Lesson 9: Modern Physics vs Wayfinding: GPS Satellites, Atomic Clocks & Relativistic Physics
GPS needs four satellites because receiver clock error is a fourth unknown. Build the trilateration model, then account for the competing relativistic shifts in its atomic clocks.
🎯 Ngā Whāinga Akoranga | Learning Intentions
Global Positioning System (GPS) physics (satellite constellation, trilateration, atomic clock synchronization, Special & General Relativity time dilations), compared to perceptual wayfinding.
Perform satellite 2D/3D sphere trilateration math, calculate relativistic time dilation corrections in GPS signals, and evaluate technology reliance.
🎥 Media Anchor & Pedagogical Scaffold
Why GPS Needs Relativity — Science Mundi
Video (Science Mundi): An explanation of how GPS works and why Einstein's theory of relativity is essential for accurate positioning, including how time dilation affects satellite clocks.
🧠 1. Before Viewing (Activate & Predict)
If physicists did not correct GPS satellite clocks for Einstein’s two relativistic effects, how far do you predict your phone’s position would drift in a single day — metres, or kilometres? Commit to a number before you watch; you will calculate the real one in Activity 2.
👁️ 2. During Viewing (Watch With a Job)
Watch the full 5-minute clip and collect evidence for how GPS relies on physics:
- How GPS works: What principle allows satellites to determine your position on Earth?
- Atomic clocks: Why are atomic clocks essential to GPS accuracy?
- Time dilation effects: How do relativistic effects impact satellite clocks?
- Accuracy requirements: Why would GPS fail without accounting for relativity?
🗣️ 3. After Viewing & Kaiako Move (Process & Apply)
Kaiako Move: Demonstrate string trilateration across a classroom floor using 3 known satellite anchor points.
Immediate Task: Complete Section 9 of your Navigation Physics Logbook: GPS Satellite Trilateration & Relativity Math.
⚡ Whakaoho | Do Now: Why Does Your Phone Know Where You Are?
Two minutes: list everything that has to be true for a phone to place you within a few metres. Be specific — how many satellites, and what are they actually transmitting?
Then add the part that sounds made up: the satellites' clocks tick at a different rate from yours. Ignore that for a single day and your position drifts by kilometres.
📖 Activity 1: Trilaterate, Then Correct Two Clocks
Find the receiver (13 min). With three known satellite positions and three distances, locate the receiver by drawing intersecting circles. Then explain why the real system needs a fourth satellite — the receiver's own clock error is a fourth unknown, and you cannot solve for four unknowns with three equations.
Two effects, opposite signs (12 min). Satellite clocks run fast because gravity is weaker at altitude, and slow because the satellites are moving quickly. Calculate both and combine them. They do not cancel — one is several times the other. Convert the net daily drift into a position error.
📝 Activity 2: Navigation Physics Logbook & Problem Solving (20 mins)
Portfolio Section 9. Submit: (1) your trilateration construction with the receiver marked and the fourth-satellite reason explained; (2) both relativistic corrections with the net daily figure and resulting position error; (3) a comparison of GPS with wayfinding — what each system needs in order to keep working, and what each one fails at. Note which of the two survives a flat battery.
🏫 Kaiako Planning & Pedagogy Notes
Year 10 Curriculum Alignment: Te Mātaiaho (2025) Science, Phase 4 — Motion and Forces; Matter Interactions and Energy. Integrates traditional Polynesian wayfinding (Mātauranga Waka) with Year 10 physics: mechanics, wave behaviour and optics. Year 10 sits at NZC Level 5, before NCEA.
“Electromagnetic waves transfer energy through fields and include visible light; they can travel through a vacuum with a constant speed, the ‘speed of light’ (c).”Te Mātaiaho (2025) · Science · Phase 4 (Years 9–10) · Matter Interactions and Energy (Knowledge)