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Trajectories in an Attractive Central Potential

Keywords: Classical Mechanics, Central Forces, Orbits, Effective Potential, Parameter Spaces, Maple, Java, Computer Visualization

Highlights of the activity

This computer visualization activity is designed to help students visualize trajectories in attractive potentials.
Students use Maple or Mathematica to plot particular effective potentials and then use java orbits.jar to generate a polar plot of the corresponding orbit; students proceed to explore the parameter space of classical orbits.
The whole class wrap-up discussion addresses how changing the total energy, angular momentum, and the reduced mass of the system affects the shape of the resulting orbit.

Reasons to spend class time on the activity

Graphical representations are often challenging for students to interpret. In classical mechanics, we use several representation to describe orbits. This activity provides an opportunity for students to make connections between two representations: a plot of the effective potential of an orbit and the polar plot of that orbit. Furthermore, students can see how changing the total energy, angular momentum, the reduced mass and the force constant of the system affects the shape of the resulting orbit.

This activity works particularly well when sequenced with other activities.