Here's a different and somewhat artistic way to encourage understanding of a conic section. Participants physically build an ellipse by choosing two foci and sketching the figure through a loop of string.
While stitching an elliptical string design they puzzle about varying the foci spread and the loop length to create more extreme ellipses and are intuitively introduced to the measurement of eccentricity.
The range and meaning of eccentricity, orbit analysis, perihelion and aphelion are all part of this visual understanding of ellipses.
For members we have an editable Word docx and solutions.
EllipseStringDesign.docx EllipseStringDesign-solution.pdf
CCSS: 8.G, HS, HSG.GPE
For more on Orbital Mechanics - Why does it stay in orbit?
P.S. Unfortunately this string design activity is very long. I would appreciate suggestions. Thanks, Leslie