1. Your phone only listens: satellites broadcast their position and the time
About 20,200 km (12,550 miles) above you, in what is called medium Earth orbit, the GPS satellites circle the planet twice a day. The U.S. commits to keeping at least 24 of them working, arranged so that you can see at least four from almost anywhere on Earth[1].
Each satellite does something very simple. It keeps broadcasting two things by radio: where it is, and what time its clock says[3]. That is all. It does not know you exist, and your phone sends nothing back. It only listens.
2. How a signal's travel time becomes a distance
Your receiver checks its own clock and sees that the "time sent" on the signal is slightly in the past. Radio waves travel at the speed of light, about 300,000 km per second (186,000 miles per second), so that gap is a distance in disguise. A satellite straight overhead is about 20,200 km away, so its signal takes roughly a fifteenth of a second to arrive. Multiply the delay by the speed of light, and you know how far away that satellite is.
One distance is not a location. It only says you are somewhere on a huge sphere centered on that satellite. Add a second satellite and the spheres overlap in a circle. A third cuts the circle down to two points, and one of them is usually out in space. You can try a flat, paper version of this in the last section.
3. Why a phone needs a fourth satellite
Three distances pin down a spot. So why does GPS need four satellites?
Because the travel time has to be measured with a clock, and the math assumes your receiver knows the time exactly. A phone's clock is nowhere near good enough. Neil Ashby, a physicist at the University of Colorado who wrote a well-known explanation of GPS for students, points out that an error of just 3 nanoseconds (3 billionths of a second) would move your position by about 1 meter (3 feet)[3]. By the same arithmetic, a one-millionth-of-a-second mistake would put you about 300 meters (1,000 feet) off.
The fix is clever. Treat your own clock error as one more unknown. Signals from at least four satellites give four equations, enough to solve for your three position coordinates and the exact time[3]. The fourth satellite is not a spare. It lets a cheap clock in your pocket borrow the accuracy of the atomic clocks in orbit.
4. Why GPS satellite clocks need Einstein's relativity
The atomic clocks in orbit have to be extraordinary. Ashby notes that good GPS satellite clocks keep time to within a few parts in 1014 over a day[3]. That is like a clock that drifts by about a second only every few million years.
With clocks this good, a strange fact from physics becomes a practical problem. Einstein's theories say that clocks run at slightly different speeds depending on gravity and motion. A satellite clock is farther from Earth's gravity, which makes it tick faster. It also moves fast, which makes it tick slower. The two effects do not cancel. Ashby calculates that, if ignored, the gravity effect alone would add up to a navigation error of 13.7 km per day, while the motion effect would pull back 2.13 km per day[3]. Subtract, and you are left with about 11.6 km (7 miles) of drift every day.
The engineers' answer was to adjust the clocks before launch. Older satellites had their atomic clock frequencies set slightly lower, by a "factory frequency offset" of 4.4647 parts in 10 billion[3]. In Ashby's words, the relativistic effects add up to a total about 10,000 times too large to ignore[3]. So the next time your phone finds a coffee shop, remember that it is quietly using relativity to do it.
5. How a military navigation system became a tool for everyone
GPS began as a U.S. military project. The Pentagon (the U.S. defense department) pulled separate service programs into one in the 1970s, and a prototype satellite launched in 1978[6]. The Air Force built in a feature called Selective Availability, which gave approved military users a stronger, more precise signal than everyone else[6]. For civilians, that meant being guaranteed only a position within about 100 meters (330 feet) of where the receiver said[5].
Then came 1990, when American forces deployed to the Arabian desert, a landscape with no roads, hills, or signs to navigate by. According to one account, drivers began getting lost by more than 10 miles (16 km), and soldiers who had shrugged off a new navigation gadget suddenly demanded it[4]. There was also a shortage. To get hand-held receivers, the military had to buy modern civilian models. Only 12 GPS satellites were working, and the program office asked one company, Trimble, to deliver as many receivers as it could make[4].
In May 2000, at the direction of U.S. President Bill Clinton, the government stopped using Selective Availability. The announcement was made on May 1, and the degradation ended a few minutes past midnight that night, Eastern time[5]. The Commerce Department's statement said the predicted error for civilians would drop to about 20 meters (66 feet), and it expected the GPS market to more than double within three years[5]. The government says it has no intention of ever using Selective Availability again[5].
Today GPS.gov says smartphones are typically accurate to within a 4.9 m (16 ft) radius under open sky, and specialized equipment can get down to a few centimeters[2]. But the same page lists what ruins a fix: signals blocked by buildings, bridges, and trees, use indoors or underground, and signals that bounce off walls before reaching you[2].
If you want to look for yourself
- Draw your own "satellites" on paper. Mark three dots on a sheet, label them A, B, and C, and have a friend secretly pick a spot on the page to be "you." The friend tells you only the distance from that spot to each dot. Use a compass (or a string and pencil) to draw a circle around each dot with that distance as the radius, and look for where they meet. Then make one distance a little wrong and see what happens. That wobble is the clock problem in miniature.
- Watch the blue dot when you are a passenger. If you are riding in a car or bus (not driving), open a map app and watch the dot. Many apps also show a pale circle around it, a rough sign of how uncertain the position is. See whether that circle grows on a street with tall buildings, under a bridge, or inside a tunnel, and shrinks again in an open park. Ask an adult before changing any phone settings.
- Read the original. Ashby's paper, "Relativistic Effects in the Global Positioning System," is written to introduce relativity to college students who are not physics majors, and it shows the calculations behind Section 4. GPS.gov also has short pages on accuracy and on how the satellites are arranged.