Scrub the day counter and toggle the relativistic correction to watch a GPS satellite's real -7 and +45 microsecond-per-day clock effects fight each other, and see the position-error budget that follows.
Every GPS satellite clock runs slightly fast on purpose - by design, ground engineers built the offset in before launch, once relativity told them how much drift to expect. Drag to orbit and scroll or pinch to zoom on the scene above.
For the pure gravitational clock-rate effect on its own, without the orbital-velocity effect layered in, see the Gravitational Redshift 3D Explorer.
GPS Time Dilation 3D Explorer
This browser explorer places a GPS satellite in orbit around Earth and totals up the two real relativistic effects fighting inside its onboard clock every single day.
A GPS satellite orbits at about 20,200 km altitude, moving at about 3.874 km/s (about 14,000 km/h). Special relativity says a fast-moving clock ticks slower than a stationary one, so the satellite's motion alone would make its clock lose about 7 microseconds per day relative to a ground clock. General relativity says a clock sitting in weaker gravity ticks faster, and at GPS altitude that effect adds about 45 microseconds per day. The two effects do not cancel: general relativity wins, and the satellite clock runs a net 38 microseconds per day fast. GPS satellite clocks are built with that 38-microsecond-per-day offset corrected in firmware before launch, once engineers calculated it from relativity. Left uncorrected, this net drift would accumulate into GPS position-fix errors of roughly 10 kilometers per day - a phone or car navigation system would drift further off the actual road with every day the correction stayed off. These figures come from Neil Ashby's widely cited paper "Relativity in the Global Positioning System" (Living Reviews in Relativity, 2003), corroborated by NASA and US Naval Observatory GPS timing documentation.
- Scrub the day counter (0-30 days) to accumulate the drift
- Toggle the relativistic correction on or off to compare a corrected system against an uncorrected one
- Watch the satellite's beacon change color as the position-error estimate grows
- Facts panel cites the real -7, +45, and +38 microsecond-per-day figures and the roughly 10 km/day uncorrected error
- Drag to orbit, scroll or pinch to zoom
- Runs fully in the browser with the vendored three.js engine - no account, no upload
| Relativistic effect | Rate | Direction |
|---|---|---|
| Special relativity (satellite velocity) | -7 microseconds/day | Clock runs slower |
| General relativity (weaker gravity at altitude) | +45 microseconds/day | Clock runs faster |
| Net effect (uncorrected) | +38 microseconds/day | Clock runs fast overall |
| Resulting position error if left uncorrected | about 10 km/day | Accumulates every day |
For the pure gravitational clock-rate effect studied on its own, without the orbital-velocity effect layered on top of it, open the Gravitational Redshift 3D Explorer.
Everything renders on your device with WebGL. The 3D engine loads once (about 0.7 MB) and is cached.
This is an educational approximation - the orbit radius and Earth size on screen are compressed for readability, not a to-scale orbital-mechanics or GPS-firmware simulation. The four relativity figures shown (-7, +45, +38 microseconds/day, and the roughly 10 km/day uncorrected error) are the real published values; every day-by-day total on screen is simple arithmetic (day count times that real per-day rate).
Frequently Asked Questions
Why do GPS satellite clocks need a relativistic correction?
Special relativity slows a fast-moving clock by about 7 microseconds per day, while general relativity speeds up a clock in weaker gravity by about 45 microseconds per day. At GPS altitude both effects act at once, and general relativity wins by a net 38 microseconds per day.
How fast does a GPS satellite move, and how high does it orbit?
About 20,200 km altitude, moving at about 3.874 km/s (about 14,000 km/h).
What happens if the relativistic correction is turned off?
The uncorrected 38-microsecond-per-day clock drift accumulates and would cause GPS position-fix errors of roughly 10 kilometers per day.
Is the correction applied in software after launch?
No - GPS satellite clocks are built with the 38-microsecond-per-day offset corrected into their firmware before launch, once engineers calculated the expected drift from relativity.
Where do these numbers come from?
Neil Ashby's paper "Relativity in the Global Positioning System" (Living Reviews in Relativity, 2003), corroborated by NASA and US Naval Observatory GPS timing documentation.
How is this different from the Gravitational Redshift explorer?
The Gravitational Redshift 3D Explorer demonstrates the pure gravitational clock-rate effect in isolation. This page is the applied engineering budget where both the velocity (special relativity) and altitude (general relativity) effects fight inside a real GPS satellite's clock at the same time.
Is the on-screen orbit to scale?
No - the orbit radius and Earth size are compressed for readability. The four relativity figures (-7, +45, +38 microseconds/day, and the roughly 10 km/day uncorrected error) are the real published values; the day-by-day totals shown are simple arithmetic from that real per-day rate.