Students are asked to explore the parameters that affect orbit shape using the supplied Maple worksheet or Mathematica notebook.
In the Mathematica Worksheet Conics.nb or the online Geogebra visualization at GMM: Graphs in Polar Coordinates, you will examine a three parameter family of curves described by the polar equation \[r(\phi)=\frac{\alpha}{1+\epsilon\cos(\phi+\delta)}.\] Describe in detail how the shape of the plot depends on the parameters \(\alpha\), \(\delta\), and \(\epsilon\). Pay particular attention to different values of \(\epsilon\).