Kepler's First Law (Java Applet)

Kepler's First Law

Watch the motion of the satellite. It traces out an elliptical orbit about the earth. The elliptical orbit has the shape of a "squashed" circle, although there is a precise mathematical equation that describes it. The earth is off-center, namely at one of the foci of the ellipse.

Move the arrow in the bar on the right up or down. This changes the eccentricity, or shape, of the elliptical orbit. An eccentricity of zero (when the arrow is at the bottom of the bar) means the orbit is a circle. An eccentricity closer to one means the orbit is more elongated.

If you move the arrow into the yellow part of the bar, the satellite comes very near to crashing into the earth during its closest approach. If you move the arrow into the red part of the bar, the satellite will actually crash.

Note that the sizes of the earth, satellite, and orbit are not drawn to realistic scales.

Kepler's Second Law (Java Applet) 

Kepler's Second Law

When the satellite orbits the earth in a highly elliptical path, you can readily see how it slows down as it moves far away from the earth, and how it speeds up as it gets close to the earth. It's the same effect you get when you throw a ball up into the air. The ball slows down as it climbs to its greatest height, and speeds up as it falls back down.

In the orbit simulation of Kepler's second law, the satellite is joined by a straight line with the center of the earth. Watch the area swept out by this line. When the satellite is far from the earth, the line is long and the satellite moves slowly. When the satellite is near the earth, the line is short and the satellite moves quickly. The length of the line and the speed of the satellite are such that no matter where in its orbit the satellite is, the line sweeps out the same area in any given time interval.

You can click on the yellow part of the bar on the right and, by dragging, enlarge the swept-out area.

Kepler's Third Law (Java Applet)

Kepler's Third Law

Kepler's third law is illustrated for circular orbits, although the law also applies to elliptical orbits. Click on either of the buttons on the right. The satellite's motion will simulate either the orbit of NASA's space shuttle or that of a satellite in a geosynchronous orbit. A geosynchronous orbit is one with an orbital period equal to the period of the rotation of the earth. This means that for circular orbits above the earth's equator, the satellite will always remain above the same point on the earth.

You can also click on the satellite and drag it to other orbits. The satellite's altitude above the earth's surface and orbital period are given on the right.

Notice how much slower the satellite moves in a large orbit, and how much longer it takes to complete an orbit than when it is closer to the earth. A mathematical relationship exists between the orbital period and the size of the orbit, i.e., the distance between the center of the earth and the satellite. The relationship states that the square of the orbital period is proportional to the cube of the size of the orbit.