Navigation and GPS

Algebra 2 · Axiom Academy

Your phone never measures where you are — it measures a time DIFFERENCE between two signals. That difference alone traces a hyperbola. Two ground stations time the same signal: 22,000 km to Station A, 24,000 km to Station B — a difference of exactly 2,000 km . That one number doesn't pin down a point. It pins down a curve. One measurement, a whole curve of guesses Drag the receiver anywhere along this curve. Its distance to Station A and to Station B both change — but their difference never does. Every point here reads the SAME time difference. Add a second reading — find the point Station C gives you a SECOND curve. Slide along curve 1 (A, B) and watch the gap to curve 2 (A, C) — it hits zero at exactly one spot. That's your position. How many stations do you actually need? Step through 2, 3, and 4 stations and watch what each additional one actually buys you — real GPS needs all four, for two different reasons. Every hyperbola in this module came from the same move: a constant difference of distances to two fixed points . GPS calls the fixed points satellites; old LORAN radio navigation called them ground towers — same curve, same algebra, decades apart.

This is the written version of the interactive lesson above. See the full Algebra 2 course.