Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Physics
Lesson Topic: understand why g is approximately constant for small changes in height near the Earth’s surface
Learning Objective/s:
  • Describe how gravitational acceleration varies with distance from Earth’s centre.
  • Explain why the change in g is negligible for heights much smaller than Earth’s radius.
  • Apply the constant‑g approximation to solve near‑surface physics problems such as projectile motion.
  • Calculate the error introduced by using g ≈ 9.81 m s⁻² for given heights up to a few kilometres.
Materials Needed:
  • Projector or interactive whiteboard
  • Slides with derivations and tables
  • Handout containing the numerical illustration table
  • Calculator or computer for quick calculations
  • Ruler or measuring tape for a simple height‑measurement demo (optional)
 Introduction:
Begin with a quick demonstration: drop two objects from a balcony and ask students why the acceleration appears the same. Recall prior learning on Newton’s law of universal gravitation and the definition of g at Earth’s surface. Explain that today’s goal is to understand why we can treat g as constant for everyday height changes, and students will be able to justify this approximation.
Lesson Structure:
  1. Do‑Now (5 '): Students answer “If you climb a 100 m tower, does g change? Why or why not?” and share responses.
  2. Mini‑lecture (10 '): Review universal gravitation, derive g(r)=GM/r², introduce Earth’s radius Rₑ and height h.
  3. Taylor‑approximation activity (10 '): Guided derivation of g(h) ≈ g₀[1‑2h/Rₑ] using a first‑order expansion; work in pairs.
  4. Numerical illustration (8 '): Use the provided table to compare exact and approximate g for various heights; discuss relative errors.
  5. Concept check (5 '): Quick quiz (exit ticket) with two questions on when the constant‑g assumption is valid.
  6. Application problem (7 '): Solve a projectile‑motion problem assuming g = 9.81 m s⁻² and compare with a calculation using the full expression for a 2 km launch.
  7. Summary discussion (5 '): Reinforce key points and answer lingering questions.
Conclusion:
Summarize that g varies with the inverse square of distance, but for h ≪ Rₑ the variation is less than a few thousandths of a percent, justifying the constant‑g approximation. Collect exit tickets to assess understanding, and assign homework: calculate the error for a 5 km altitude and decide whether to use the approximation. Remind students that the full formula is needed for high‑altitude or orbital scenarios.