Kepler's First Law
(The orbit of a planet forms an ellipse with the Sun at one focus)

We will begin by examining some properties of ellipses and the terminology involved in describing them.  An ELLIPSE can be defined as the locus of points the sum of whose distance from two fixed points (the foci) is constant.

We can draw an ellipse making use of the above definition.

The JAVA applet below shows a planet orbiting a star.  Click the button labeled Lines to see how the orbit is in fact an ellipse.  The sun and the additional point which appears to the left are the two foci.  Two lines - r(1) and r(2) - show the distance from the foci to the Earth.   The table in the lower left of the applet shows how the sum of these distances is constant - that is, the length of the "string" does not change.

*** YOUR BROWSER DOES NOT SUPPORT JAVA AND SO CANNOT DISPLAY THE APPLET ***

The degree of flatness or roundness of the ellipse is called its ECCENTRICITY. The eccentricity is given by the ratio of the distance between the foci to the length of the major axis.

Experiment with varying the eccentricity in the JAVA applet above by dragging the slider at the bottom.

A CIRCLE is just an ellipse of eccentricity zero, that is, when the foci lie on top of one another and the major and minor axes are the same length.

Most of the planets in the solar system have orbits that are nearly - but not quite - circular.

Calculate and record the eccentricity for the ellipse you drew on the cardboard.  Answer the additional questions about ellipses on the worksheet.

Kepler’s Laws apply not only to the nine planets, but also to asteroids and comets in their motion around the Sun and to any orbital motions, for example that of the Moon or artificial satellites around the Earth.