Free module / Lesson 3 of 3

Big Idea 01 · Lesson 3 of 3 · Use It

Falling Forever

Nothing is holding anything up.

Runs
30 minutes
Ages
8–11
Materials
$0, household
Supervision
Hands-on throughout
Hazards
Wet floor, thrown ball
In one minute

This is the payoff lesson. Your child learns that the space station, the Moon, and every satellite above your house are all falling — they just keep missing — and that we trust that picture enough to bet the world’s navigation system on it every day.

The moment that matters is a cup of water with a hole in it. While you hold it, water pours out. The instant you drop it, the stream stops.

It ends the whole Big Idea, so the last minute is written to be read slowly.

What to gather

ItemHow manyNotes
Paper or plastic cup1–2With a pencil-width hole punched near the bottom. A spare is worth having.
WaterOver a sink, bath, basin, or outside.
Towel1Not optional. Mop between drops rather than at the end.
A ball1Outdoors, anything throwable. Indoors, something soft.
Chalk or tapeTo mark where the ball lands each time.

The lesson

11 beats
011½ min

The Mystery

There are people living in a metal tube going around the Earth right now. They’ve been up there, in shifts, for about twenty-five years.

There’s no rope holding it up. There’s no rocket firing underneath it. There’s nothing beneath it at all.

So why doesn’t it fall down?

And here’s the other thing. Inside, the astronauts float. Their pens float. Their food floats. If they let go of a hammer it just hangs there in the air. Why?

021 min

The Prediction

Commit first
Choose before you go on

Why do astronauts float inside the space station?

Write it down

Nearly everyone picks the first one, including nearly every adult. Write their answer where they can see it — this is the one you’ll come back to.

033 min

Throw the Ball

Hands on

Three throws, three marks

Outside, or down a long hallway.

  1. Throw the ball level — not up, straight out — as gently as you can. Mark where it lands.
  2. Throw it harder. Mark it.
  3. Harder again. Mark it.

The marks march away in a line.

Every single time, the ball fell. It never stopped falling. It just went further sideways before it got to the ground.

So here’s a question, and I don’t want you to answer it yet.

If I could throw it hard enough — ridiculously hard, harder than any person could ever throw — where would it land?

Don’t answer it

Let the question sit for the next ten minutes. If your child gets there on their own during the cup demo, that’s the best possible outcome and you should let them say it.

046 min

The Falling Cup

The turn
held stilllet gostreamstays in
Held still, water pushes out. Falling with the cup, it has nothing to push against.

Hole near the bottom of the cup. Hold it over the sink or basin and fill it. Water streams out of the hole.

Look at that. Why is the water coming out?

Because it’s heavy, right? All that water is pressing down on the bottom of the cup, and it squeezes out through the hole. That’s why the stream is stronger when the cup is full and weaker when it’s nearly empty.

Choose before you go on

Now I’m going to let go of the cup. Predict what the stream does.

The look-alike — 20 seconds

Refill the cup. Now, instead of dropping it, lower it smoothly downward by hand, at a steady speed, all the way to the basin.

It’s going down — and the water keeps pouring the whole way.

That looked like falling, didn’t it? It was going down. And the water came out the whole time. So going down isn’t the thing. My hand was still holding it.

And the other way round

Refill. Now toss it gently upward a foot or so and catch it.

The stream stops on the way up, too.

It was going up. And the water still stopped coming out.

So put those two together. Going down with my hand on it: water pours. Going up with my hand off it: water stops.

“Falling” doesn’t mean going down. Falling means nothing is holding you.

What you’ll actually see, so it doesn’t throw you

While your hand is still pushing the cup upward, the water squirts harder for an instant — and again when you catch it. So the sequence is: spurt, stop, spurt. Name it rather than gloss it: “while I’m pushing, it’s heavier than usual. The moment I let go, nothing.”

051 min

The Naming

Words last

Names for what the cup just did — and one idea we can stop believing.

Free fall

falling with nothing holding you. It does not have to mean going down.

Weightless

what free fall feels like. The water in the cup was weightless.

Orbit

falling around something instead of into it.

And one idea we’re going to stop believing.

People say there’s no gravity up there. You’ll hear it on TV. That’s the wrong idea — the Earth is bending time just as hard 250 miles up as it is in this room.

What’s gone isn’t gravity. What’s gone is the floor.

One sentence that keeps the three lessons honest with each other

Last lesson you told your child nothing is pulling you down. Today you’re about to use Newton’s picture, where gravity is a force, because for orbits it’s far easier to think with. Say so out loud: “Last time we used Einstein’s picture. Today we’re using Newton’s, because it’s easier for this — and for orbits they give the same answer.”

066 min

The Deeper Look

Two halves
cannonorbit — falling and missing
Fire it hard enough and the ground curves away as fast as the ball falls. It keeps missing.

The cannonball

Remember the question I wouldn’t answer? Isaac Newton asked himself the same one about three hundred and forty years ago, and he drew a picture of it.

He imagined a cannon on top of a mountain so tall it stuck out above the sky. And he imagined firing it sideways.

Fire it gently: the cannonball arcs over and lands nearby. Fire it harder: it lands further away. Harder still: further again — and now something interesting is happening, because the Earth is round, and the ground is starting to curve away underneath the ball while it flies.

So fire it harder still. And harder. Until you fire it so hard that the ground curves away exactly as fast as the ball falls.

Now the ball is falling — it’s falling the whole time, it never stops falling — but it never gets any closer to the ground. It goes all the way around the world and hits you in the back of the head.

It never stopped falling. It just kept missing.

That is exactly what the space station is doing. About 250 miles up, going sideways at around 17,500 miles an hour — five miles every second. It falls. The Earth curves away. It misses. All the way round, every ninety minutes.

And the astronauts inside? They’re the water in the cup.

Where this picture’s horizon is

What it shows: Why an orbit is falling, and why nothing has to hold it up.

What it doesn’t: There’s no air in Newton’s picture — a real cannonball would burn up. The mountain is impossible. Real orbits aren’t neat circles. And this is Newton’s picture, not Einstein’s — it gets the right answer here, and last lesson’s is the deeper one.

Now the receipt

Last lesson we said time runs slower down low, near heavy things. If that’s really true — and not just a nice story — then a clock way up in space should run faster than a clock down here. So let’s check.

The satellites that tell your phone where it is carry the most accurate clocks ever built. They’re 12,500 miles up, where gravity is weaker, so their clocks gain about 45 millionths of a second every day. They’re also moving very fast, and going fast makes clocks run slow, so that gives about 7 millionths back.

Add it up: those clocks gain about 38 millionths of a second every single day.

That sounds like nothing at all. But your phone works out where you are by timing radio signals travelling at the speed of light. And in 38 millionths of a second, light goes about seven miles.

So if nobody fixed it, every distance your phone worked out would be seven miles off after a single day — and worse every day after that. It would be useless before dinner.

Every one of those satellites is launched with its clock deliberately set to run slow — by exactly the right amount — so that when it gets up there, it runs right.

After this lesson we’ll sit with that properly — how the timing works, why seven miles, and the switch they built to check. You’ll be able to explain it to anyone.

073 min

The Human Story — the switch

Here’s my favourite thing in this whole Big Idea.

In 1977 the Americans were building the very first satellites for this system. They knew what Einstein’s equations said the clocks would do.

But somebody wasn’t sure.

We don’t know exactly who doubted it, and that’s alright — we know somebody did, because of what they built next.

And you can see why they’d doubt it. It’s one thing to write an equation on a blackboard. It’s another to bet a satellite on it — something that costs a fortune, that you launch on a rocket, and that you cannot go up and fix.

So they built a switch.

The satellite was called NTS-2. It went up in June 1977 carrying an atomic clock, and a little device that would correct the clock for Einstein’s effect — and that could be left switched off.

They launched it. They left the correction off. And they watched the clock.

Einstein’s equations predicted the clock would gain 446.5 parts in a trillion. It gained 442.5.

That’s a match. That’s as close as their clock could possibly tell. Getting within one part in a hundred of a number nobody had ever measured before is a bullseye.

They turned the switch on. It has been on ever since — in every satellite, every day, for nearly fifty years.

That’s what a test looks like. Not “we believe Einstein.” Not “the maths is beautiful.” A switch, a measurement, and a number that either matches or it doesn’t.

They built in a way to find out they were wrong. That’s the whole trick. That’s the thing.

082 min

The Layer Stack

All of it
The ideaWhere it standsWhat it couldn’t explain
0Heavy things fall faster — Aristotle, ~350 BCSuperseded
1Take the air away and everything falls the same — Galileo, 1638Well established
2Gravity is a force between heavy things — Newton, 1687Useful modelStill flying spacecraft
3Heavy things bend space and time; falling is going straight — Einstein, 1915Well established
4?Open questionThis is where the map runs out

Einstein’s picture has worked everywhere anyone has ever pointed it. Every test, for a hundred and ten years.

But there’s a problem, and it’s a big one.

There’s another set of rules, for very tiny things — atoms, and the bits inside atoms. Those rules work perfectly too. Every test.

And in one particular place, the two sets of rules don’t fit together. Anywhere something is both incredibly heavy and incredibly tiny, you’d have to use both at once — and then you get answers like infinity.

Infinity isn’t an answer. It’s the universe telling you you’ve asked the question wrong.

Nobody has fixed it. Not one person, in a hundred years of trying.

Which means nobody knows what happens at the exact middle of a black hole. Nobody knows what space and time are actually made of.

This is where the map runs out. Not a long time ago. Now. Today.

091½ min

Where You Meet It

You have already felt this. You use it. The Moon has been doing it for as long as there has been a Moon.

Your phone. Right now, this second.

Every time it knows where you are, it’s using a clock correction that a man worked out with a pencil in 1915.

Every satellite over your house

Weather, television, mapping — all of them falling, all of them missing.

The Moon

Falling and missing for four and a half billion years.

Roller coasters

That lift in your stomach at the top of the big drop — for that moment, nothing is holding you up. You have already felt free fall. You were the water in the cup.

103 min

The Checkpoint

Ask, don’t grade

1. On a roller coaster, right at the top of a big drop, your stomach feels like it’s floating. Why?

2. The Moon has been going around the Earth for about four and a half billion years. Which of these is true?

3. You take an incredibly precise clock up a very tall mountain and leave it for a year. An identical clock stays at sea level. What do you find?

4. A scientist is inside an aeroplane flying a special falling arc, so everyone inside is floating. She holds out a hammer and a feather and lets go of both at the same moment. What happens?

Answered 0 of 4
112 min

What’s Still Hidden

The end of the Big Idea
Read this one slowly

It closes ninety minutes of work, and it’s the last thing your child hears about gravity for a while.

What’s still hidden

Three lessons ago, you thought heavy things fall faster.

Then you found out that everything falls exactly the same — a hammer, a feather, a person — and that it doesn’t matter at all what the thing is made of.

Then you found out why. Nothing is pulling you. Time runs slower down low, and falling is just going as straight as you possibly can.

And today you found out that the Moon is falling. And the space station is falling. And every satellite over your head is falling. And that we were so sure about all of this that we bet the world’s maps on it — and it worked.

And here’s where it stops.

Nobody knows how to fit Einstein’s rules together with the rules for tiny things. Nobody knows what happens at the middle of a black hole. Nobody knows what space and time are actually made of.

Not “it’s complicated.” Not “you’ll learn it later.” Nobody knows. The smartest people alive have been working on it for a hundred years and they are stuck.

So there’s a layer 4 out there. Somebody is going to find it.

They’re probably alive right now.

They might be about your age.

If it didn’t work

What happenedWhat to do
The water kept pouring while the cup fellAlmost always the drop is too short. You need at least two or three feet — stand and hold it at head height over a bathtub. Also check the hole isn’t so big the water simply falls out under its own momentum; pencil-width is about right.
The cup tipped over on the way down and sprayed everywhereLet go cleanly with both hands rather than releasing from a pinch grip, and don’t fill it more than about two-thirds. Plastic behaves better than paper.
Your child says the water stopped because it was falling out of viewA sharp objection, and a fair one. Do it again and film it in slow motion — every phone can. The stream visibly stops. Good moment to say that “let’s look more carefully” is always a legitimate response to a surprising result.
The upward toss didn’t workToss it higher, not gentler — a few inches gives you about a sixth of a second in the air, far too quick to see. Aim for a foot or so, and watch the hole rather than the cup.
“But the astronauts aren’t falling, they’d hit the ground”The right objection at the right moment. Back to the ball marks: “each throw went further sideways before it landed. What if it went so far sideways that the ground curved away underneath it?” Draw a circle and an arrow. Worth an extra two minutes.
Your child is upset by the “nobody knows” endingSome children find open questions thrilling and a few find them unsettling. Reframe rather than retreat: “it’s not that everything is uncertain — look how much we DO know, enough to land on the Moon and build your phone. It’s that there’s still something left to find. That’s good news.”

For the grown-up

The real science

An orbit is free fall with enough tangential velocity that the trajectory’s curvature matches the curvature of the body being orbited. The ISS at ~400 km experiences about 88% of surface gravity; it orbits at roughly 7.66 km/s with a period near 90 minutes. Apparent weightlessness is not reduced gravity — it is the absence of any contact force. In the cup, hydrostatic pressure at the hole is ρgh only in a supported frame; in free fall the effective g in the cup’s frame is zero, the pressure gradient vanishes, and flow stops.

The GPS figures: at 20,200 km the gravitational blueshift runs satellite clocks fast by about +45 μs/day; orbital velocity slows them by about −7 μs/day; net +38 μs/day. Because position derives from signal timing at c, an uncorrected 38 μs is roughly 11 km of ranging error per day. Satellite oscillators are offset before launch — broadcast frequency set to 10.22999999543 MHz rather than 10.23 MHz.

On the NTS-2 story: real and well documented in Neil Ashby’s Living Reviews in Relativity survey. The satellite carried a frequency synthesizer that could be enabled after launch once the orbital clock rate was confirmed. Measured +442.5 parts in 10¹² against a predicted +446.5. Historians note the extent of engineering scepticism isn’t precisely documented — the switch itself is the hard evidence that someone thought a test was worth building in.

Questions they may ask

“Why doesn’t the space station slow down and fall?”

It does, slightly — there’s a whisper of atmosphere even at 250 miles, and it drags. The station has to be boosted back up every few months, and always will.

“Could I throw something hard enough to orbit?”

No — you’d need about five miles per second, and air resistance would destroy it long before that. But the idea is right, and it’s exactly what a rocket is doing: not going up so much as going sideways, extremely fast.

“What would happen if the Moon stopped moving sideways?”

It would fall straight at us. The right answer, and a slightly alarming one, which children generally enjoy.

“Do the astronauts age differently?”

Yes. On the ISS, speed wins over altitude, so astronauts age very slightly slower. One cosmonaut has accumulated about a fiftieth of a second over his career.

“If nobody knows what’s at the middle of a black hole, how do we know they exist?”

We’ve photographed the shadow of one, and heard two of them collide. We know they’re there and how they behave from outside. It’s the exact centre where our equations stop giving sensible answers.

Misconceptions to watch for

  • “There’s no gravity in space.” The big one, reinforced by every cartoon and half the news coverage. It’s the opening prediction and checkpoint question 2 for exactly that reason.
  • “Free fall means going down.” Quietly fatal — it makes orbit impossible to understand. The lower-by-hand and upward-toss pair exists solely to kill it.
  • “Weightless means massless.” A floating hammer is still hard to swing. Weight goes away; stuff doesn’t.
  • “Orbiting means escaping gravity.” The opposite. An orbit is gravity winning continuously and the object continuously missing.
  • “There’s no gravity up there” vs “nothing is pulling you.” These two lessons use two different pictures — Einstein’s last time, Newton’s today — and a sharp child will notice. That’s a good thing to have noticed. Say out loud which picture you’re using and why.
  • “Scientists don’t really know anything.” The one to actively guard against at the layer stack. Precision about the edge of knowledge is the opposite of vagueness about all of it.

If you have more time

Film the cup in slow motion. Every phone can do this. The moment the stream cuts off is genuinely startling at 240 frames per second, and children will want to watch it ten times.

Spin a bucket of water — adult only. Outside, a small bucket a quarter full, swung fast in a vertical circle. The water stays in at the top. This is the most dangerous thing in the whole Big Idea and it is not a child’s job. Check the handle, dry your hands, stand well away from windows, faces and your child. If that gives you pause, film the cup instead — it teaches the same thing.

Track the space station. Free sites tell you when the ISS passes over your house. It’s visible to the naked eye, and there is nothing quite like a child pointing at a bright dot and saying “that’s falling.”

Newton’s actual drawing. The cannonball diagram is online, and it’s exactly what you’d sketch on a napkin. Worth seeing that the founding picture of orbital mechanics is a doodle of a mountain.

Status & sources

Draft — reviewed for accuracy, not yet run with a timer. Outstanding: one timed read-aloud and one session with a real 8–11 year old.

Sources: Ashby, “Relativity in the Global Positioning System,” Living Reviews in Relativity 6, 1 (2003) · Kaiser, on GPS and general relativity (AIP) · Newton, A Treatise of the System of the World (1728) · NIST 2010 clock experiment · ISS orbital parameters.

The module’s last stop

Next · Why your phone knows where you are

After the three lessons: how general relativity is running in GPS — written for a child and a grown-up at the same table.