Kepler's Laws of Orbital Motion

Directions: Click on one of the ten eccentricity buttons (labeled "e = 0.0", "e = 0.1", "e = 0.2", etc.) to display an orbit diagram.

Click the "PLAY" button to display a movie of a planet (small blue dot) following the orbit you have chosen. Click the "STOP" button to return to the orbit diagram. If you do not click another eccentricity button first, hitting "PLAY" again will resume the planet's motion.

For reference, here are the eccentricities of some objects in our Solar System:

Mercury: 0.206 Venus: 0.007 Earth: 0.017
Mars: 0.093 Ceres: 0.080 Jupiter: 0.049
Saturn: 0.056 Uranus: 0.044 Neptune: 0.009
Pluto: 0.249 Eris: 0.442 Halley's Comet: 0.967

Questions to Consider:

1. What is another name for a planet's period of revolution (i.e. the time that the planet takes to orbit the Sun once)? (Click for Answer)

This time interval is called the year. If you live on Earth, you are used to a year that lasts 365 Earth days. The Martian year is 669 Martian days or 687 Earth days. Neptune takes almost 165 Earth years to orbit the Sun.

2. What do the terms "perihelion" and "aphelion" mean? (Click for Answer)

Both of these terms are derived from the ancient Greek word for the Sun, helios. Perihelion is the closest point of an orbit to the Sun. Aphelion is the farthest point of an orbit to the Sun.

3. How does a planet's speed compare at perihelion and aphelion? (Click for Answer)

Imagine throwing a ball into the air. As the ball moves upward, it slows down due to Earth's gravitational pull. At some point, it reaches its maximum height. The ball begins to fall back to the ground. The speed of the ball increases constantly, again due to Earth's gravitational pull.

Any object orbiting the Sun behaves the same way. As a planet moves toward the Sun, it falls inward and its speed increases. At perihelion, the planet is at a minimum distance from the Sun and has its highest orbital speed. After perihelion, the planet falls outward from the Sun and decreases in speed. At aphelion, the planet is at a maximum distance from the Sun and has its lowest orbital speed.

4. What is special about an orbit with an eccentricity of zero? (Click for Answer)

If an orbit has an eccentricity of zero, it is perfectly circular. This means that the planet's speed and distance from the Sun do not change during the whole orbit.

5. Why was Mars the best choice for Johannes Kepler to study the shape of planetary orbits? (Click for Answer)

Of the three brightest planets (Venus, Jupiter, and Mars), Mars has the largest eccentricity. If Kepler had studied Venus, he might have concluded that planets really do have circular orbits.

On the other hand, if any of the brightest planets had very eccentric orbits (e > 0.5) the true shape of planetary orbits might have been discovered thousands of years ago.

Created by Kevin Healy, 2007