Lesson Plan

• Recall the formula g = GM / r² and its orbital form g = GM / r.
• Explain the derivation linking gravitational force to centripetal acceleration for circular orbits.
• Apply the formula to calculate gravitational field strength at a given distance.
• Use v = √(GM / r) to determine orbital speed and period.
• Identify and avoid common mistakes when using the g = GM / r relationship.

• Projector and screen
• Whiteboard and markers
• Scientific calculators (or calculator app)
• Worksheet with practice problems
• Printed diagram of a sphere with radius r
• Laptop with a simple gravity/orbit simulation

Begin with a short video of a satellite launch to spark interest in how gravity keeps objects in orbit. Review Newton’s law of universal gravitation and the definition of gravitational field strength. Explain that by the end of the lesson students will be able to derive and use g = GM / r to solve orbital‑motion problems.

1. Do‑now (5′): Quick written recall of F = GMm / r² and substitution to obtain g = GM / r².
2. Mini‑lecture (10′): Derive g = GM / r by equating gravitational force to centripetal force; introduce v = √(GM / r).
3. Guided example (10′): Solve the provided sample problem (g at 4 × 10⁶ m) step‑by‑step.
4. Interactive simulation (10′): Students manipulate M and r on a laptop to see real‑time changes in g and orbital speed.
5. Practice questions (15′): Pairs work through three textbook problems, teacher circulates for support.
6. Check for understanding (5′): Exit ticket – one sentence explaining why the radius must be measured from the centre of mass.

Summarise how the gravitational field strength formula links directly to orbital motion and why correct units and the squared radius are crucial. Collect exit tickets and clarify any lingering misconceptions. Assign homework: two additional problems requiring calculation of g at different altitudes and determination of orbital speed for a given planet.