This applet demonstrates that the sum of the distances from the two focal points (foci) to any point on an ellipse is a constant. This simulates the same path that planets take while in orbit around the sun.
To try this
Right click and drag your mouse to change the shape of the ellipse. To rotate the image, left click and drag.
What's Going On?
You are seeing the same shapes that the planets travel along as they go around the sun. Our applet’s ellipse has two Focal Points or FOCI – with the distances between the Focal Points and any point on the ellipse forming a triangle. Mathematically any point on the ellipse is always the sum of the distances from the Focal Points.
Ignore the base of the triangle and concentrate on the two legs. You will see an interesting relationship. As you change your ellipse, you can see that as one of the triangle’s legs gets shorter, the other gets longer. The meter at the top of the applet helps you visualize this by measuring and color coding the relative lengths of each line.
Satellites orbiting the earth (or any other object in space) travel in an elliptical orbit. At times the satellite will be closest to the earth at a point called perigee. Since it is closer, it is pulled harder by the earth’s gravity and has a higher speed. At its farthest point from earth, or apogee, the satellite moves slower.
An orbit where the perigee and apogee distances are the same is nothing more than a circle, which is a special type of ellipse.