1. T HE G EOMETRY OF P LANETARY O RBITS How do we define the path that planets take as they revolve around the Sun?

2. V OCABULARY D EFINITIONS ELLIPSE : A flattened circle or oval; ECCENTRICITY : measures the deviation of a shape from a circle. FOCI : Two fixed points that determine the shape and position of an ellipse. LENGTH OF MAJOR AXIS : The distance of a line through the widest part of an ellipse

3. T HE G EOMETRY OF O RBITS The orbits of the planets around the Sun are ellipses, not circles. An ellipse is defined by two fixed points called the foci (singular: focus). These points lie on either side of the center of the major axis, which is a line through the widest part of an ellipse as shown in diagram. The more elliptical the shape of the orbit the more eccentric is the path.

4. Major Axis Focus 1 Focus 2

5. S HAPES OF E LLIPSES Eccentricity = 0 (a circle) Eccentricity = 0.5 Eccentricity = 1.0 (a line)

6. E CCENTRICITY F ORMULA Find the eccentricity of the ellipse in the following diagram.

7. Focus 1 Focus 2 Solution: Distance between Foci = 5.0 centimeters Length of Major Axis = 10.0 centimeters therefore: E = 5.0 cm/ 10.0 cm = 0.5 5.0 cm 10 cm. Major Axis Focal Distance

8. J OHANNES K EPLER ’ S T HREE L AWS OF P LANETARY M OTION 1. Orbits are ellipses rather than circles. So, the distance between a planet and the Sun changes. At some parts of the orbit, the planet is closer to the Sun, and at other parts it is farther away. 2. The radius between a planet and the sun sweeps out equal areas in equal times. When a planet is closer to the Sun, it moves faster than when it is farther away. 3. The farther way a planet is from the Sun, the longer it takes to orbit the Sun.