Fog over Alsea Bay at dusk with fishing boats and the bridge receding into mist

Anchors & Algorithms / Boat electronics / Relativity

Einstein in the wheelhouse.

A charter boat off Newport can hold a fix to a few meters because clocks in orbit do not keep the same time as clocks at sea level, and GPS was built around that fact rather than in denial of it.¹²

The quiet scandal

Most people trust GPS the way they trust a light switch. Tap it, and the thing works. The strange part is that it works only because the system keeps admitting that time itself slips between the boat and the satellites.

GPS satellites carry atomic clocks, and the system uses those clocks to time radio signals that let a receiver solve for position and time.² The satellites orbit about 20,000 kilometers above Earth’s surface, with periods of 11 hours and 58 minutes, and the system is arranged so a user on Earth can usually see at least four above the horizon.²

If those clocks were treated as if orbit were just a higher room with better weather, the system would fail. NIST states that special relativity makes GPS satellite clocks fall behind Earth clocks by about 7 microseconds per day, while general relativity makes them run faster by about 45 microseconds per day, for a net gain of 38 microseconds per day in orbit.¹

Speed

−7 μs

Motion through orbit slows the satellite clocks relative to clocks on Earth.¹

Gravity

+45 μs

Weaker gravity in medium Earth orbit lets those same clocks run faster than clocks near sea level.¹

What remains

+38 μs

That daily mismatch is the difference between a working chartplotter and a system that drifts away from you.¹²

The chalkboard part

This is the whole argument in one line: light has a speed, the clocks stamp the signal, and the receiver turns time into distance.

From transmission time to range

|r − r_i| = c(t − t_i)

Ashby writes the core GPS propagation-delay equations in exactly this form: the distance from receiver to satellite equals the speed of light multiplied by the difference between reception and transmission times.²

He also notes that a receiver needs four simultaneous equations because it must solve for three spatial coordinates and its own clock offset.²

That is why GPS feels so ordinary while being built on something severe. It is not measuring place directly. It is measuring time, then multiplying by the speed of light, then trusting the clocks enough to turn nanoseconds into where your hull is right now.²

Ashby points out that if navigation errors larger than a meter are to be avoided, an atomic clock must stay within about 4 nanoseconds of perfect synchronization with the others.² That is the scale where theory stops being philosophy and starts becoming helm work.

How a fix appears

The icon on the screen looks calm because a lot of geometry is happening out of sight.

Four signals, one boat, one hidden clock error.

GPS receivers compare their own clock with the transmission times encoded by the satellites and measure pseudoranges from those differences.² Four satellites are enough because the receiver is solving not only for latitude, longitude, and height, but for its own clock bias as well.²

Atomic clocks are not decoration.

Ashby calls modern atomic clocks the reason accurate navigation is possible and writes that only atomic clocks have the stability required for the system.²

The system is corrected, not lucky.

NIST says the engineers who launched GPS realized they had to correct for relativity to provide accurate time on Earth.¹ Ashby adds that orbit and clock data are continuously monitored, computed on the ground, and uploaded back to the satellites for retransmission to users.²

What happens if you lie

Pretend relativity does not matter, and the error is not poetic. It is navigational.

Ashby writes that if the relativistic effects were not corrected, satellite clock errors building up in one day would cause navigational errors of more than 11 kilometers, quickly making the system useless.² NIST gives the same story in a shorter form: the clocks in GPS satellites run 38 microseconds per day faster than Earth clocks, so the system must correct for that mismatch.¹

For a boater, that means the price of bad physics is not an abstract disagreement with Einstein. It is a wrecked waypoint, a track line that no longer lands where yesterday’s line did, and a machine that slowly drifts out of trust.

The useful surprise

The elegant part is not that relativity makes GPS difficult. It is that the system works because the builders accepted that difficulty and designed around it.

The result is a strange kind of everyday grace. Each fix on a chartplotter is a small agreement between atomic clocks, orbit mechanics, the speed of light, and the fact that gravity touches time.¹²

So the next time the boat settles on a number and the cursor holds still, the right thought is not that electronics are magic. The right thought is that Einstein is onboard, and the machine is honest enough to admit it.

References

National Institute of Standards and Technology. Putting Einstein to the Test. NIST; 2025. Available from: https://www.nist.gov/atomic-clocks/a-powerful-tool-for-science/putting-einstein-test ↩
Ashby N. Relativity and the Global Positioning System. Physics Today; 2002. Available from: http://webs.ftmc.uam.es/juancarlos.cuevas/Teaching/GPS_relativity.pdf ↩