The Global Positioning System, or GPS, is a constellation of navigation satellites that lets receivers find their position almost anywhere on Earth. Each satellite carries precise atomic clocks and broadcasts its location and the exact time the signal was sent. By comparing that send time with the receive time, a GPS receiver computes how far away the satellite is.
This matters for mapping, transportation, emergency response, farming, science, and everyday navigation.
Understanding Astronautics: The GPS Constellation
A navigation receiver does more than measure travel time. It must identify which satellite sent each signal and know where that satellite was at that moment. Satellites send a coded radio pattern, so the receiver can match the incoming pattern with a copy it generates internally.
The shift between the two patterns gives the travel time. The message includes orbital data called ephemeris data.
This lets the receiver calculate the satellite position instead of treating it as fixed in space. Ground control stations continually track the satellites and send updated orbit and clock information to them.
The fourth satellite signal is needed because the receiver clock is not as accurate as the clocks carried in orbit. A phone or car receiver uses a small quartz clock, which gains or loses time slightly. Even an error of a tiny fraction of a second would create a very large distance error because radio waves move so fast.
The receiver solves for its location and one shared clock correction at the same time. This is a clever part of the system. It allows ordinary receivers to work without needing their own atomic clocks.
Several effects can make a calculated position less accurate. The signal slows a little as it passes through Earth’s upper atmosphere and through water vapour lower down. Buildings, cliffs, and trees can block signals or reflect them.
A reflected signal travels farther before reaching the receiver, so it appears to come from a more distant satellite. This effect is called multipath. Satellite geometry matters too.
Signals arriving from widely separated parts of the sky give a stronger position calculation than signals clustered in one direction. Receivers estimate these errors using models, repeated measurements, and information from augmentation systems where available.
Relativity is part of the design, not just a theory from textbooks. Motion makes a satellite clock run slightly slow compared with a clock on Earth. The weaker gravity high above Earth makes it run faster.
The gravity effect is larger, so without correction the satellite clocks would drift enough to cause major navigation errors each day. Engineers adjust the clock rates and apply further corrections in the receiver calculations. When learning this topic, keep the ideas separate.
A signal gives a distance estimate, multiple distance estimates locate a point, and timing corrections make those estimates trustworthy. Notice that GPS is not a satellite taking a picture of a phone. The receiver mainly listens, calculates, and can find its location without sending its position to the satellites.
Key Facts
- GPS satellites orbit in medium Earth orbit at about 20,200 km above Earth's surface.
- Distance from a satellite is found from signal travel time: d = cΔt.
- The speed of GPS radio signals is approximately the speed of light: c = 3.00 × 10^8 m/s.
- A receiver needs signals from at least 4 satellites to solve for x, y, z position and clock error.
- Orbital period for a circular orbit is T = 2π√(r^3/GM).
- GPS uses trilateration, finding position from the intersection of distance spheres around satellites.
Vocabulary
- GPS constellation
- A coordinated group of navigation satellites arranged in orbit so that multiple satellites are visible from most places on Earth.
- Medium Earth orbit
- An orbital region above low Earth orbit and below geostationary orbit, used by GPS satellites at about 20,200 km altitude.
- Atomic clock
- A highly precise clock that uses atomic vibrations to keep time accurately enough for satellite navigation.
- Trilateration
- A method of finding position by using measured distances from several known points.
- Pseudorange
- The apparent distance from a GPS satellite to a receiver, calculated from signal travel time but still affected by receiver clock error and other delays.
Common Mistakes to Avoid
- Confusing trilateration with triangulation is wrong because GPS mainly uses distances from satellites, not measured angles between directions.
- Using only three satellites for full GPS positioning is wrong because the receiver clock is not as accurate as satellite atomic clocks, so a fourth satellite is needed to correct time error.
- Ignoring the speed of light units is wrong because a tiny timing error creates a large distance error, such as 1 microsecond corresponding to about 300 m.
- Assuming GPS satellites are geostationary is wrong because GPS satellites orbit Earth about twice per sidereal day and move across the sky relative to a ground receiver.
Practice Questions
- 1 A GPS signal takes 0.0700 s to travel from a satellite to a receiver. Using c = 3.00 × 10^8 m/s, what is the signal path distance in kilometers?
- 2 A receiver clock is off by 2.0 microseconds. About how much range error does this create if the signal travels at 3.00 × 10^8 m/s?
- 3 Explain why a GPS receiver usually needs four satellite signals instead of three to determine an accurate three-dimensional position.