Planetary motion and Kepler's laws

Three animations allow you to explore each of Kepler's three laws of planetary motion. Choose a law to start.

1. Law of Orbits

Choose a planet or moon from the drop-down box and then click on the Start button to set the planet into motion. A series of markers will display the elliptical orbit of the planet with the Sun at one focus of the ellipse. These markers show the location of the planet at equal time intervals.

2. Law of Areas

Choose a planet or moon from the drop-down box and then click the Start button to set the planet into motion. A series of markers will display the elliptical orbit of the planet with the Sun at one focus of the ellipse. These markers show the location of the planet at equal time intervals.

To verify the law of areas, click on a marker at one part of the orbit. A sector of the ellipse with its vertex at the Sun/Neptune will be drawn from the chosen marker to another one, four markers down. Then, click on another marker at another part of the orbit to draw another sector with same number of markers (representing the number of time steps taken by the planet/moon). Estimate the area of each sector by clicking on the button "Grid." Count the number of squares within each area to estimate the area swept out by the planet.

3. Law of Periods

Choose a planet from the drop-down box and then click on the Start button to set the planet into motion. A series of markers will display the position of the planet at equal time intervals.

To calculate the period of the planet, count the number of markers the planet travels while Earth travels half of its orbit. The result of this count is equivalent to half a year. Use this number to calculate the period of the planet's orbit (the number of years the planet takes to orbit the Sun).

To change the animation speed, move the animation speed slider.

To return to the opening screen, click the Return button.

Note: Images of planets, the Sun, and Nereid are not to scale.