The Global Positioning System (GPS) lets a phone or car work out where it is from radio signals sent by satellites about 20,200 kilometers overhead. This explainer covers how the system is built, how a receiver turns timing signals into a position, and why it depends on corrections from Einstein’s special and general relativity.

1. Three parts of one system

According to GPS.gov, which is maintained by the National Coordination Office for Space-Based Positioning, Navigation, and Timing, GPS is a US-owned utility that provides positioning, navigation and timing services through three segments. The space segment is the satellites. The control segment is a worldwide network of monitor and control stations that keeps the satellites in their proper orbits, adjusts the satellite clocks and uploads updated navigational data. The user segment is the receiver equipment. The US Space Force operates the space and control segments, and the civilian service is free to all users worldwide.

2. The satellites

GPS satellites fly in medium Earth orbit at an altitude of approximately 20,200 km (12,550 miles), and each circles Earth twice a day, according to the GPS.gov space segment page. They are arranged in six equally spaced orbital planes. This 24-slot arrangement ensures users can see at least four satellites from virtually any point on the planet. The United States commits to keeping at least 24 operational satellites available 95% of the time; as of July 3, 2023, there were 31 operational satellites in the constellation.

3. How a receiver finds itself

Each satellite transmits one-way signals giving its current position and the time. A receiver uses that information to calculate its own three-dimensional position and time. Physicist Neil Ashby of the University of Colorado, Boulder, explains in a 2003 review in Living Reviews in Relativity that the method rests on the constancy of the speed of light: pulses from four synchronized atomic clocks at known positions give four equations that can be solved for the receiver’s position and the time of reception.

That is why timing matters so much. Ashby writes that a timing error of one nanosecond leads to a positioning error on the order of 30 cm. Astronomer Richard Pogge of Ohio State University puts the requirement at 20 to 30 nanoseconds of accuracy in the satellite clock ticks.

4. Where relativity comes in

The satellites carry atomic clocks, and two relativistic effects push those clocks out of step with clocks on the ground. Pogge’s explanation, which draws on Ashby’s calculations, sets out the numbers:

  • Special relativity: the satellites travel at about 14,000 km per hour relative to observers on Earth, so their clocks tick more slowly and fall behind ground clocks by about 7 microseconds per day.
  • General relativity: clocks farther from a massive object tick faster than those closer to it, so the satellite clocks, high above Earth, gain about 45 microseconds per day.
  • Net effect: the satellite clocks run fast by about 38 microseconds, or 38,000 nanoseconds, per day.

Left uncorrected, Pogge writes, a navigational fix would be false after only two minutes, and position errors would keep growing by about 10 kilometers each day. Ashby’s abstract makes the same point: the clocks’ gravitational and motional frequency shifts are so large that, “without carefully accounting for numerous relativistic effects, the system would not work.”

5. How the correction is built in

Engineers handle most of the problem before launch. Pogge explains that the onboard clocks were designed to tick at a slower frequency than ground reference clocks, so that once in orbit they tick at about the correct rate. Ashby describes the uncorrected orbiting clock as “beating too fast, primarily because its frequency is gravitationally blueshifted.”

Some corrections are left to the receiver. Ashby notes that for a satellite whose orbit has an eccentricity of 0.01, meaning it is slightly non-circular, one relativistic term reaches about 23 nanoseconds and must be corrected by the receiver. Pogge adds that receivers make such calculations using data provided by the satellites.

Common problems

When GPS puts a user in the wrong place, relativity is not the culprit. The GPS.gov accuracy page lists the usual causes:

  • Blocked or reflected signals. Buildings, bridges and trees block signals, indoor or underground use cuts them off, and signals bouncing off walls (called multipath) mislead receivers. GPS-enabled smartphones are typically accurate to within a 4.9 m (16 ft) radius under open sky, but accuracy worsens near buildings, bridges and trees.
  • Bad maps, not bad positioning. In many cases the GPS hardware works fine and the mapping software is faulty, with incorrectly drawn maps, mislabeled businesses or missing roads. The US government cannot correct mapping errors in consumer devices.
  • Rarer causes. Radio interference or jamming, major solar storms, satellite maintenance and devices that do not comply with GPS specifications.
  • Confusing signal accuracy with user accuracy. The government commits to a global average user range error of 2.0 m (6.6 ft) or less, 95% of the time; on April 20, 2021, the figure was 0.643 m (2.1 ft) or less. GPS.gov stresses this is not the accuracy a user sees, which also depends on satellite geometry, the atmosphere and receiver quality. Receivers that use two GPS frequencies correct atmospheric distortions and can do better.

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