UBC Mathematics Department
http://www.math.ubc.ca/
This page demonstrates Kepler's Laws: both the position and velocity are plotted for an object moving under the gravitational influence of a large mass at the origin (e.g. the Sun). Directions: You can control the eccentricity of the orbit through the scrollbar and the speed of motion through the buttons "Slow" and "Fast." Choose a value for the eccentricity and then click "Start" to begin. When the "Area" button is selected, the areas swept out by a line joining the origin to the object in a fixed time interval is displayed (thus demonstrating Kepler's Second Law). Selecting "Area" again turns off the demonstration. When the eccentricity is very close to 1, you may notice some slightly unusual behavior due to the numerical method (Euler's method) used to solve the differential equation. Enjoy!
