Your phone runs on Einstein
Why the blue dot on your map would be kilometres off by tomorrow without relativity.
Twenty thousand kilometres above you, about thirty satellites circle the Earth twice a day. Each one carries an atomic clock. Your phone never talks to them. It only listens, and from what it hears it works out where you are to within a few metres.
That trick only works because the clocks agree to within billionths of a second. And keeping them in agreement means taking Einstein seriously, twice over.
The constellation
This is the GPS constellation drawn to scale: six tilted orbital rings with at least four satellites each, all at about 20,200 km up. The glowing dot is you. The lines are the satellites you can “hear” right now.
What a satellite says
Each satellite keeps broadcasting the same two facts: where it is and what time it is, read from its onboard atomic clock. That’s all it sends.
Time becomes distance
The signal travels at the speed of light, so it arrives a little late, about 0.07 seconds. Your phone compares the timestamp with its own clock. Delay × speed of light = distance to that satellite.
Where the circles meet
One distance puts you somewhere on a huge sphere around one satellite. A second and third sphere narrow it to a single point. (A fourth satellite lets your phone fix the error of its own cheap clock.)
The catch
Light covers about 30 centimetres in a billionth of a second. So if a satellite’s clock is off by just one millionth of a second, its distance is off by 300 metres, and the circles no longer meet.
Einstein, part one: speed
Satellites move at about 3.9 km/s. Special relativity says a moving clock ticks slower than one at rest. For a GPS satellite that adds up to roughly 7 microseconds lost per day.
Einstein, part two: gravity
General relativity says clocks tick faster where gravity is weaker. Up in orbit, far from Earth’s mass, the satellite clock gains about 45 microseconds a day, which more than wins the tug-of-war.
The net effect
Together, the satellite clocks run 38 microseconds a day fast compared with clocks on the ground. That sounds like nothing, but remember that every microsecond is 300 metres.
One day without Einstein
Left uncorrected, 38 microseconds of drift each day becomes about 11 kilometres of range error, growing by about the same amount every day after.
The fix
So engineers slow the clocks down before launch. Each one is set to tick at 10.22999999543 MHz instead of 10.23 MHz. Once in orbit, relativity speeds it up to exactly the right rate.
Hidden in plain sight
Every time your map finds you, two of the strangest ideas in physics are quietly being proven right: moving clocks run slow, and gravity bends time. The correction is built into hardware launched into space, on the assumption that Einstein was right. So far he has been.
Go deeperThe exact numbers
The rate change of a satellite clock compared with a clock on the ground (on the geoid) has two parts:
Δf/f ≈ (Φ_ground − Φ_sat)/c² − v²/2c²
The gravitational term is about +5.3 × 10⁻¹⁰ (≈ +45.7 µs/day). The velocity term is about −0.83 × 10⁻¹⁰ (≈ −7.2 µs/day). The net is +4.465 × 10⁻¹⁰, or 38.6 µs per day. Applying that fraction to the 10.23 MHz reference gives the factory setting of 10.22999999543 MHz.
GPS orbits are also slightly elliptical. With an eccentricity of 0.02 that adds a periodic error of up to about 45.8 ns, which your receiver corrects in software. Earth’s rotation (the Sagnac effect) needs correcting too.
Go deeperWould GPS really drift 11 km a day?
The “about 10 km a day” figure is the standard way to show how big the effect is: 38 µs × the speed of light ≈ 11.4 km. Ashby gives roughly 13.7 km/day for gravity alone and 2.1 km/day for velocity alone.
Real behaviour would be messier. Your receiver already solves for its own clock offset (that’s the fourth satellite), so part of a drift shared by every satellite would be absorbed. But the satellites would fall out of step with ground time and with the orbit predictions they broadcast, and accuracy would collapse quickly. Either way, GPS doesn’t work without the correction.