001 How GPS finds you

Summary

GPS turns time into distance: each satellite broadcasts the exact time, the delay of its signal becomes a circle, and the circles meet at you. Up in orbit those clocks gain 38 µs a day. Left uncorrected, that is roughly 10 km of error per day.

Claims 7

Each claim as said or shown in the video, with the value it states, its source and the date it was checked.

1. 01

   Claim 1: “clocks falling around the Earth at fourteen thousand kilometers an hour”; on screen 14 000 km/h

   Value

   ≈ 14 000 km/h

   Source

   P

   Checked

   2026-10-24. Cross-check: v = √(GM/r), r = 26 560 km → 3.87 km/s ≈ 13 950 km/h

2. 02

   Claim 2: “Each one keeps broadcasting the exact time”

   Value

   satellite clock time in the navigation signal

   Source

   A

   Checked

   2026-10-24

   Simplified

   The signal also carries the satellite’s orbit (ephemeris), which the receiver needs. Not mentioned.

3. 03

   Claim 3: “that delay is a distance”; on screen d = c·Δt

   Value

   1 ns ≈ 30 cm

   Source

   A

   Checked

   2026-10-24. “Timing errors of one ns will lead to positioning errors of the order of 30 cm”

4. 04

   Claim 4: “A third — and there’s only one. You.”

   Value

   3 circles meet in one point

   Source

   A

   Checked

   2026-10-24. four measurements give three position components plus the receiver clock bias

   Simplified

   Drawn in 2D. A real receiver intersects spheres and needs a fourth satellite to solve for its own clock error.

5. 05

   Claim 5: “gravity is weaker, so their clocks run fast — thirty-eight millionths of a second a day”; on screen Δt = +38 µs/d

   Value

   +38.6 µs/day net

   Source

   A, P

   Checked

   2026-10-24. A gives the net rate; P gives the parts, +45 µs/day (gravity) and −7 µs/day (orbital speed)

   Simplified

   The narration credits weaker gravity alone. 38 is the net of the +45 from gravity and the −7 from speed.

6. 06

   Claim 6: “your dot drifts ten kilometers every day”; on screen 10 km

   Value

   ≈ 10 km/day

   Source

   P

   Checked

   2026-10-24. “about 10 kilometers each day”. From A’s 30 cm/ns, c × 38.6 µs ≈ 11.6 km

   Simplified

   This is the standard back-of-envelope figure (c × clock error). A common offset shared by all satellites would partly be absorbed by the receiver’s clock solution, so the real failure mode is messier.

7. 07

   Claim 7: “So every satellite is corrected — for Einstein.”; on screen ALL CLOCKS −38 µs/d

   Value

   clock frequency set low before launch (fractional −4.465 × 10⁻¹⁰)

   Source

   A

   Checked

   2026-10-24. 10.23 MHz reference, satellite clocks offset so they read 10.23 MHz from the ground

Simplifications

As stated in the post’s caption.

Simplified and not to scale: drawn in 2D, where three circles are enough. A real receiver uses a fourth satellite to solve for its own clock error. And the 38 µs a day is a net effect: weaker gravity speeds the clocks up by about 45 µs, their orbital speed slows them by about 7.

Sources 2

1. A

   Source A: N. Ashby, “Relativity in the Global Positioning System”, Living Reviews in Relativity 6, 1 (2003). doi:10.12942/lrr-2003-1

   Claims 2, 3, 4, 5, 7

2. P

   Source P: R. W. Pogge, “Real-World Relativity: The GPS Navigation System”, Ohio State University. https://www.astronomy.ohio-state.edu/pogge.1/Ast162/Unit5/gps

   Claims 1, 5, 6

Transcript

Your phone has no idea where you are.

It just listens — to clocks falling around the Earth at fourteen thousand kilometers an hour.

Each one keeps broadcasting the exact time. Your phone hears it a little late — and that delay is a distance.

One satellite puts you somewhere on this circle. A second leaves just two places you could be. A third — and there’s only one. You.

But up there, gravity is weaker, so their clocks run fast — thirty-eight millionths of a second a day. Ignore that, and your dot drifts ten kilometers every day. So every satellite is corrected — for Einstein.

Your phone doesn’t know where you are. It knows when.

Timing