Fs²)","Weight of 40 kg","Compared with Earth","Time to fall 20 m",[147,153,159,165,171,177],[148,149,150,151,152],"Pluto","0.62","24.8 N","about 1\u002F16","8.03 s",[154,155,156,157,158],"Moon","1.62","64.8 N","about 1\u002F6","4.97 s",[160,161,162,163,164],"Mars","3.72","148.8 N","about 1\u002F2.6","3.28 s",[166,167,168,169,170],"Earth","9.8","392 N","1 (home)","2.02 s",[172,173,174,175,176],"Jupiter (cloud tops)","24.79","991.6 N","about 2.5 times","1.27 s",[178,179,180,181,182],"Sun (visible surface)","274","10,960 N","about 28 times","0.38 s",{"id":184,"type":50,"variant":185,"title":186,"markdown":187},"u-nuance-g-varies","nuance","Even on Earth, g is not exactly 9.8","Measured carefully, g varies a little from place to place:\n\n- **9.78 N\u002Fkg at the equator**, **9.83 at the poles.** The Earth bulges at the equator, so you are further from the centre there, and the spin also throws you very slightly outward.\n- **On top of Mount Everest** (8,849 m), g falls to about **9.79** — a drop of only **0.28 %**.\n- **In a cruising aeroplane** at 11 km, it is about 9.79 as well.\n\nSo \"gravity is much weaker high up\" is not true for any height a person can reach. You have to go thousands of kilometres out before the change is dramatic.",{"id":189,"type":190,"component":191,"componentVersion":5,"config":192,"objective":222,"textAlternative":223,"help":224},"u-lab-drop-air","interactive","gravity-drop",{"worlds":193,"objects":197,"modes":218,"dropHeightM":221},[194,195,196],"earth","moon","mars",[198,202,206,211,215],{"id":199,"label":200,"massKg":5,"draggy":201},"steel","Steel ball (1 kg)",false,{"id":203,"label":204,"massKg":205,"draggy":201},"tennis","Tennis ball (0.058 kg)",0.058,{"id":207,"label":208,"massKg":209,"draggy":210},"balloon","Air-filled balloon (0.01 kg)",0.01,true,{"id":212,"label":213,"massKg":214,"draggy":210},"paper","Flat sheet of paper (0.005 kg)",0.005,{"id":216,"label":217,"massKg":214,"draggy":201},"crumpled","Crumpled paper (0.005 kg)",[219,220],"drop","weigh",20,"Drop five objects on Earth, the Moon and Mars, and separate what mass does from what air does.","Five objects fall 20 m on a world you choose, with a stopwatch each.\n\n**On Earth (with air):** steel ball, tennis ball and crumpled paper all land around **2.0 s**, despite very different masses. The **flat sheet** and **balloon** drift down over many seconds.\n\n**On the Moon:** all five land together at **4.97 s** — the balloon falls exactly as fast as the steel ball.\n\n**On Mars:** all five land together at **3.28 s** (its thin atmosphere is ignored here).\n\nTwo conclusions: flat vs crumpled paper (identical mass, different fall) shows **shape and air**, not mass, slow a fall; the same object across worlds shows **g** sets the rate.",{"simplerExplanation":225,"hints":226},"Air changes falls. Mass does not. g changes how fast the falling speeds up.",[227,228],"Race the flat paper against the crumpled paper on Earth, then on the Moon.","Switch to weigh mode: the steel ball weighs 9.8 N on Earth, 1.62 N on the Moon, 3.72 N on Mars.",{"id":230,"type":56,"title":231,"eyebrow":232,"navLabel":233},"u-ch3","How far, how fast: the falling rules","Chapter 03","3 How far, how fast",{"id":235,"type":46,"markdown":236},"u-fall-rules","Two short rules describe any fall that starts from rest, as long as air resistance can be ignored.\n\n**Speed after t seconds:  v = g × t**\n\n**Distance fallen in t seconds:  d = ½ × g × t²**\n\nThe first is just the meaning of g: add 9.8 m\u002Fs of speed for each second.\n\nThe second needs a moment's thought. Why the ½, and why t squared? Because the object is *not* travelling at its final speed the whole way — it started at zero and finished at g × t. Its average speed over the fall is halfway between, which is ½ × g × t. Multiply an average speed by the time and you get the distance:\n\ndistance = average speed × time = (½ × g × t) × t = ½ × g × t²\n\nThat is the whole derivation, and it is worth being able to rebuild it rather than memorising it.",{"id":238,"type":90,"items":239},"u-formulas-fall",[240,243,246,249,252],{"expression":241,"caption":242},"v = g × t","Speed after falling for t seconds from rest. On Earth, v = 9.8 t.",{"expression":244,"caption":245},"d = ½ × g × t²","Distance fallen in t seconds from rest. On Earth, d = 4.9 t².",{"expression":247,"caption":248},"t = √(2d ÷ g)","Rearranged: how long a drop of d metres takes.",{"expression":250,"caption":251},"v = √(2 × g × d)","Speed after falling d metres, without needing the time.",{"expression":253,"caption":254},"d = 4.9 t²","The Earth shortcut. t = 1, 2, 3 gives 4.9, 19.6, 44.1 m.",{"id":256,"type":111,"title":257,"problem":258,"steps":259,"help":264},"u-we-fall-3s","How far, and how fast, after three seconds?","A small stone is dropped from a tall cliff. Ignoring air resistance, find its speed and the distance it has fallen after **1 s, 2 s and 3 s** on Earth.",[260,261,262,263],"Speed uses v = g × t: after 1, 2, 3 s that is **9.8**, **19.6**, **29.4 m\u002Fs** — or **35.3**, **70.6**, **105.8 km\u002Fh**.","Distance uses d = ½ × 9.8 × t² = 4.9 t²: after 1, 2, 3 s that is **4.9**, **19.6**, **44.1 m**.","Those distances are in ratio **1 : 4 : 9** — doubling time quadruples distance; tripling it multiplies distance by nine.","Distance *within* each second: 4.9, then 14.7, then 24.5 — ratio **1 : 3 : 5**, Galileo’s odd numbers.",{"simplerExplanation":265,"anotherExample":266},"Speed grows in step with time. Distance grows with time squared, so it runs away much faster.","After 5 s: v = 49 m\u002Fs (176 km\u002Fh), d = 122.5 m, roughly a 40-storey building.",{"id":268,"type":111,"title":269,"problem":270,"steps":271,"help":278},"u-we-fall-time","How long does a drop take?","A coconut falls from a palm tree **11 metres** high. Ignoring air resistance, how long does it take to reach the ground, and how fast is it moving when it arrives?",[272,273,274,275,276,277],"Use d = ½ g t² and rearrange for t: t = √(2d ÷ g).","t = √(2 × 11 ÷ 9.8) = √(22 ÷ 9.8) = √2.245 = **1.50 s**.","Now the landing speed: v = g × t = 9.8 × 1.50 = **14.7 m\u002Fs**.","In km\u002Fh: 14.7 × 3.6 = **about 53 km\u002Fh**.","Check with the other formula: v = √(2 × 9.8 × 11) = √215.6 = 14.68 m\u002Fs. ✓","A one-and-a-half-second fall ending at highway-ish speed. This is why you do not stand under a coconut palm, and why real coconut falls (which do feel a little air resistance) are still dangerous.",{"hints":279},[280,281],"Divide 2 × height by g, then take the square root.","A useful landmark: a 5 m fall takes about 1 s, and a 20 m fall about 2 s.",{"id":283,"type":284,"title":285,"note":286,"scale":287,"rungs":288},"u-ladder-falls","ladder","How long does it take to fall?","Heights on Earth, ignoring air resistance. Notice how slowly the time grows: to double the time you must quadruple the height.","log",[289,293,297,301,305,309,312,316,320],{"label":290,"value":291,"display":292},"Dropped from a table (0.75 m)",0.39,"0.39 s",{"label":294,"value":295,"display":296},"A 30 cm ruler past your fingers",0.247,"0.25 s",{"label":298,"value":299,"display":300},"Dropped from your hand (1 m)",0.45,"0.45 s",{"label":302,"value":303,"display":304},"From a first-floor balcony (5 m)",1.01,"1.01 s",{"label":306,"value":307,"display":308},"From a coconut palm (11 m)",1.5,"1.50 s",{"label":310,"value":311,"display":170},"From a 20 m rooftop",2.02,{"label":313,"value":314,"display":315},"From the top of the Pisa tower (55 m)",3.35,"3.35 s",{"label":317,"value":318,"display":319},"From the Qutub Minar (73 m)",3.86,"3.86 s",{"label":321,"value":322,"display":323},"From a 3,000 m skydive",24.74,"24.7 s (no air)",{"id":325,"type":326,"itemId":327,"prompt":328,"check":329,"hints":334,"feedback":337},"u-practice-fall-45m","practice","gravity.understand-fall-45m","A ball is dropped from a window and falls freely for **3 seconds**. How far, in metres, has it fallen? Use g = 9.8 m\u002Fs² and ignore air resistance.",{"kind":330,"answer":331,"tolerance":332,"unit":333},"number",44.1,0.2,"m",[335,336],"Use d = ½ × g × t².","½ × 9.8 = 4.9, and t² = 9.",{"correct":338,"incorrect":339},"Correct: d = 4.9 × 3² = 4.9 × 9 = **44.1 m**. That is roughly a fifteen-storey building.","Use d = ½ × 9.8 × t². With t = 3, t² = 9, so d = 4.9 × 9 = 44.1 m. (29.4 is the *speed* in m\u002Fs after 3 s, not the distance.)",{"id":341,"type":326,"itemId":342,"prompt":343,"check":344,"hints":348,"feedback":351},"u-practice-fall-speed-2s","gravity.understand-speed-2s","A stone falls freely for **2 seconds**. What is its speed, in metres per second, at that moment? (g = 9.8 m\u002Fs²)",{"kind":330,"answer":345,"tolerance":346,"unit":347},19.6,0.1,"m\u002Fs",[349,350],"Use v = g × t.","Each second of falling adds 9.8 m\u002Fs.",{"correct":352,"incorrect":353},"Correct: v = 9.8 × 2 = **19.6 m\u002Fs**, which is about 70.6 km\u002Fh.","Multiply g by the time: 9.8 × 2 = 19.6 m\u002Fs. (19.6 m is also the distance fallen, which is a coincidence that only happens at t = 2 s.)",{"id":355,"type":50,"variant":356,"title":357,"markdown":358},"u-aha-coincidence","aha","A coincidence worth spotting","At exactly **t = 2 seconds**, a freely falling object has fallen **19.6 metres** and is moving at **19.6 metres per second**. The two numbers match.\n\nIt is nothing deep — it happens because ½ × 9.8 × 2² and 9.8 × 2 both come to 19.6 — but it catches out a lot of people in exams, who then assume distance and speed are always the same number. At t = 3 s the distance is 44.1 m and the speed is 29.4 m\u002Fs. They part company immediately.",{"id":360,"type":56,"title":361,"eyebrow":362,"navLabel":363},"u-ch4","Why heavy things do not fall faster","Chapter 04","4 Why mass cancels",{"id":365,"type":46,"markdown":366},"u-why-mass-cancels","Here is the puzzle stated properly.\n\nA 10 kg rock is pulled by the Earth with ten times the force of a 1 kg rock: 98 N against 9.8 N. Ten times the pull. So surely it must fall faster?\n\nNo — and the reason is the second job mass does.\n\nThe 10 kg rock also has **ten times the inertia**. It is ten times harder to get moving. So it receives ten times the push *and* needs ten times as much push to produce the same result.\n\nThe two tens cancel exactly. Written out:\n\n**acceleration = force ÷ mass = (m × g) ÷ m = g**\n\nThe mass appears on the top and on the bottom of the fraction and vanishes. Whatever number you put in, the answer is g. A grain of sand, a cricket ball, an elephant and a lorry all accelerate downwards at exactly 9.8 m\u002Fs².\n\nThis is the deep reason a hammer and a feather land together on the Moon. It is not a coincidence, and it is not about the air. It is because the quantity that makes gravity pull on you is the very same quantity that makes you hard to move.",{"id":368,"type":50,"variant":356,"title":369,"markdown":370},"u-aha-equivalence","The same number twice, and nobody knows why","Gravitational mass (how hard gravity pulls you) and inertial mass (how hard you are to shove) are measured in completely different experiments. There is no obvious reason for them to be the same number.\n\nYet every experiment ever done says they are, to an astonishing precision — better than one part in a hundred trillion in modern tests using satellites.\n\nNewton noticed the coincidence and could not explain it. Two and a half centuries later Einstein took it as a *clue* rather than a coincidence, and built general relativity on it. It is called the **equivalence principle**, and you will meet it again in **Extend**.",{"id":372,"type":373,"prompt":374,"options":375,"explanation":388},"u-predict-two-stones","prediction","Two stones are dropped together in a vacuum: one of 1 kg and one of 10 kg. Which statement is true?",[376,379,382,385],{"id":377,"label":378},"a","The 10 kg stone is pulled with ten times the force and lands first",{"id":380,"label":381},"b","Both are pulled with the same force, so both land together",{"id":383,"label":384},"c","The 10 kg stone is pulled ten times harder but is also ten times harder to move, so they land together",{"id":386,"label":387},"d","The 1 kg stone lands first, being easier to move","**(c) is the right reasoning.** Option (b) has the right answer for the wrong reason — the forces are definitely *not* equal: the 10 kg stone is pulled with 98 N and the 1 kg stone with 9.8 N.\n\nWhat makes the fall identical is that acceleration = force ÷ mass. Ten times the force divided by ten times the mass gives the same acceleration, 9.8 m\u002Fs².\n\nGetting this right matters, because the wrong reason (\"gravity pulls everything equally\") breaks the moment you meet a problem about forces rather than falling.",{"id":390,"type":111,"title":391,"problem":392,"steps":393,"help":400},"u-we-acceleration","Proving mass cancels, with numbers","Work out the downward acceleration of (a) a 0.16 kg cricket ball and (b) a 3,000 kg elephant, on Earth, with no air resistance.",[394,395,396,397,398,399],"Weight of the cricket ball: W = 0.16 × 9.8 = **1.568 N**.","Its acceleration: a = W ÷ m = 1.568 ÷ 0.16 = **9.8 m\u002Fs²**.","Weight of the elephant: W = 3,000 × 9.8 = **29,400 N**.","Its acceleration: a = W ÷ m = 29,400 ÷ 3,000 = **9.8 m\u002Fs²**.","The elephant is pulled with about **18,750 times** more force than the ball (29,400 ÷ 1.568), and is 18,750 times harder to move. Identical acceleration.","General case: a = (m × g) ÷ m = g, for any m at all. The mass never gets a chance to matter.",{"simplerExplanation":401},"More mass gets more pull, but needs more pull. The two effects cancel perfectly.",{"id":403,"type":56,"title":404,"eyebrow":405,"navLabel":406},"u-ch5","Air resistance, terminal velocity and parachutes","Chapter 05","5 Air and drag",{"id":408,"type":46,"markdown":409},"u-drag-detail","Real falls happen in air, and air is not nothing.\n\n**Air resistance (drag)** is the backwards push of air on anything moving through it. Three things control how big it is:\n\n- **Speed.** Drag grows roughly with the *square* of the speed at everyday sizes: go twice as fast and the air pushes back about four times as hard. This is the key to the whole chapter.\n- **Frontal area.** How much air you have to shove aside. A flat sheet of paper has a huge frontal area for its mass; the same paper crumpled has a tiny one.\n- **Shape.** A smooth, tapering shape lets air close in behind it; a flat, blunt one leaves a churning wake that drags it back.\n\nNow watch what those three do to a fall. At the start, speed is zero, so drag is zero, and the object accelerates at the full 9.8 m\u002Fs². As it speeds up, drag grows rapidly. The **net** downward force (weight minus drag) shrinks, so the acceleration shrinks. Eventually drag grows all the way up to equal the weight. Net force zero. Acceleration zero. **The speed stops changing.**",{"id":411,"type":50,"variant":106,"title":412,"markdown":413},"u-def-terminal","Terminal velocity","**Terminal velocity** is the steady speed a falling object reaches when air resistance has grown to exactly equal its weight.\n\nAt terminal velocity the two forces are balanced, so there is no net force and no further acceleration. The object keeps falling — but at a constant speed, all the way to the ground.\n\nIt is not a maximum imposed by gravity. It is a balance point, and it is different for every object.",{"id":415,"type":416,"title":417,"items":418},"u-steps-forces-fall","steps","One fall, second by second, as a balance of two forces",[419,423,427,431,434,438],{"title":420,"tag":421,"text":422},"Release","v = 0","Drag is zero because speed is zero. Net force = full weight. Acceleration = 9.8 m\u002Fs².",{"title":424,"tag":425,"text":426},"Speeding up","drag growing","Drag rises with the square of speed. Net force shrinks, so acceleration shrinks, but speed still rises.",{"title":428,"tag":429,"text":430},"Half-way there","drag = ½ weight","Net force is half the weight, so acceleration is about 4.9 m\u002Fs². Still gaining, more slowly.",{"title":412,"tag":432,"text":433},"drag = weight","Forces balanced. Net force zero. Speed now constant for the rest of the fall.",{"title":435,"tag":436,"text":437},"Parachute opens","area jumps","Drag leaps far above the weight. Net force is now *upwards*, so the skydiver slows down sharply.",{"title":439,"tag":440,"text":441},"New balance","drag = weight again","At about 5.5 m\u002Fs the big canopy makes drag equal the weight once more. Steady, survivable descent.",{"id":443,"type":46,"markdown":444},"u-why-heavy-wins","This finally explains, properly, the thing that fooled everybody for two thousand years.\n\nTwo objects of the **same shape and size** but different mass — say a hollow plastic ball and a solid steel ball of identical diameter — meet exactly the same drag at any given speed. But the steel ball has far more weight for the drag to balance, so it has to go much faster before the two match. Its terminal velocity is much higher.\n\nSo in air, **the heavier of two identically shaped objects really does fall faster** — not because gravity accelerates it more, but because it takes more drag to stop it accelerating.\n\nAristotle was not blind. He was generalising from a world full of air, and he never took the air away. Galileo's leap was to ask what would happen **without** the air, and to design experiments that got the air out of the way.",{"id":446,"type":138,"caption":447,"columns":448,"rows":453},"u-table-terminal-detail","Terminal velocity: the speed where drag finally equals weight (approximate measured values)",[449,450,451,452],"Falling object","Terminal speed","In km\u002Fh","What sets it",[454,459,464,469,474,479,484,489],[455,456,457,458],"Skydiver, belly to earth","≈ 55 m\u002Fs","≈ 200 km\u002Fh","Heavy, wide, blunt — a big area for the drag to work on",[460,461,462,463],"Skydiver, head-down","≈ 90 m\u002Fs","≈ 320 km\u002Fh","Same weight, much smaller area, so a higher balance point",[465,466,467,468],"Under an open parachute","≈ 5.5 m\u002Fs","≈ 20 km\u002Fh","Enormous area: drag matches weight at walking pace",[470,471,472,473],"Hailstone, 2 cm","≈ 20 m\u002Fs","≈ 70 km\u002Fh","Dense ice in a compact ball",[475,476,477,478],"Raindrop, 2 mm","≈ 6.5 m\u002Fs","≈ 23 km\u002Fh","Small mass, and drag catches up with it almost immediately",[480,481,482,483],"Drizzle drop, 0.5 mm","≈ 2 m\u002Fs","≈ 7 km\u002Fh","Smaller still: area falls more slowly than mass does",[485,486,487,488],"Mist droplet","≈ 0.03 m\u002Fs","≈ 0.1 km\u002Fh","Effectively floating; it can hang in the air for hours",[490,491,492,493],"A single sheet of A4 paper","≈ 1 m\u002Fs","≈ 4 km\u002Fh","Almost no weight spread over a very large area",{"id":495,"type":50,"variant":356,"title":496,"markdown":497},"u-aha-rain","Why the monsoon is survivable","A cloud sits about 2 to 3 km above the ground. If raindrops simply accelerated the whole way down with no air in the way, they would arrive at about **242 metres per second** — roughly **873 km\u002Fh**, faster than an airliner.\n\nDrag saves us. A 2 mm raindrop reaches its terminal velocity of about 6.5 m\u002Fs within the first few metres of its fall and then comes down at a steady 23 km\u002Fh, whether it fell from 2 km or 10 km up.\n\nThe same physics means a hailstone, being far denser and more compact, arrives at about 70 km\u002Fh — which is exactly why hail dents cars and rain does not.",{"id":499,"type":373,"prompt":500,"options":501,"explanation":510},"u-predict-parachute-weight","Two skydivers jump together with identical parachutes. One, with all her gear, has a mass of 60 kg; the other has a mass of 90 kg. Both open their canopies at the same moment. What happens?",[502,504,506,508],{"id":377,"label":503},"They descend at exactly the same speed — the canopies are identical",{"id":380,"label":505},"The heavier one descends faster",{"id":383,"label":507},"The lighter one descends faster",{"id":386,"label":509},"The heavier one descends faster only until the canopies fill","**The heavier one descends faster.** Identical canopies give identical drag at any given speed, but the 90 kg jumper has 50 % more weight for that drag to balance. So the balance point — the terminal velocity — is higher for her.\n\nThis is the same reasoning as the steel ball versus the plastic ball, and it is why parachute canopies come in different sizes: a heavier jumper needs more area to land at the same gentle speed.\n\nNote that **(a)** confuses \"equal drag at equal speed\" with \"equal terminal speed\". The canopies are equal; the loads are not.",{"id":512,"type":50,"variant":513,"title":514,"markdown":515},"u-model-limit-drag","model_limit","What \"drag grows with speed squared\" leaves out","The neat rule that drag is proportional to speed squared is a good everyday approximation, not a law.\n\nFor very small, very slow things — mist droplets, dust, bacteria in water — drag is proportional to speed itself, not its square. For objects moving near or above the speed of sound, the rules change again and shock waves appear.\n\nReal drag also depends on how rough a surface is, whether the object tumbles, and how the air swirls behind it. Golf balls have dimples precisely because a slightly *rougher* surface can reduce drag, which the simple rule cannot explain at all.\n\nEverything in this chapter is true for skydivers, raindrops and dropped balls. Do not expect it to size a parachute for a spacecraft.",{"id":517,"type":56,"title":518,"eyebrow":519,"navLabel":520},"u-ch6","Newton, the apple, and the universal law","Chapter 06","6 Newton’s law",{"id":522,"type":46,"markdown":523},"u-newton-apple","**Isaac Newton** was born in 1642 in Woolsthorpe, England. When plague closed his university in 1665–66, he went home and spent two years thinking — later calling them his years of greatest invention.\n\nThe apple story is real, but not as usually told. **What almost certainly did not happen:** an apple landing on Newton's head, and him instantly shouting \"gravity!\"\n\n**What Newton himself described**, in a 1752 account by his friend **William Stukeley**: an apple fell in the Woolsthorpe orchard, setting him wondering *why* it always fell straight down — and then, the actual leap, **how far up that pull goes**. To the treetop? The clouds? All the way to the Moon?\n\nThat question, not the apple, is the discovery: nobody before had supposed the force dropping fruit and the force steering the heavens might be the **same force**.\n\nNewton then calculated: if the pull weakens with distance in a particular way, he could predict how fast the Moon should be falling, and compare it with how fast it *is* falling. It matched. Twenty years later he published it all in the **Principia** (1687).",{"id":525,"type":526,"title":527,"items":528},"u-timeline-idea","timeline","How the idea of gravity was built",[529,533,537,541,545,549,553,557,561,565],{"time":530,"title":531,"text":532},"c. 350 BCE","Aristotle","Heavy things fall faster, and heavenly bodies obey entirely different rules from earthly ones. Believed for nearly 2,000 years.",{"time":534,"title":535,"text":536},"499 CE","Aryabhata","In the Aryabhatiya, argues that the Earth is a rotating sphere and that objects on it stay put rather than flying off.",{"time":538,"title":539,"text":540},"628 CE","Brahmagupta","Writes in the Brahmasphutasiddhanta that it is in the nature of the Earth to attract things towards itself, as it is the nature of water to flow.",{"time":542,"title":543,"text":544},"1150","Bhaskara II","In the Siddhanta Shiromani, describes an attractive power of the Earth that draws objects towards it.",{"time":546,"title":547,"text":548},"1604","Galileo","Working with ramps, finds that falling distance grows with the square of the time, and that mass does not change the rate.",{"time":550,"title":551,"text":552},"1609-19","Kepler","Three laws describing how planets actually move around the Sun: ellipses, and periods tied to distance.",{"time":554,"title":555,"text":556},"1687","Newton","The Principia. One law of universal gravitation explains falling apples, the Moon, the planets and the tides together.",{"time":558,"title":559,"text":560},"1798","Cavendish","Measures the tiny attraction between lead balls in a laboratory, and so finds how strong gravity really is.",{"time":562,"title":563,"text":564},"1915","Einstein","General relativity: gravity reinterpreted as the curving of space and time by mass.",{"time":566,"title":567,"text":568},"2015","LIGO","The first direct detection of gravitational waves, from two black holes merging over a billion years ago.",{"id":570,"type":50,"variant":185,"title":571,"markdown":572},"u-nuance-india","Earlier ideas from India, fairly stated","Long before Newton, Indian astronomers wrote about attraction towards the Earth.\n\n**Brahmagupta**, around 628 CE in the *Brahmasphutasiddhanta*, wrote that bodies fall towards the Earth because it is in the nature of the Earth to attract bodies, just as it is in the nature of water to flow. **Bhaskara II** (1150) described a similar attractive power, and **Aryabhata** (499 CE) argued that a rotating Earth would not fling things off.\n\nThese are genuine, important insights, and they deserve to be taught. It is also fair to say what they were not: none of them gave a **quantitative law** — a formula relating force to the two masses and to the square of the distance — or used it to calculate the Moon's motion. Newton's contribution was to make the idea calculable and testable.\n\nBoth things can be true. The idea of attraction was reached in more than one place; the mathematics of it was completed in one.",{"id":574,"type":46,"markdown":575},"u-universal-law","Newton's **law of universal gravitation**, in words:\n\n**Every object in the universe attracts every other object, with a force that grows in proportion to each of their masses and shrinks in proportion to the square of the distance between their centres.**\n\nThree things are packed in. **Every object** — not planets only, every pair of masses, always. **Grows with each mass** — double one mass and the force doubles; double both and it quadruples, why Earth's pull dominates your life but the building next door's does not. **Shrinks with distance squared** — double the distance and the force is not halved but **one quarter**; triple it and it is one **ninth**.\n\nMeasured from the Earth's **centre**, not its surface: at 6,371 km, g is 9.8; twice as far out, g drops to 9.8 ÷ 4 = **2.45**. The formula and the symbol G wait in **Go deeper**.",{"id":577,"type":138,"caption":578,"columns":579,"rows":584},"u-table-inverse-square","How the pull fades with distance from the Earth’s centre",[580,581,582,583],"Distance from centre","How far up","g there","Fraction of surface g",[585,590,595,600,605,610,615],[586,587,588,589],"1 Earth radius (6,371 km)","on the ground","9.8 N\u002Fkg","1",[591,592,593,594],"1.06 radii","ISS, about 400 km up","8.7 N\u002Fkg","about 89 %",[596,597,598,599],"2 radii","about 6,371 km up","2.45 N\u002Fkg","one quarter",[601,602,603,604],"3 radii","about 12,700 km up","1.09 N\u002Fkg","one ninth",[606,607,608,609],"4 radii","about 19,100 km up","0.61 N\u002Fkg","one sixteenth",[611,612,613,614],"6.6 radii","geostationary, 35,786 km up","0.22 N\u002Fkg","about 1\u002F44",[616,617,618,619],"60.3 radii","the Moon, 384,400 km away","0.0027 N\u002Fkg","about 1\u002F3,640",{"id":621,"type":326,"itemId":622,"prompt":623,"check":624,"hints":636,"feedback":639},"u-practice-inverse-square","gravity.understand-inverse-square","A satellite is moved from a distance of 2 Earth-radii from the centre out to 4 Earth-radii. What happens to the gravitational force on it?",{"kind":625,"options":626,"correct":635},"choice",[627,629,631,633],{"id":377,"label":628},"It halves",{"id":380,"label":630},"It becomes one quarter",{"id":383,"label":632},"It becomes one eighth",{"id":386,"label":634},"It stays the same",[380],[637,638],"The distance doubled. The law involves the *square* of the distance.","2 squared is 4.",{"correct":640,"incorrect":641},"Right: doubling the distance divides the force by 2² = 4, so it becomes **one quarter**.","Distance doubled from 2 radii to 4 radii. Because the force depends on 1 ÷ distance², the force falls by a factor of 2² = 4 — to one quarter, not one half.",{"id":643,"type":56,"title":644,"eyebrow":645,"navLabel":646},"u-ch7","Orbits: falling sideways fast enough","Chapter 07","7 Orbits",{"id":648,"type":46,"markdown":649},"u-orbit-explained","Newton's cannon, done properly.\n\nPut a cannon on a mountain so tall it pokes above the air, and fire horizontally. The ball leaves at some sideways speed and immediately falls at 9.8 m\u002Fs², exactly like a dropped stone. Two motions happen at once and do not interfere: steady sideways speed, and ever-faster falling.\n\nThe result is a curve — fire faster and it is longer and flatter, but the ball falls at the same rate throughout.\n\nThe Earth is round, so its surface curves away from any straight line at a fixed rate: go **8 kilometres** and the ground has dropped roughly **5 metres** below where you started.\n\nBut 5 metres is exactly how far you fall in one second! So a ball travelling 8 km sideways per second sees the ground fall away just as fast as it does — the gap never closes, and it falls forever without landing.\n\nThat speed — about **7.9 km\u002Fs**, or 28,400 km\u002Fh — is the **orbital speed** just above Earth's surface. Slower, you land. Faster, you swing into a stretched oval. At about **11.2 km\u002Fs** the ball never comes back: **escape velocity**.",{"id":651,"type":50,"variant":106,"title":652,"markdown":653},"u-def-orbit","Orbit, orbital speed and escape velocity","**Orbit** — the closed path of an object that is falling towards a world while moving sideways fast enough to keep missing it.\n\n**Orbital speed** — the sideways speed needed for that to happen. Just above Earth's surface it is about **7.9 km\u002Fs**; at the ISS's altitude it is about **7.7 km\u002Fs**; the further out you go, the *slower* you need to travel.\n\n**Escape velocity** — the speed at which an object leaves for good and never returns. From Earth's surface it is about **11.2 km\u002Fs**, which is exactly √2 (about 1.414) times the orbital speed.",{"id":655,"type":190,"component":656,"componentVersion":5,"config":657,"objective":680,"textAlternative":681,"help":682},"u-lab-cannon","orbit-lab",{"speedKmS":658,"presets":662,"showMoon":210},{"min":659,"max":660,"initial":661},2,14,7.9,[663,666,668,671,674,677],{"label":664,"speedKmS":665},"Sub-orbital: comes down",5,{"label":667,"speedKmS":661},"Circular orbit: 7.9 km\u002Fs",{"label":669,"speedKmS":670},"ISS altitude: 7.7 km\u002Fs",7.7,{"label":672,"speedKmS":673},"Oval orbit: 9.5 km\u002Fs",9.5,{"label":675,"speedKmS":676},"Escape: 11.2 km\u002Fs",11.2,{"label":678,"speedKmS":679},"Straight out: 13 km\u002Fs",13,"Find the three thresholds: the speed that lands, the speed that circles, and the speed that never comes back.","Newton's cannon fires horizontally above the atmosphere. A slider sets speed from 2 to 14 km\u002Fs, with the Moon's orbit drawn for scale.\n\n**5 km\u002Fs** — a long arc, then impact: sub-orbital, like a sounding rocket.\n\n**7.9 km\u002Fs** — closes into a circle just above the surface: orbit, never landing.\n\n**7.7 km\u002Fs** — a circle at 400 km, the ISS's orbit. The *higher* orbit needs the *slower* speed.\n\n**9.5 km\u002Fs** — stretches into an ellipse: races out, slows, turns, rushes back past the cannon.\n\n**11.2 km\u002Fs** — never closes: escape velocity, leaving the Earth system.\n\n**13 km\u002Fs** — barely bent at all, heading for interplanetary space.\n\nSame gravity throughout — only the sideways speed changed.",{"simplerExplanation":683,"hints":684},"Slow: you land. Just right: you circle. Fast: you leave.",[685,686],"Look for the slowest speed at which the ball never touches the ground.","Try 7.9 and then 11.2, and note the ratio: 11.2 ÷ 7.9 ≈ 1.41, which is the square root of 2.",{"id":688,"type":111,"title":689,"problem":690,"steps":691,"help":696},"u-we-8km-5m","Why 8 kilometres and 5 metres is the magic pair","Show that an object moving horizontally at about 8 km per second above a smooth Earth never gets any closer to the ground. Earth's radius is 6,371 km.",[692,693,694,695],"In **one second**, a dropped object falls d = ½ × 9.8 × 1² = **4.9 m** — call it about 5 m.","The round Earth curves away by about d²\u002F(2R) over a horizontal distance d, with R its radius: 8,000² ÷ (2 × 6,371,000) = **5.02 m**.","The two drops match — over 8 km, in one second, both the object and the ground drop about 5 m — so height above ground is unchanged. Repeat every second: that is an orbit.","The exact circular speed at the surface is **7.91 km\u002Fs**; 8 km\u002Fs was a good round-number approximation.",{"simplerExplanation":697},"Fall 5 m while travelling 8 km sideways, and the curved Earth has dropped 5 m too. You never get closer.",{"id":699,"type":326,"itemId":700,"prompt":701,"check":702,"hints":706,"feedback":709},"u-practice-escape-ratio","gravity.understand-escape-ratio","A world's circular orbital speed just above its surface is **2 km\u002Fs**. Escape velocity is always √2 times bigger. What is the escape velocity from that world, in km\u002Fs? Give your answer to two decimal places.",{"kind":330,"answer":703,"tolerance":704,"unit":705},2.83,0.02,"km\u002Fs",[707,708],"√2 is about 1.4142.","2 × 1.4142.",{"correct":710,"incorrect":711},"Correct: 2 × 1.4142 = **2.83 km\u002Fs**. The same ratio holds everywhere: Earth’s 7.91 km\u002Fs orbital speed gives 11.2 km\u002Fs escape velocity.","Multiply the orbital speed by √2 ≈ 1.4142: 2 × 1.4142 = 2.83 km\u002Fs.",{"id":713,"type":56,"title":714,"eyebrow":715,"navLabel":716},"u-ch8","Satellites: two very useful heights","Chapter 08","8 Satellites",{"id":718,"type":46,"markdown":719},"u-satellites","A satellite is simply something put into orbit on purpose. India has done this since **Aryabhata**, its first satellite, in 1975; ISRO's **PSLV** and **LVM3** rockets now launch payloads from Sriharikota for India and customers worldwide.\n\nWhere you put a satellite depends on the job, and two heights matter most.\n\n**Low Earth orbit, a few hundred km up.** The ISS sits at about **400 km**, needing about **7.7 km\u002Fs** (≈27,600 km\u002Fh) for a circular orbit, with one lap taking about **92 minutes** — a sunrise roughly every 90 minutes, about **16 times a day**. Earth-observation and weather satellites live here too, close enough to see detail.\n\n**Geostationary orbit, 35,786 km up.** Further out, orbits get slower. At exactly **35,786 km above the equator**, one lap takes **23 hours 56 minutes** — exactly Earth's spin — so the satellite keeps pace with the ground and appears to **hang motionless**.\n\nThat is why a dish antenna is bolted in place, aimed once at a satellite that never wanders.",{"id":721,"type":65,"tone":722,"items":723},"u-spec-orbits","copper",[724,728,732,736,740,744,748],{"label":725,"big":726,"value":727},"ISS altitude","≈ 400 km","Low Earth orbit. Gravity there is about 8.7 N\u002Fkg, roughly 89 % of ground level.",{"label":729,"big":730,"value":731},"ISS speed","≈ 7.7 km\u002Fs","About 27,600 km\u002Fh. One lap of the planet in about 92 minutes.",{"label":733,"big":734,"value":735},"Sunrises a day","≈ 16","24 hours divided by 92 minutes gives about 15.6 orbits per day.",{"label":737,"big":738,"value":739},"Geostationary","35,786 km","Above the equator only. One lap in 23 h 56 min, matching Earth’s spin.",{"label":741,"big":742,"value":743},"Geostationary speed","≈ 3.07 km\u002Fs","Much slower than the ISS, because it is much further out.",{"label":745,"big":746,"value":747},"Orbital speed at ground","≈ 7.91 km\u002Fs","The theoretical speed to circle a smooth, airless Earth at sea level.",{"label":749,"big":750,"value":751},"Escape velocity","≈ 11.2 km\u002Fs","About 40,300 km\u002Fh. The speed to leave Earth and never return.",{"id":753,"type":50,"variant":754,"title":755,"markdown":756},"u-example-isro","example","Why India’s communication satellites sit over the equator","ISRO's communication satellites — the GSAT series and the older INSAT family — are placed in geostationary orbit, about 35,786 km above the equator, roughly over the longitudes of the Indian Ocean.\n\nFrom that height a single satellite can see almost half the planet at once, and because it never appears to move, a receiving dish in Leh and a receiving dish in Kanyakumari can both be aimed once and then left alone for years.\n\nThe cost is distance. A signal has to travel 35,786 km up and 35,786 km back down, which takes about a quarter of a second — the small delay you sometimes hear on a satellite phone call or a live broadcast from a distant place. Low-orbit satellites have no such delay, but they whip past overhead in minutes, so you need a whole swarm of them and a dish that can track.",{"id":758,"type":50,"variant":185,"title":759,"markdown":760},"u-nuance-higher-slower","Higher orbits are slower, not faster","It surprises most people. The ISS, at 400 km, races round at 7.7 km\u002Fs. A geostationary satellite, ninety times higher, ambles at 3.07 km\u002Fs. The Moon, far beyond that, does barely 1 km\u002Fs.\n\nThe reason is the inverse-square law. Further out, gravity is weaker, so less sideways speed is needed to be bent into a circle. The path is also much longer, so a slower satellite takes far longer to get round: 92 minutes for the ISS, 24 hours for geostationary, 27.3 days for the Moon.\n\nThere is a catch that trips up beginners: to *get* to a higher orbit you must fire your engines and add energy, even though you will end up moving more slowly once you are there.",{"id":762,"type":326,"itemId":763,"prompt":764,"check":765,"hints":768,"feedback":771},"u-practice-orbits-per-day","gravity.understand-orbits-per-day","The ISS takes about **90 minutes** to circle the Earth once. Roughly how many complete orbits does it make in a 24-hour day?",{"kind":330,"answer":766,"tolerance":767},16,0.5,[769,770],"How many minutes are there in 24 hours?","1,440 ÷ 90.",{"correct":772,"incorrect":773},"Correct: 24 × 60 = 1,440 minutes, and 1,440 ÷ 90 = **16 orbits**. (Using the more precise 92.4 minutes gives 15.6 orbits, which is why NASA says \"about 16 sunrises a day\".)","There are 24 × 60 = 1,440 minutes in a day. Divide by 90 minutes per orbit: 1,440 ÷ 90 = 16.",{"id":775,"type":56,"title":776,"eyebrow":777,"navLabel":778},"u-ch9","Weightlessness, done properly","Chapter 09","9 Weightlessness",{"id":780,"type":46,"markdown":781},"u-weightless-proper","This is the chapter to get right, because almost every popular account gets it wrong.\n\nAstronauts aboard the ISS are **not** beyond gravity. At 400 km, gravity is about **8.7 N\u002Fkg**, roughly **89 %** of ground strength. A 70 kg astronaut is pulled with about **608 N** up there, against 686 N at home. The Earth has barely let go.\n\nSo why do they float? Because **weight is not what you feel** — what you feel is the *floor pushing back*. Gravity pulls you down, the chair pushes up, and it is the chair's push you experience as heaviness. Remove the chair and you feel nothing while falling, the same odd stomach-drop as a lift starting down.\n\nOn the ISS, the station and everything inside it — astronaut, floor, water, pen — are all in free fall together. Nothing presses on anything. It is that lift-starting-down moment, stretched out for months.\n\nThe correct name is **free fall**; the right word for the environment is **microgravity** — tiny residual effects, not an absence of gravity.",{"id":783,"type":50,"variant":133,"title":784,"markdown":785},"u-misconception-zero-g","\"Astronauts float because there is no gravity up there\"","Wrong in two separate ways.\n\n**First**, there is plenty of gravity at 400 km — about 89 % of what you feel now. If gravity really stopped there, the station would not orbit; it would fly off in a straight line and be gone.\n\n**Second**, floating is not caused by an absence of gravity anywhere. It is caused by everything falling **together**. The same effect happens in an aircraft flying a careful parabola (NASA's training aircraft gives about 20 seconds of it), in a drop tower, and in your own body for the fraction of a second you are in the air after a jump.\n\nThe single sentence to remember: **they float because they are falling, not because gravity has stopped.**",{"id":787,"type":788,"title":789,"prompt":790,"options":791},"u-explorer-weightless","explorer","Four ways to be weightless, and one way not to be","Pick a situation and see whether the people inside float, and why.",[792,805,816,827,838],{"id":793,"label":794,"chain":795,"badge":801,"note":804},"iss","The space station",[796,797,798,799,800],"Gravity 8.7 N\u002Fkg","Station falls","Crew falls too","Nothing pushes","They float",{"text":802,"tone":803},"Floating: free fall","yes","At 400 km, gravity is about 89 % of ground strength. Moving sideways at 7.7 km\u002Fs turns that fall into an orbit, and because station and crew fall at exactly the same rate, nothing presses on anything. Months of this is why bones and muscles weaken.",{"id":806,"label":807,"chain":808,"badge":814,"note":815},"parabola","A parabolic flight",[809,810,811,812,813],"Aircraft climbs steeply","Pushes over the top","Falls on a curve","Cabin falls with you","20 seconds floating",{"text":802,"tone":803},"A large aircraft flies a carefully shaped falling arc. For about 20 seconds everyone inside floats, before the pilot pulls out. Astronauts train this way, since it is far cheaper than a rocket launch for a few seconds of microgravity.",{"id":817,"label":818,"chain":819,"badge":825,"note":826},"lift","A falling lift",[820,821,822,823,824],"Cable cut (in theory)","Lift falls at g","You fall at g","Floor does not push","You float inside",{"text":802,"tone":803},"Einstein's favourite thought experiment: a freely falling lift's occupants would float, unable to tell the difference from deep space far from any star. This is the equivalence principle, the seed of general relativity. (Purely imaginary — real lifts have independent brakes.)",{"id":828,"label":829,"chain":830,"badge":836,"note":837},"jump","Jumping off the floor",[831,832,833,834,835],"Push off hard","Leave the ground","Only gravity acts","Nothing pushes you","Weightless briefly",{"text":802,"tone":803},"From leaving the floor to landing, you are in genuine free fall — for perhaps half a second, too brief to notice. Drop towers stretch the same effect to a few seconds inside a tall evacuated shaft.",{"id":839,"label":840,"chain":841,"badge":847,"note":850},"plane","A normal flight",[842,843,844,845,846],"Wings push air down","Air pushes wings up","Lift balances weight","Seat pushes you","You feel normal",{"text":848,"tone":849},"Not floating","no","At 11 km, gravity is still about 9.79 N\u002Fkg. The aircraft is not falling: wings generate lift balancing its weight, so your seat pushes on you normally. Height alone never causes weightlessness; falling does.",{"id":852,"type":46,"markdown":853},"u-body-effects","Months of free fall have real effects on a human body, because our bodies quietly depend on being pulled.\n\n- **Bone.** Weight-bearing bones — hip, spine, thigh — lose roughly **1 % of their mineral per month**, since bone rebuilds itself in response to load, and there is none. Close to **6 %** over six months.\n- **Muscle.** Postural leg and back muscles, unemployed without gravity to hold you upright, shrink.\n- **Fluid shift.** Gravity normally keeps fluids low in the body; in free fall they redistribute upwards, giving puffy faces and thin legs for the first days.\n- **Height.** Spinal discs expand without the constant squeeze, and astronauts gain a few centimetres — lost again within days of landing.\n\nThe countermeasure is exercise: crews spend about **two hours a day** on a treadmill or resistance machine, re-creating gravity's loads. It helps a great deal, but does not fully replace a planet.",{"id":855,"type":856,"conceptId":857,"relation":858,"explanation":859},"u-connect-body","connection","body-systems","related_to","Bone, muscle and the circulation are all tuned to a lifetime of resisting gravity, which is why months of free fall weaken astronauts.",{"id":861,"type":856,"conceptId":862,"relation":863,"explanation":864},"u-connect-tides","tides","helps_understand","Tides come from the same inverse-square law: the Moon pulls the near ocean slightly harder than it pulls the far ocean.",{"id":866,"type":856,"conceptId":867,"relation":868,"explanation":869},"u-connect-four-ops","four-operations","applied_in","Working out weight on another world is one multiplication, and comparing two worlds is one division — arithmetic with a surprising answer.",{"id":871,"type":56,"title":872,"eyebrow":873,"navLabel":874},"u-ch10","Putting it together","Chapter 10","10 Putting it together",{"id":876,"type":190,"component":877,"componentVersion":5,"config":878,"objective":937,"textAlternative":938},"u-lab-sort-forces","sort-game",{"prompt":879,"bins":880,"items":887,"seconds":936},"Is this statement about gravity true or false?",[881,884],{"id":882,"label":883},"true","True",{"id":885,"label":886},"false","False",[888,892,896,900,904,908,912,916,920,924,928,932],{"id":889,"label":890,"bin":882,"why":891},"s1","A hammer and a feather land together in a vacuum","Mass cancels: acceleration = (m x g) \u002F m = g, whatever m is.",{"id":893,"label":894,"bin":885,"why":895},"s2","g = 9.8 means falling objects travel at 9.8 m\u002Fs","g is a gain in speed of 9.8 m\u002Fs every second, not a speed.",{"id":897,"label":898,"bin":882,"why":899},"s3","Your mass is the same on the Moon as on Earth","Mass is the amount of matter; travelling changes none of it.",{"id":901,"label":902,"bin":885,"why":903},"s4","There is no gravity on the space station","Gravity at 400 km is about 8.7 N\u002Fkg, roughly 89 % of ground strength.",{"id":905,"label":906,"bin":885,"why":907},"s5","A parachute works by making the jumper lighter","Weight is unchanged. The canopy increases area, so drag balances weight at a much lower speed.",{"id":909,"label":910,"bin":882,"why":911},"s6","Doubling the distance quarters the gravitational force","The force depends on 1 \u002F distance squared, and 2 squared is 4.",{"id":913,"label":914,"bin":885,"why":915},"s7","Higher satellites orbit faster than lower ones","The opposite: the ISS does 7.7 km\u002Fs, geostationary only 3.07 km\u002Fs.",{"id":917,"label":918,"bin":882,"why":919},"s8","In air, a heavier ball of the same size falls faster","Same drag but more weight, so the balance point (terminal velocity) is higher.",{"id":921,"label":922,"bin":882,"why":923},"s9","An apple pulls the Earth up as hard as the Earth pulls it down","Gravitational pulls always come in equal, opposite pairs.",{"id":925,"label":926,"bin":885,"why":927},"s10","Weight is measured in kilograms","Weight is a force, measured in newtons. Kilograms measure mass.",{"id":929,"label":930,"bin":882,"why":931},"s11","A raindrop would be lethal if there were no air","Falling 3 km with no drag would bring it to about 242 m\u002Fs, roughly 873 km\u002Fh.",{"id":933,"label":934,"bin":885,"why":935},"s12","Gravity stops at the edge of the atmosphere","Gravity has infinite reach. It holds the Moon 384,400 km away.",0,"Sort twelve statements about gravity into true and false, and read why each one lands where it does.","Twelve statements to sort into **true** and **false**.\n\n**True:** hammer and feather land together in a vacuum; mass is unchanged on the Moon; doubling distance quarters the force; a heavier ball of the same size falls faster in air; an apple pulls the Earth as hard as the Earth pulls it; a no-air raindrop would be lethal (≈873 km\u002Fh after 3 km).\n\n**False:** \"g = 9.8 means 9.8 m\u002Fs\" (it's a gain **each second**); \"no gravity on the space station\" (≈89 % of ground strength); \"a parachute makes you lighter\" (it makes you wider); \"higher satellites orbit faster\" (they're slower — 3.07 km\u002Fs geostationary vs 7.7 km\u002Fs ISS); \"weight is in kilograms\" (newtons); \"gravity stops at the atmosphere\" (infinite reach).",{"id":940,"type":190,"component":941,"componentVersion":5,"config":942,"objective":972,"textAlternative":973},"u-lab-match-numbers","match-pairs",{"prompt":943,"mode":944,"pairs":945},"Match each quantity to its value.","connect",[946,948,951,954,957,959,961,964,967,969],{"a":947,"b":588},"g on Earth",{"a":949,"b":950},"g on the Moon","1.62 N\u002Fkg",{"a":952,"b":953},"g on Mars","3.72 N\u002Fkg",{"a":955,"b":956},"g on Jupiter","24.79 N\u002Fkg",{"a":958,"b":168},"Weight of 40 kg on Earth",{"a":960,"b":156},"Weight of 40 kg on the Moon",{"a":962,"b":963},"Distance fallen in 3 s","44.1 m",{"a":965,"b":966},"Escape velocity from Earth","11.2 km\u002Fs",{"a":968,"b":738},"Geostationary altitude",{"a":970,"b":971},"One ISS orbit","About 92 minutes","Match ten gravity quantities to the numbers you should now know by heart.","A matching game of ten pairs.\n\ng on Earth goes with 9.8 N\u002Fkg; on the Moon, 1.62; on Mars, 3.72; on Jupiter, 24.79.\n\nA 40 kg child weighs 392 N on Earth and 64.8 N on the Moon.\n\nA freely falling object covers 44.1 m in 3 seconds.\n\nEscape velocity from Earth is 11.2 km\u002Fs; geostationary orbit sits 35,786 km above the equator; and one ISS orbit takes about 92 minutes.",{"id":975,"type":976,"title":977,"terms":978},"u-glossary","glossary","Words and units you now own",[979,983,987,990,994,997,1001,1005,1008,1012,1016,1020,1024,1027,1031],{"term":980,"meaning":981,"example":982},"Newton (N)","The unit of force. 1 N is the force that makes 1 kg speed up by 1 m\u002Fs every second.","About the weight of a small apple.",{"term":984,"meaning":985,"example":986},"Weight","The gravitational force on an object: W = m × g, measured in newtons.","40 kg × 9.8 = 392 N on Earth.",{"term":69,"meaning":988,"example":989},"The amount of matter, in kilograms. It sets both how hard gravity pulls and how hard the object is to move.","Unchanged anywhere in the universe.",{"term":991,"meaning":992,"example":993},"g","The strength of gravity at a place. Read as N\u002Fkg it gives weight; read as m\u002Fs² it gives the falling acceleration.","Earth 9.8; Moon 1.62; Mars 3.72.",{"term":81,"meaning":995,"example":996},"How much the speed changes each second, measured in m\u002Fs².","Free fall on Earth: 9.8 m\u002Fs².",{"term":998,"meaning":999,"example":1000},"Free fall","Motion with gravity as the only force acting — no air, no floor, no rope.","The ISS and everyone inside it.",{"term":1002,"meaning":1003,"example":1004},"Drag","Air resistance: the backwards push of air on a moving object. It grows roughly with speed squared.","What slows a flat sheet of paper.",{"term":412,"meaning":1006,"example":1007},"The steady speed at which drag exactly balances weight, so the falling stops speeding up.","A skydiver: about 55 m\u002Fs.",{"term":1009,"meaning":1010,"example":1011},"Inertia","An object’s resistance to any change in its motion. It depends on mass, not on gravity.","A trolley is just as hard to shove on the Moon.",{"term":1013,"meaning":1014,"example":1015},"Inverse-square law","A rule in which a quantity falls off as one over the distance squared.","Twice as far, a quarter of the pull.",{"term":1017,"meaning":1018,"example":1019},"Orbit","A closed path around a world, produced by falling while moving sideways fast enough to keep missing.","The ISS: about 92 minutes per lap.",{"term":1021,"meaning":1022,"example":1023},"Orbital speed","The sideways speed needed for a circular orbit. Higher orbits need slower speeds.","7.91 km\u002Fs at the surface; 3.07 at geostationary.",{"term":749,"meaning":1025,"example":1026},"The speed at which an object can leave a world for good: √2 times the orbital speed.","11.2 km\u002Fs from Earth.",{"term":1028,"meaning":1029,"example":1030},"Geostationary orbit","A circular orbit 35,786 km above the equator, where one lap takes exactly one day.","Where communication satellites sit.",{"term":1032,"meaning":1033,"example":1034},"Microgravity","The near-weightless environment of free fall, where everything falls together.","Aboard the ISS, or 20 s on a parabolic flight.",{"id":1036,"type":1037,"title":1038,"questions":1039},"u-quiz","quiz","Understand: check yourself",[1040,1053,1066,1079,1092,1105,1118,1130,1143,1156,1169,1182],{"itemId":1041,"prompt":1042,"options":1043,"correct":380,"why":1052},"gravity.understand-q-g-units","What does \"g = 9.8 m\u002Fs²\" tell you about a freely falling object?",[1044,1046,1048,1050],{"id":377,"label":1045},"It always falls at 9.8 metres per second",{"id":380,"label":1047},"It gains 9.8 metres per second of speed every second",{"id":383,"label":1049},"It falls 9.8 metres every second",{"id":386,"label":1051},"It weighs 9.8 newtons","g is an acceleration: a 9.8 m\u002Fs gain in speed each second. After 3 s the speed is 29.4 m\u002Fs and the distance fallen is 44.1 m.",{"itemId":1054,"prompt":1055,"options":1056,"correct":380,"why":1065},"gravity.understand-q-mass-cancels","Why do a 1 kg and a 10 kg stone fall at the same rate in a vacuum?",[1057,1059,1061,1063],{"id":377,"label":1058},"Gravity pulls both with the same force",{"id":380,"label":1060},"The heavier one has more pull but is proportionally harder to move",{"id":383,"label":1062},"The air balances the difference",{"id":386,"label":1064},"The 10 kg stone is larger, so it has more drag","The 10 kg stone gets 98 N, the 1 kg stone 9.8 N — not equal. But force and mass are both ten times bigger, so a = force ÷ mass cancels to g for both.",{"itemId":1067,"prompt":1068,"options":1069,"correct":383,"why":1078},"gravity.understand-q-distance-4s","How far does an object fall from rest in 4 seconds, ignoring air resistance?",[1070,1072,1074,1076],{"id":377,"label":1071},"39.2 m",{"id":380,"label":1073},"19.6 m",{"id":383,"label":1075},"78.4 m",{"id":386,"label":1077},"156.8 m","d = ½ × 9.8 × 4² = 4.9 × 16 = 78.4 m. (39.2 m\u002Fs is the speed, a different quantity.)",{"itemId":1080,"prompt":1081,"options":1082,"correct":383,"why":1091},"gravity.understand-q-weight-jupiter","A 30 kg suitcase is taken to Jupiter’s cloud tops, where g = 24.79 N\u002Fkg. What does it weigh there?",[1083,1085,1087,1089],{"id":377,"label":1084},"30 N",{"id":380,"label":1086},"294 N",{"id":383,"label":1088},"743.7 N",{"id":386,"label":1090},"24.79 N","W = m × g = 30 × 24.79 = 743.7 N, about 2.5 times the 294 N it weighs on Earth.",{"itemId":1093,"prompt":1094,"options":1095,"correct":383,"why":1104},"gravity.understand-q-terminal","At terminal velocity, what is true of the forces on a skydiver?",[1096,1098,1100,1102],{"id":377,"label":1097},"Gravity has stopped acting",{"id":380,"label":1099},"Air resistance is bigger than the weight",{"id":383,"label":1101},"Air resistance exactly equals the weight, so there is no net force",{"id":386,"label":1103},"The weight has become zero","Balanced forces mean no acceleration — falling continues at a constant speed of roughly 55 m\u002Fs.",{"itemId":1106,"prompt":1107,"options":1108,"correct":380,"why":1117},"gravity.understand-q-two-parachutes","Two skydivers with identical parachutes have masses of 60 kg and 90 kg. Who reaches the ground first?",[1109,1111,1113,1115],{"id":377,"label":1110},"The 60 kg jumper",{"id":380,"label":1112},"The 90 kg jumper",{"id":383,"label":1114},"They land together",{"id":386,"label":1116},"It depends on the weather only","Identical canopies give identical drag, but the heavier jumper needs a higher speed to balance her greater weight.",{"itemId":1119,"prompt":1120,"options":1121,"correct":383,"why":1129},"gravity.understand-q-inverse-square","At three times the distance from Earth’s centre, the gravitational pull is...",[1122,1124,1126,1127],{"id":377,"label":1123},"one third",{"id":380,"label":1125},"one sixth",{"id":383,"label":604},{"id":386,"label":1128},"unchanged","Force ∝ 1 ÷ distance². Three times the distance gives 1 ÷ 3² = one ninth, so g drops to about 1.09 N\u002Fkg.",{"itemId":1131,"prompt":1132,"options":1133,"correct":377,"why":1142},"gravity.understand-q-orbit-speed","Which satellite travels fastest?",[1134,1136,1138,1140],{"id":377,"label":1135},"The ISS at 400 km",{"id":380,"label":1137},"A geostationary satellite at 35,786 km",{"id":383,"label":1139},"The Moon at 384,400 km",{"id":386,"label":1141},"They all travel at the same speed","Lower orbits are faster: ISS ≈ 7.7 km\u002Fs, geostationary 3.07 km\u002Fs, the Moon only about 1 km\u002Fs.",{"itemId":1144,"prompt":1145,"options":1146,"correct":380,"why":1155},"gravity.understand-q-geostationary","Why does a satellite at 35,786 km above the equator appear to stay still in the sky?",[1147,1149,1151,1153],{"id":377,"label":1148},"It is beyond gravity, so it does not move",{"id":380,"label":1150},"It takes exactly one day to orbit, matching Earth’s spin",{"id":383,"label":1152},"It is held up by a very long cable",{"id":386,"label":1154},"It uses engines to hover","One orbit there takes 23 h 56 min, exactly Earth’s spin, so satellite and ground keep pace.",{"itemId":1157,"prompt":1158,"options":1159,"correct":383,"why":1168},"gravity.understand-q-float","An astronaut on the ISS releases a pen and it hangs in mid-air. Why?",[1160,1162,1164,1166],{"id":377,"label":1161},"Gravity does not reach 400 km",{"id":380,"label":1163},"The pen is too light to fall",{"id":383,"label":1165},"The pen, the astronaut and the station are all falling at the same rate",{"id":386,"label":1167},"The station spins to cancel gravity","Gravity there is still about 8.7 N\u002Fkg; everything just falls together, so nothing catches up with anything.",{"itemId":1170,"prompt":1171,"options":1172,"correct":380,"why":1181},"gravity.understand-q-scale-moon","An Earth-calibrated bathroom scale is taken to the Moon and a 40 kg child stands on it. What does it read?",[1173,1175,1177,1179],{"id":377,"label":1174},"40 kg",{"id":380,"label":1176},"About 6.6 kg",{"id":383,"label":1178},"240 kg",{"id":386,"label":1180},"64.8 kg","The scale reads force (64.8 N) then divides by Earth’s 9.8: 64.8 ÷ 9.8 ≈ 6.6. Mass is still 40 kg.",{"itemId":1183,"prompt":1184,"options":1185,"correct":383,"why":1194},"gravity.understand-q-everest","How much weaker is gravity on the summit of Mount Everest than at sea level?",[1186,1188,1190,1192],{"id":377,"label":1187},"About half",{"id":380,"label":1189},"About 10 % weaker",{"id":383,"label":1191},"About 0.3 % weaker",{"id":386,"label":1193},"It is stronger up there","Everest’s 8.8 km is tiny next to Earth’s 6,371 km radius: g falls from about 9.82 to 9.79, about 0.28 %.",{"id":1196,"type":1197,"title":1198,"points":1199},"u-cheat-sheet","summary","Cheat sheet: the rules and the numbers",[1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215],"**Force** is a push or pull, in **newtons**. 1 N = 1 kg·m\u002Fs², about the weight of a small apple.","**weight = mass × g.** Mass in kg never changes; weight in N changes with the world you are on.","**g has two readings, same number.** 9.8 **N\u002Fkg** gives weight; 9.8 **m\u002Fs²** gives falling acceleration.","**v = g × t, d = ½ g t².** On Earth, d = 4.9 t². After 1, 2, 3 s: 4.9, 19.6, 44.1 m — ratio 1:4:9.","**Mass cancels in free fall:** a = (m × g) ÷ m = g — why a hammer and feather land together in a vacuum.","**Mass does two jobs:** how hard gravity pulls *and* how hard it is to move. Always the same number, unexplained.","**Drag** grows with speed squared and frontal area. **Terminal velocity** is where drag equals weight.","**Terminal speeds:** skydiver ≈ 55 m\u002Fs (200 km\u002Fh), parachute ≈ 5.5 m\u002Fs (20 km\u002Fh), raindrop ≈ 6.5 m\u002Fs (23 km\u002Fh).","**In air**, a heavier object of the same shape falls faster — more drag needed to balance more weight.","**Newton’s law, in words:** every mass attracts every mass, more for bigger masses, as **1 ÷ distance²**.","**Inverse square:** twice as far, a quarter of the pull. g: 9.8 at the surface, 2.45 at 2×radius, 0.0027 at the Moon.","**An orbit is a permanent miss:** fall 5 m while going 8 km sideways and the curved Earth drops away just as fast. Surface orbital speed: **7.91 km\u002Fs**.","**Escape velocity = √2 × orbital speed** ≈ **11.2 km\u002Fs** from Earth.","**ISS:** ≈400 km up, 7.7 km\u002Fs, ≈92 min\u002Flap, 16 sunrises\u002Fday, gravity still ≈89 % of ground level.","**Geostationary:** 35,786 km up, one lap in 23 h 56 min — appears to hang still; where comsats live.","**Astronauts float because they are falling** with the station — not because gravity stopped. The right word: **microgravity**.",{"id":1217,"type":1218,"prompt":1219},"u-reflect","reflection","A friend says: \"Astronauts float because they are so far from Earth that gravity cannot reach them.\"\n\nWrite a reply of four or five sentences that corrects them **without** using the phrase \"you are wrong\". Include at least one number, and end with a comparison to something your friend has felt themselves — a lift, a swing or a jump.",{"id":1221,"type":1222,"sourceIds":1223},"u-sources","sources",[1224,1225,1226,1227,1228,1229,1230],"gravity-hyperphysics-gravity","gravity-physicsclassroom-free-fall","gravity-physicsclassroom-universal-gravitation","gravity-nasa-planetary-factsheet","gravity-nasa-iss","gravity-mactutor-brahmagupta","gravity-britannica-gravity",[1224,1225,1226,1227,1228,1229,1230],"needs_review",{"generatedBy":1234,"notes":1235},"claude-code","Draft. All numbers computed and asserted in Python: fall tables, weights on six worlds, terminal speeds, ISS and geostationary orbits, inverse-square ladder, the 8 km \u002F 5 m orbit argument. Apple story sourced to Stukeley 1752 and hedged. Indian precursors credited and their limits stated plainly. Pending owner review.","81123a15c992c2447f4a0f87584879ece94b49818eb94c61d674d0de1a3050dd",{"component:gravity-drop@1":1238,"logic:practice":1239,"component:orbit-lab@1":1240,"component:sort-game@1":1241,"component:match-pairs@1":1242,"source:gravity-britannica-gravity":1243,"source:gravity-hyperphysics-gravity":1244,"source:gravity-mactutor-brahmagupta":1245,"source:gravity-nasa-iss":1246,"source:gravity-nasa-planetary-factsheet":1247,"source:gravity-physicsclassroom-free-fall":1248,"source:gravity-physicsclassroom-universal-gravitation":1249},"60b1b2628472895c3a36f45610b158c8d87f74e411a582d1c8293f4f80ecf53b","3d6b0fe1b15255975a32b0fcd94e8019bc959ad45cbf12e136e86149549c6878","e59aa1a3427977ca02681e15776a720cd37d878bd774ea8c5531e2116616b667","b164f45a2c8ca08f26c450768ff0231e113e9fe45381eddb34dc6d0548596c38","2a8ee4ac87460b4e1175a4bb13c96b03d577db06dde95670eb7fcfe4ad787899","8a68b69eee24a181ce32e96e29a3f9d05221ee983d659a93152038805c82ae06","ad0b66634225092960d8f417463e2d74017822199cc2886992381487d6b8cbd9","dfd38636150223e38cae9fcd289578027a6479424bc8a7171951451f887e05b3","bfc3220795160e3b0ddf890b11835e5452f06f2c29b03d7541b29110035b675a","9c57a129761cacac5b2946c90eff33acba841871c7bbd0b69bdd1ec642680db9","8c311b8ddd919ef66d07a631e86b5823f4c525e1b8bf33ae94ffd5f066a7d201","a331b2d122b65b125c1004d73ef7cb3806c57d8dcb358b67a4f6cc16473bfe0f",{"state":1251,"reviewer":1252,"selfReview":210,"reviewedAt":1253,"method":1254},"approved","The library owner","2026-09-20T10:18:37.581Z","owner_bulk","preview-7e1cbbcc4f",1789899596975]