1. Kepler’s Laws of Planetary Motion By: Alize Habib, Ahmed Daniyal Mirza, Anwar Harris and Erick Spong Johannes Kepler

2. Before Kepler’s Laws  The geocentric model was one of the most ubiquitous ideas on the rotations of the planets, among ancient civilizations. It also was supported by the Catholic and Islamic astronomers.  The geocentric model depicted the earth at the center. The planets, stars, moon, and sun all rotated around the earth while it stood still. This idea persisted for the next 2 millennia.  A once unpopular idea was revived in the 1500’s. It was Copernicus’s version of the heliocentric model. In Copernicus’s model, the sun is at the center. All the planets, including earth, orbit the sun at different distances. Another revolutionary idea was that the earth rotated while in orbit.  The Copernican model still depicted the orbits as perfect spheres. It began the slowly began to replace the geocentric model, even against the efforts of the church.  Johannes Kepler improved upon the Copernican model by asserting three laws. The Geocentric Model The Heliocentric Model (see fig. 4)

3. Kepler’s First Law 1. The orbit of every planet is an ellipse with the Sun at one of the two foci.  Kepler stated that planets are orbiting the sun in a path of an ellipse.  An ellipse is a shape that somewhat looks like a vertically or horizontally stretched circle.  Each ellipse contains two focal points; one is always the sun.  The sum of the distances from any point on the curve of the ellipse to any of the focal point, or foci is constant.  The focal points are not located at the center of the ellipse, rather they are equidistant from the sides of the ellipse. (see fig.1)

4. Kepler’s Second Law 2. A line joining a planet and the Sun sweep out equal areas during equal intervals of time.  This law describes the speed that any planet will move while orbiting the sun.  While a planet moves, its speed is not constant; it changes depending the on the distance from the Sun.  When a planet is closest to the Sun, it moves fastest, whereas when it is furthest from the Sun, it moves its slowest.  If you draw a line from a Planet to the Sun, the area swept out would be the same area in the same amount of time.  For example, if you draw a line from a particular planet to the Sun, the area swept out every 15 days would be the same.

5. Kepler’s Third Law 3. The square of the orbital period of a planet is directly proportional to the cub of the semi-major axis of its orbit.  This law (also called the harmonic law) deals with the relationship between the motion characteristics of different planets.  This law compares planets orbital periods and radius of the orbits.  This comparison confirms that the ratio of the squares of the periods to the cubes of their average distances from the sun are the same for every single planet.

6. After Kepler’s Laws  Kepler’s laws have changed the way we think about planetary motion and have led to other discoveries in science.  Kepler’s first law about planets traveling in ellipse patterns around the sun was revolutionary for astrology and inspired people to research more about the way planets move.  Kepler’s second law is important to physics because it led to the laws about centripetal acceleration and how it relates to the velocity and radius of an object.  Finally, his third law led to Newton’s law of gravitation, which has changed the way we think about motion and many other fields.  Because of all these advancements that stemmed from Kepler’s research, he is sometimes called “the founder of celestial mechanics.”

7. Works Cited  Fig. 1. Kepler’s First Law. zebu.uoregon.edu, n.d; Web; 6 October 2011.  Fig. 2. Kepler's Second Law: on Areas. schools.wikia.com, n.d; Web; 6 October 2011.  Fig. 3. How fast do the planets move on their orbits? ircamera.as.arizona.edu, n.d; Web; 6 October 2011.  Fig. 4. God and Astronomy. 0490l.wordpress.com, 6 October 2009; Web; 6 October 2011.  Fig. 6. Kepler's Laws of Planetary Motion. projects.astro.illinois.edu, 29 August 2000; Web; 7 October 2011.  Fig. 7. Formula - Centripetal acceleration. wikipremed.com, n.d; Web; 7 October 2011.  Fig. 8. Sir Isaac Newton: The Universal Law of Gravitation. csep10.phys.utk.edu, n.d; Web; 7 October 2011.  “Kepler's Three Laws.” physicsclassroom.com, ThePhysicsClassroom, n.d. Web. 6 October 2011.  "Johannes Kepler: His Life, His Laws and Times." Ames Research Center. NASA, 14 May 2011. Web. 7 Oct. 2011.  Paar, D. "Johannes Kepler." Famous Physicists and Astronomers. 9 Mar. 1996. Web. 07 Oct. 2011.