In this unit, you will explore the classical mechanics of central forces, especially gravitational orbits like the earth going around the sun.

Motivating Questions

• What shapes can the orbits have?
• What are Kepler's laws and why are they true?
• What is an effective potential diagram and how can it be used to predict the shape of an orbit?

Key Activities/Problems

• Problem: Undo Formulas for Center of Mass (Geometry)
• Activity: Acting Out Effective Potentials (In class, only)
• Activity: Effective Potentials
• Problem: Hockey
• Problem: Scattering

Unit Learning Outcomes

At the end of this unit, you should be able to:

• List the properties that define a central force system.
• Calculate a reduced mass for a two-body system and describe why it is important.
• Use the solution (algebraic or geometric) to a reduced mass system to describe the motion of the original system.
• Describe the role that conservation of energy and angular momentum play in a central force system. In particular, where do these properties appear in the solutions of the equations of motion?
• Use an effective potential diagram to predict the possible orbits in a central force system: which orbits are bound or unbound? which are closed or open? where will the turning points be?

Equation Sheet for This Unit

• Classical Orbits Equation Sheet