1. KEPLER: KEPLER: the laws of planetary motion Physics Chapter 7—Circular Motion KEPLER’S FIRST LAW KEPLER’S SECOND LAW KEPLER’S THIRD LAW INTERESTING APPLETS

2. Johannes Kepler Born on December 27, 1571 in Germany Studied the planetary motion of Mars  Used observational data of Brahe HOME

3. Tyco Brahe Danish astronomer who hired Kepler as his assistant Came up with accurate observations of Mars with his naked eyes Assigned Kepler to develop a theory of planetary motion using his observations HOME

4. Instruments Tyco Brahe  only compass and sextant  No telescope – naked eye HOME

5. Kepler’s FIRST Law “The orbit of each planet is an ellipse and the Sun is at one focus” Kepler proved Copernicus wrong – planets didn’t move in circles HOME

6. Ellipse Elongated & flattened circle Characterized by eccentricity and length of major axis Eccentricity – degree of flatness Major axis – longer axis HOME KEPLER’S FIRST LAW

7. Focus Focus – one of two special points on the major axis of an ellipse Foci – plural of focus A+B is always the same on any point on the ellipse KEPLER’S FIRST LAW HOME

8. Eccentricity Eccentricity is the degree of flatness Eccentricity (e) = 0 is circle Earth e = 0.017 e = c/a  c = center to focus  a = half of major axis/ semi-major axis KEPLER’S FIRST LAW HOME

9. Aphelion & Perihelion Aphelion is the point on the orbit farthest from the sun Perihelion is the point on the orbit closest to the sun KEPLER’S FIRST LAW HOME

10. Kepler’s SECOND Law “The line joining the planet to the sun sweeps out equal areas in equal intervals of time” HOME

11. In Another Words… The area from one time to another time is equal to another area with the same time interval All of the areas (in yellow and peach) have equal intervals of time KEPLER’S SECOND LAW HOME

12. Acceleration of Planets Planet moves faster when closer to the sun  Force acting on the planet increases as distance decreases and planet accelerates in its orbit Planet moves slower when farther from the sun HOME KEPLER’S SECOND LAW

13. Kepler’s THIRD Law “The square of the period of any planet is proportional to the cube of the semi-major of its axis” Also referred to as the Harmonic Law HOME

14. T²  a³ T = orbital period in years a = semi-major axis in astronomical unit (AU) Can calculate how long it takes (period) for planets to orbit if semi- major axis is known HOME KEPLER’S THIRD LAW

15. Astronomical Unit Astronomical unit – AU AU is the mean distance between Earth and the Sun 1 AU ≈ 1.5 x 10 8 km ≈ 9.3 x 10 7 miles HOME KEPLER’S THIRD LAW

16. Examples of 3 rd Law Calculating the orbital period of 1AU  T² = a³  T² = (1)³ = 1  T = 1 year Calculating the orbital period of 4AU  T² = a³  T² = (4)³ = 64  T = 8 years HOME KEPLER’S THIRD LAW

17. Orbital Data The orbital data of various planets HOME

18. Comets Although Kepler’s laws were intended to describe the motion of planets around the sun, the laws also apply to comets Comets are good examples because they have very elliptical orbits HOME

19. Kepler’s Three Laws Orbit of each planet is an ellipse & Sun is at one focus Equal areas in equal intervals of time T² = a³ HOME

20. Contributions Kepler’s second law (equal area) helped Newton come up with his Law of Universal Gravitation Motions of satellite and spacecraft in orbit near planets HOME

21. Interesting Applets http://www.fed.cuhk.edu.hk/sci_lab/ntnu java/Kepler/Kepler.html http://www.fed.cuhk.edu.hk/sci_lab/ntnu java/Kepler/Kepler.html http://csep10.phys.utk.edu/astr162/lect/bi naries/visual/kepleroldframe.html http://csep10.phys.utk.edu/astr162/lect/bi naries/visual/kepleroldframe.html http://www.ioncmaste.ca/homepage/reso urces/web_resources/CSA_Astro9/files/ multimedia/unit4/keplers_laws/keplers_la ws.html http://www.ioncmaste.ca/homepage/reso urces/web_resources/CSA_Astro9/files/ multimedia/unit4/keplers_laws/keplers_la ws.html HOME

22. Works Cited Drennon, Bill. “Kepler’s laws.” Central Valley Christian High School. 14 March 1997. 23 May 2008. http://home.cvc.org/science/kepler.htm Fendt, Walter. “Kepler’s First Law.” Java Applets on Physics. 18 January 2003. 23 May 2008. http://www.walter-fendt.de/ph14e/keplerlaw1.htm Fendt, Walter. “Kepler’s Second Law.” Java Applets on Physics. 18 January 2003. 25 May 2008. http://www.walter-fendt.de/ph14e/keplerlaw2.htm "Johannes Kepler." World of Earth Science. Online. Thomson Gale, 2006. Reproduced in Biography Resource Center. Farmington Hills, Mich.: Gale, 2008. http://galenet.galegroup.com/servlet/BioRC “Johannes Kepler: The Laws of Planetary Motion.” University of Tennessee. 25 May 2008. http://csep10.phys.utk.edu/astr161/lect/history/kepler.html HOME

23. Works Cited II “Kepler’s Laws.” Orbitessera. 26 May 2008 http://www.mindspring.com/~n2wwd/html/kepler_s_laws.html "Kepler's laws of planetary motion." Encyclopædia Britannica. 2008. Encyclopædia Britannica Online. 25 May 2008. http://www.britannica.com/eb/article-9045134. Nave, R. “Kepler’s Laws.” HyperPhysics. 25 May 2008. http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html Soper, Davison. “Kepler’s First Law.” University of Oregon. 2002. 23 May 2008. http://zebu.uoregon.edu/~soper/Orbits/kepler1.html Weisstein, Eric. “Kepler’s Third Law.” Eric Weisstein’s World of Physics. 2007. 26 May 2008. http://scienceworld.wolfram.com/physics/KeplersThirdLaw.html HOME