Lesson Plan

• Describe the concepts of average orbital speed, orbital radius, and orbital period.
• Derive the equation v = 2πr / T from the geometry of a circular orbit.
• Apply the equation to calculate speed, radius, or period for a given planet.
• Re‑arrange the formula to solve for any of the three variables.
• Explain why planets nearer the Sun have higher orbital speeds.

• Projector or interactive whiteboard
• Slide deck with derivation and example
• Calculator worksheets
• Printed data tables for Earth, Mars, and a hypothetical planet
• Diagram of a planetary orbit (circular)
• Practice question handout
• Whiteboard and markers

Begin with a quick visual of Earth’s orbit to spark curiosity about how fast planets travel. Ask students to recall the formula for a circle’s circumference and link it to orbital distance. State that by the end of the lesson they will be able to use v = 2πr / T to solve real‑world problems.

1. Do‑now (5 min): Write the circumference formula and discuss its relevance to orbital distance.
2. Mini‑lecture (10 min): Derive v = 2πr / T step‑by‑step, highlighting each variable.
3. Guided example (10 min): Calculate Earth’s average orbital speed using provided data, modelling each algebraic step.
4. Partner practice (15 min): Solve the Mars speed problem and the hypothetical planet radius problem from the handout.
5. Conceptual discussion (5 min): Explain why inner planets move faster, referencing the equation.
6. Exit ticket (5 min): Write one sentence summarising the relationship between orbital radius and speed.

Review the key steps of the derivation and the calculations completed today. Collect exit tickets to gauge understanding, and assign the remaining practice questions as homework to reinforce rearranging the formula.