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.
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.