Ellipses

We are working our way through Objects in Motion: Principles in Classical Mechanics by Paul Fleisher. The first lesson is about Kepler's Laws of Planetary Motion.

A key moment for Kepler was when he abandoned circular orbits for elliptical ones, so I designed an activity around ellipses.  I cut a large foam board into quarters, one for each student, and tacked paper to it.  They put two push pins along the horizontal midline of the paper, slipped a string with the ends tied together over it, and drew an ellipse by drawing the string taut with a pencil and circling the push pins.  They moved the pins progressively farther, then closer, and observed what happened to the ellipse.  We discussed how a circle is a special form of an ellipse, just as a square is a special form of a rectangle.

I then discussed Kepler's Second Law and shaded in a pie piece away from the sun and close to the sun.

For the elementary group we skipped the third law.  For the middle school kids I simply wrote the formula and we discussed what it meant, including exponents and proportionality.  They got the fact that distant planets orbit more slowly and related that to the force of gravity.

If you use ExploreLearning Gizmos like we do, there's one on Ellipse and another on Kepler's Laws.