Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Physics
Lesson Topic: use ϕ = –GM / r for the gravitational potential in the field due to a point mass
Learning Objective/s:
  • Describe the relationship between the gravitational field and the gravitational potential for a point mass.
  • Derive the expression ϕ = –GM / r from the definition of potential difference.
  • Apply the formula to calculate gravitational potential and potential energy for given masses and distances.
  • Identify and correct common sign‑ and reference‑point errors in gravitational‑potential problems.
Materials Needed:
  • Projector or interactive whiteboard
  • Slide deck with derivation and examples
  • Worksheet containing practice questions
  • Scientific calculators
  • Printed diagram of radial field lines
  • Whiteboard and markers
 Introduction:
Imagine a satellite being released from “infinity” and falling toward a planet; students will see how the energy changes. They already know the gravitational field g = –GM/r² and how to integrate functions. By the end of the lesson they will be able to derive and correctly use ϕ = –GM/r, avoiding sign and zero‑level mistakes.
Lesson Structure:
  1. Do‑now (5 '): Quick quiz on the gravitational field formula and its direction.
  2. Mini‑lecture (10 '): Derive ϕ = –GM/r step‑by‑step, highlighting the reference point at infinity.
  3. Guided example (10 '): Calculate the potential at Earth’s surface and near the Sun, using the derived formula.
  4. Paired practice (15 '): Students work through three practice questions from the source, checking each other’s work.
  5. Class discussion (5 '): Review common mistakes (sign error, wrong reference point, confusing ϕ with g).
  6. Exit ticket (5 '): Write one correct expression for ϕ and one typical error to avoid.
Conclusion:
We recap the derivation, the meaning of the negative sign, and how the formula links to potential energy. Students hand in their exit tickets and receive a brief homework set of additional calculations to reinforce the concept.