GPS turns space-based astronomy into everyday navigation by using satellites as very accurate moving clocks. A phone or receiver finds its position by measuring how long radio signals take to travel from several satellites in orbit. Because radio waves move at the speed of light, tiny timing differences become distance measurements.
This matters because maps, aircraft, ships, farming equipment, and emergency services all depend on precise location and time.
Key Facts
- Signal distance is found with d = ct, where c = 3.00 x 10^8 m/s.
- GPS satellites orbit about 20,200 km above Earth in medium Earth orbit.
- A receiver needs signals from at least 4 satellites to solve for 3 position coordinates and clock error.
- Each satellite broadcasts its position and the exact time the signal was sent.
- A 1 nanosecond timing error causes about 0.30 m of distance error.
- Relativity corrections are needed because satellite clocks run differently due to speed and weaker gravity.
Vocabulary
- Trilateration
- Trilateration is the method of finding a position by measuring distances from several known points.
- Atomic clock
- An atomic clock is an extremely precise clock that uses atomic vibrations to keep time.
- Medium Earth orbit
- Medium Earth orbit is the region of space between low Earth orbit and geostationary orbit where GPS satellites travel.
- Pseudorange
- A pseudorange is the measured satellite distance that includes error from the receiver clock.
- Relativistic correction
- A relativistic correction is an adjustment for changes in clock rate caused by motion and gravity.
Common Mistakes to Avoid
- Using only one satellite to find a location, which is wrong because one distance only places the receiver somewhere on a sphere around that satellite.
- Forgetting the receiver clock error, which is wrong because phones do not contain atomic clocks and their time offset changes all distance measurements.
- Treating GPS signals as instant, which is wrong because even light-speed radio waves take measurable time to travel from orbit to Earth.
- Ignoring satellite motion, which is wrong because satellites move several kilometers per second while signals are traveling.
Practice Questions
- 1 A GPS signal takes 0.0700 s to travel from a satellite to a receiver. Using c = 3.00 x 10^8 m/s, what is the signal distance in kilometers?
- 2 A receiver clock is late by 20 ns. About how much distance error does this create, using c = 3.00 x 10^8 m/s?
- 3 Explain why a GPS receiver usually needs four satellites instead of three, even though three distances can locate a point in three-dimensional geometry.