Your phone finds itself with the SIM out and no internet, because GPS is one-way: it never transmits, it only listens. Around 30 satellites circle 20,200 km above the surface, sweeping across the sky twice a day, each carrying an atomic clock and broadcasting the same three things — who I am, where I am, when I sent this. The phone compares the timestamp with its own clock, multiplies the difference by the speed of light, and turns each satellite into a sphere it must be standing on. Three spheres would be enough with a perfect clock; the phone has a cheap quartz one, so a fourth satellite solves the clock error as a fourth unknown alongside x, y and z. This interactive walkthrough builds that whole chain, from a fable about letters in a small town to the relativistic corrections without which every measured distance would gain 11.6 km of error a day.
Each GPS satellite broadcasts its own position and the exact time it sent the message. Your phone measures how long the message took to arrive and multiplies by the speed of light, which gives its distance to that satellite — placing it somewhere on a sphere around it. Four such spheres intersect at a single point, and that point is your position.
Three distances would be enough if your phone had a perfect clock, because a position has only three unknowns: x, y and z. But a phone's quartz clock is off by far more than the nanoseconds this measurement needs, and that error shifts all three spheres together, so the fix looks perfectly clean while being kilometres wrong. A fourth satellite adds a fourth equation, which lets the receiver solve for the clock error as a fourth unknown — and as a side effect your phone ends up knowing atomic time.
Yes. GPS is receive-only — your phone never sends anything to the satellites, it just listens to signals that are broadcast to everyone. What needs internet is the map you draw the position on, not the position itself. Offline maps plus GPS work in airplane mode, in the desert, and with the SIM removed; the first fix just takes longer, because a connected phone normally gets a head start from assistance data over the network.
The satellites carry atomic clocks that do not tick at the same rate as a clock on the ground. Compared with that ground clock, timed in the Earth-centred frame, special relativity makes them run about 7.2 µs per day slow because they move at roughly 3.87 km/s, while general relativity makes them run about 45.8 µs per day fast because they sit higher in Earth's gravitational field. The net effect is +38.6 µs per day, and since one microsecond of timing is about 300 m of distance, an uncorrected system would put about 11.6 km of error into every measured range each day — and because the satellites do not drift in step with each other, the fix falls apart rather than simply sliding. The fix for it is built in: the satellite's oscillator is deliberately set slightly low before launch, and the receiver applies the remaining, orbit-dependent terms itself.
No — it is trilateration. Triangulation measures angles to known landmarks; GPS never measures an angle at all. It measures travel times, converts them into distances, and intersects the resulting spheres.
Two different errors. The ionosphere delays every signal a little — similarly for satellites high in the sky, more for low ones whose signal slants further through it — so the shared part of it is absorbed by the clock error the receiver already solves for, and only the mismatch survives. A tall building is worse: it blocks the direct view of a satellite, so what arrives is a reflection off a wall that travelled further, making that one range read too long. That single wrong distance drags the fix around as you walk — which is why the dot pins sharply on an open beach.