Your turn
Each lab is one step from the video. Change things and see what happens.
Each lab isolates one step. The models are flat 2D sketches of a 3D problem, simplified to show the idea.
Tap the buttons and drag the dots.
Switch the satellite signals off. What happens to the blue dot?
The phone transmits nothing. Cut the incoming satellite signals and see whether it can still fix its position.
Turn the satellites off. Can the phone still find you?
Drag the pin around Earth. Are there always at least four satellites above you?
Move the observer around the globe. Six orbital planes keep at least four satellites above the horizon almost everywhere.
Move the red dot around the world. Count the satellites above it.
Simplified: a flat 2D view of the orbits, not to scale.
Drag the satellite up and down. How does the signal delay change?
Change the range and watch the travel time: range = time × speed of light.
Move the satellite. Does the message come sooner or later?
The distances here are shrunk to fit the picture; the numbers are real.
Drag the blue dot, then pick 1, 2 or 3 satellites. How many does it take to pin down one spot?
With one range you are on a circle, with two on one of two points, with three on a single point. Drag the receiver and compare.
Pick 1, 2 or 3 satellites. When do the circles meet in just one spot?
Add clock error with the slider, then switch on the 4th satellite. What happens to the dot?
A receiver clock bias adds the same range error to every satellite. Add bias, then add a fourth range so the solver can estimate it.
Map scale: 1 microsecond of clock error ≈ 300 m.
Switch the tall buildings and the Wi-Fi and cell helpers on and off. When is the dot most accurate?
Blocked and reflected (multipath) signals degrade the fix among tall buildings; Wi-Fi, cell and sensor data help. Compare the cases.
Turn the buildings and the helpers on and off. When does the dot sit still?
Halo sizes are illustrative, except the ~5 m open-sky figure.
GPS helps a phone show a little blue dot on a map. That dot is you! But how does the phone know where you are?
High above Earth, lots of satellites fly around and around the world. Each one carries a super careful clock. Each one calls out, again and again: "Here I am, and here is the time!"
Your phone never talks to the satellites. It only listens, like a boat watching a lighthouse. The satellites can't see you.
If a friend far away shouts to you, you hear it a moment later. The farther away they are, the later it gets to you. The phone checks how late each satellite message is. That tells it how far away each satellite is.
Knowing how far one satellite is puts you somewhere on a big circle. Two satellites make two circles, and they cross in two spots. A third circle narrows it to one spot, and a fourth satellite fixes your phone's clock. That's you!
GPS (the Global Positioning System) is a group of about 31 satellites circling Earth about 20,200 km (12,550 miles) up.2 Each satellite carries atomic clocks and keeps broadcasting a simple message: where it is and exactly what time it is.16 Your phone listens for those messages. From how long each one took to arrive, it works out how far away each satellite is.16 With distances to four or more satellites, it can find the one spot on Earth that fits, plus the exact time.9
The surprising part: your phone never sends anything to the satellites. GPS satellites are one-way beacons, like lighthouses.7
GPS is a U.S.-owned system run by the U.S. Space Force. It has three parts, called segments:1
| Segment | What it is | What it does |
|---|---|---|
| Space | About 31 satellites in six orbital rings2 | Broadcast their position and the time |
| Control | A master control station, 11 command antennas and 16 monitoring sites around the world3 | Track the satellites, adjust their clocks and upload fresh navigation data |
| User | Receivers in phones, cars, watches, planes and farm tractors | Listen to the signals and calculate position and time1 |
Each satellite goes all the way around Earth twice a day (once every 11 hours 58 minutes).210 They are not parked over one spot like TV satellites. The six rings are arranged so that at least four satellites are in view from almost anywhere on the planet.2
Imagine a friend far away shouts "It's twelve o'clock!" You hear it a moment late, because sound takes time to travel. If you knew exactly when they shouted and how fast sound moves, you could work out how far away they are.
GPS does the same thing with radio waves, which travel at the speed of light: 299,792,458 metres per second, or about 300,000 km every second.5 Each message says when it was sent. Your phone notes when it arrived. Then:
distance = travel time × speed of light
A signal from a satellite straight overhead, about 20,200 km away, takes roughly 0.067 seconds (67 thousandths of a second) to reach you: 20,200 km ÷ 300,000 km/s.25 Satellites lower in the sky are farther away, so their signals take a little longer, but always less than a tenth of a second.9
One distance isn't enough. If you know you're 20,200 km from one satellite, you could be anywhere on a giant sphere around it. (On a flat map, that's a circle.)5
This is called trilateration, which literally means "positioning from distances".5 It's often called triangulation, but triangulation really means using angles, and GPS uses distances. In real space the circles are spheres, but the idea is the same. NOAA even made a classroom version where you find your position on a map with four pieces of string.5
Three distances would be enough if your phone had a perfect clock. It doesn't. The satellites carry atomic clocks, which keep time using a frequency set by atoms of rubidium or cesium that is the same everywhere in the universe.1014 Your phone has a cheap quartz clock, and quartz drifts much more.14
Timing errors matter a lot, because light is so fast. If your phone's clock is off by just one millionth of a second (one microsecond), light travels about 300 metres in that time, so every distance comes out about 300 metres wrong.5 The circles no longer meet at one point.
The clever fix is to listen to a fourth satellite. Your phone's clock error is the same for every signal, so it's just one more unknown. With four distances, the receiver can solve for four unknowns at once: its position in three directions (east-west, north-south and up-down) and its own clock error.9 As a bonus, your phone ends up knowing the time to within a tiny fraction of a second.6 In practice phones use many more than four satellites when they can see them, often 6 to 12.11
GPS is one of the few everyday machines that only works because engineers take Einstein seriously.11
Together, satellite clocks run fast by about 38 microseconds a day compared with clocks on the ground. That sounds tiny, but if nobody corrected for it, GPS positions would drift by about 10 km every day. So the satellite clocks are built to tick very slightly slow, and receivers do the rest of the maths.11 Want to know why gravity changes time at all? See how gravity works, and for why the speed of light is the key number, how light travels.
| Effect | Why | Change per day |
|---|---|---|
| Special relativity | Satellites move fast | −7 µs |
| General relativity | Weaker gravity up high | +45 µs |
| Total | +38 µs |
Under open sky, a GPS-enabled smartphone is typically accurate to within about 4.9 metres (16 feet).4 The main things that make it worse are:4
Sometimes the GPS is fine and the map is wrong: a missing road or a business in the wrong place.4 Special receivers that use two radio frequencies and correction services can reach a few centimetres.4
No. GPS signals come straight from space, so a GPS receiver works in the middle of the ocean or on a mountain with no phone signal at all.1 But your phone does more than GPS. It also uses the positions of nearby Wi-Fi networks, mobile phone towers and its own motion sensors. This matters most indoors or between tall buildings, where GPS signals are weak.12 Cell towers on their own are rough, though: they can be off by a few thousand metres.13 Your phone also needs data to download the map itself, and that part does travel over the internet.
GPS is also a free clock for the whole planet. Receivers can find the time to within 100 billionths of a second, without owning an atomic clock.6 Phone networks use GPS time to keep their towers in step, power companies use it to synchronise the grid, and banks use it to time-stamp transactions.6
GPS was built by the U.S. Department of Defense. Its roots go back to the Sputnik era, when scientists tracked the first Soviet satellite using shifts in its radio signal (the Doppler effect). The first NAVSTAR GPS satellite launched in 1978, and the full 24-satellite system was working in 1993.8 Many people contributed. One of them, mathematician Gladys West, did work on modelling Earth's shape that helped make GPS accurate.15 Until 2000, the civilian signal was deliberately made less accurate (a feature called Selective Availability). Since then, everyone gets the full civilian service for free.9 Other countries run similar systems: Russia's GLONASS, Europe's Galileo and China's BeiDou.9 Some modern receivers can use signals from all four systems at once.10
About 31 working GPS satellites circle Earth (2023), each broadcasting its position and the exact time from its atomic clocks. Your phone measures how long each signal took to arrive, turns that time into a distance (using the speed of light), and finds the one spot that fits the distances to four or more satellites.
GPS stands for Global Positioning System. It is owned by the United States and run by the U.S. Space Force, and the civilian signal is free for anyone in the world to use.
The U.S. commits to at least 24 working GPS satellites, and has flown about 31 for more than a decade. They orbit about 20,200 km (12,550 miles) up in six rings, so at least four are in view from almost anywhere on Earth.
Three distances would be enough to pin down a position if your phone had a perfect clock. But phones have cheap quartz clocks, and an error of one millionth of a second shifts every distance by about 300 metres. A fourth satellite lets the phone solve for its own clock error as well as its position.
No. GPS signals come straight from the satellites, so a receiver works anywhere with a clear view of the sky. Phones do use mobile data, Wi-Fi and cell towers to download maps and to find your position faster, especially indoors.
No. GPS satellites are one-way beacons, like lighthouses. They only send signals and receive nothing from your phone. Apps or phone companies can share your location, but the GPS satellites themselves can't see you.
Under open sky, a GPS-enabled smartphone is typically accurate to within about 4.9 metres (16 feet). Tall buildings, bridges and trees make it worse by blocking signals or bouncing them. Special survey receivers can get down to a few centimetres.