cover

Satellite Time-Choir

How does a GPS know exactly where you are on Earth?
You're standing in the middle of a strange city, holding your phone, and a little blue dot announces with total confiden

You're standing in the middle of a strange city, holding your phone, and a little blue dot announces with total confidence: you are HERE. How does that dot know? You never told it anything. The secret isn't magic โ€” it's a tiny choir of satellites, all singing the same odd little song.

Way up above you โ€” **about 20,000 kilometers up** โ€” there are dozens of satellites circling the Earth. They don't beam a

Way up above you โ€” about 20,000 kilometers up โ€” there are dozens of satellites circling the Earth. They don't beam a picture of you down. They don't even know you exist. Each one just keeps shouting the same simple message, over and over, in every direction: "It is exactly this time, and I am satellite number so-and-so."

That message travels down to you as a radio signal, riding at the speed of light. Light is **blisteringly fast** โ€” but i

That message travels down to you as a radio signal, riding at the speed of light. Light is blisteringly fast โ€” but it is not infinitely fast. It takes a tiny sliver of time to make the journey down. And that tiny sliver of time is the whole trick.

~~Here's the idea.~~ The satellite stamps its message with the exact moment it was sent. Your phone notes the exact mome

Here's the idea. The satellite stamps its message with the exact moment it was sent. Your phone notes the exact moment it arrived. Subtract one from the other, and you get the travel time. Multiply travel time by the speed of light, and โ€” ta-da โ€” you know how far away that satellite is. You've turned a moment of time into a distance.

~~But knowing your distance from one satellite isn't enough.~~ "You are 21,000 kilometers from me" only tells you that y

But knowing your distance from one satellite isn't enough. "You are 21,000 kilometers from me" only tells you that you're somewhere on a giant invisible bubble around that satellite. That's a lot of places. You could be over the ocean, or over a mountain, or right where you are.

So your phone listens to a second satellite. Now you're on ~~TWO bubbles at once~~ โ€” and **two bubbles only touch along

So your phone listens to a second satellite. Now you're on TWO bubbles at once โ€” and two bubbles only touch along a ring. Add a third satellite, a third bubble, and the possibilities shrink to just a couple of points. One of those points is way out in space (easy to ignore). The other one is you.

This bubble-crossing trick has a fancy name: ++trilateration++. It just means "*finding a spot by measuring distances fr

This bubble-crossing trick has a fancy name: trilateration. It just means "finding a spot by measuring distances from things you already know." It's the same way you'd find a hidden treasure if a map said "30 steps from the oak, 12 from the well, 8 from the rock." Cross the circles, and X marks the you.

~~There's one more wrinkle.~~ Because light is so fast, even being **off by a millionth of a second** would put your dot

There's one more wrinkle. Because light is so fast, even being off by a millionth of a second would put your dot in the wrong neighborhood. The satellites carry incredibly precise atomic clocks. Your phone's cheap clock can't keep up โ€” so it cleverly listens to a fourth satellite, and uses that extra measurement to correct its own time. Now everything lines up.

And that's the whole song. Several satellites, each ~~shouting the time~~. Your phone catches the messages, measures how

And that's the whole song. Several satellites, each shouting the time. Your phone catches the messages, measures how long each took to arrive, turns those slivers of time into distances, and crosses the bubbles until only one spot is left. No one watched you. No one tracked you. The sky just did some very fast arithmetic.

So next time that little blue dot says "~~you are HERE~~" with such certainty, you'll know its secret. **It's not magic,

So next time that little blue dot says "you are HERE" with such certainty, you'll know its secret. It's not magic, and it's not spying. It's a handful of patient satellites, a few clocks more precise than anything in your house, and the speed of light doing the math. You are here โ€” and now you know exactly how it knows.

How was this book?

A Wonderleaf Book

Satellite Time-Choir

โ€” How does a GPS know exactly where you are on Earth? โ€”

Wonderleaf Editions
โ€” ex libris โ€”
A Wonderleaf Book

Satellite Time-Choir

How does a GPS know exactly where you are on Earth?

Wonderleaf Editions ยท MMXXVI
Scene 1
You're standing in the middle of a strange city, holding your phone, and a little blue dot announces with total confiden
Satellite Time-Choir2
Scene 1

You're standing in the middle of a strange city, holding your phone, and a little blue dot announces with total confidence: you are HERE. How does that dot know? You never told it anything. The secret isn't magic โ€” it's a tiny choir of satellites, all singing the same odd little song.

3Satellite Time-Choir
Scene 2
Way up above you โ€” **about 20,000 kilometers up** โ€” there are dozens of satellites circling the Earth. They don't beam a
Satellite Time-Choir4
Scene 2

Way up above you โ€” about 20,000 kilometers up โ€” there are dozens of satellites circling the Earth. They don't beam a picture of you down. They don't even know you exist. Each one just keeps shouting the same simple message, over and over, in every direction: "It is exactly this time, and I am satellite number so-and-so."

5Satellite Time-Choir
Scene 3
That message travels down to you as a radio signal, riding at the speed of light. Light is **blisteringly fast** โ€” but i
Satellite Time-Choir6
Scene 3

That message travels down to you as a radio signal, riding at the speed of light. Light is blisteringly fast โ€” but it is not infinitely fast. It takes a tiny sliver of time to make the journey down. And that tiny sliver of time is the whole trick.

7Satellite Time-Choir
Scene 4
~~Here's the idea.~~ The satellite stamps its message with the exact moment it was sent. Your phone notes the exact mome
Satellite Time-Choir8
Scene 4

Here's the idea. The satellite stamps its message with the exact moment it was sent. Your phone notes the exact moment it arrived. Subtract one from the other, and you get the travel time. Multiply travel time by the speed of light, and โ€” ta-da โ€” you know how far away that satellite is. You've turned a moment of time into a distance.

9Satellite Time-Choir
Scene 5
~~But knowing your distance from one satellite isn't enough.~~ "You are 21,000 kilometers from me" only tells you that y
Satellite Time-Choir10
Scene 5

But knowing your distance from one satellite isn't enough. "You are 21,000 kilometers from me" only tells you that you're somewhere on a giant invisible bubble around that satellite. That's a lot of places. You could be over the ocean, or over a mountain, or right where you are.

11Satellite Time-Choir
Scene 6
So your phone listens to a second satellite. Now you're on ~~TWO bubbles at once~~ โ€” and **two bubbles only touch along
Satellite Time-Choir12
Scene 6

So your phone listens to a second satellite. Now you're on TWO bubbles at once โ€” and two bubbles only touch along a ring. Add a third satellite, a third bubble, and the possibilities shrink to just a couple of points. One of those points is way out in space (easy to ignore). The other one is you.

13Satellite Time-Choir
Scene 7
This bubble-crossing trick has a fancy name: ++trilateration++. It just means "*finding a spot by measuring distances fr
Satellite Time-Choir14
Scene 7

This bubble-crossing trick has a fancy name: trilateration. It just means "finding a spot by measuring distances from things you already know." It's the same way you'd find a hidden treasure if a map said "30 steps from the oak, 12 from the well, 8 from the rock." Cross the circles, and X marks the you.

15Satellite Time-Choir
Scene 8
~~There's one more wrinkle.~~ Because light is so fast, even being **off by a millionth of a second** would put your dot
Satellite Time-Choir16
Scene 8

There's one more wrinkle. Because light is so fast, even being off by a millionth of a second would put your dot in the wrong neighborhood. The satellites carry incredibly precise atomic clocks. Your phone's cheap clock can't keep up โ€” so it cleverly listens to a fourth satellite, and uses that extra measurement to correct its own time. Now everything lines up.

17Satellite Time-Choir
Scene 9
And that's the whole song. Several satellites, each ~~shouting the time~~. Your phone catches the messages, measures how
Satellite Time-Choir18
Scene 9

And that's the whole song. Several satellites, each shouting the time. Your phone catches the messages, measures how long each took to arrive, turns those slivers of time into distances, and crosses the bubbles until only one spot is left. No one watched you. No one tracked you. The sky just did some very fast arithmetic.

19Satellite Time-Choir
Scene 10
So next time that little blue dot says "~~you are HERE~~" with such certainty, you'll know its secret. **It's not magic,
Satellite Time-Choir20
Scene 10

So next time that little blue dot says "you are HERE" with such certainty, you'll know its secret. It's not magic, and it's not spying. It's a handful of patient satellites, a few clocks more precise than anything in your house, and the speed of light doing the math. You are here โ€” and now you know exactly how it knows.

21Satellite Time-Choir

~ finis ~

Tiny picture books for big little questions.

โ€” a small constellation of questions โ€”
โœฆWonderleaf
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