#### Transcript KEPLER: the laws of planetary motion

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 Johannes Kepler Born on December 27, 1571 in Germany Studied the planetary motion of Mars Used HOME observational data of Brahe 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 Instruments Tyco Brahe only compass and sextant No telescope – naked eye HOME Kepler’s FIRST Law HOME “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 Ellipse Elongated & flattened circle Characterized by eccentricity and length of major axis Eccentricity – degree of flatness Major axis – longer axis KEPLER’S FIRST LAW HOME Focus HOME 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 Eccentricity HOME 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 Aphelion & Perihelion HOME 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 Kepler’s SECOND Law HOME “The line joining the planet to the sun sweeps out equal areas in equal intervals of time” In Another Words… HOME 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 Acceleration of Planets HOME 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 KEPLER’S SECOND LAW Kepler’s THIRD Law HOME “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 T² a³ HOME 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 semimajor axis is known KEPLER’S THIRD LAW Astronomical Unit HOME Astronomical unit – AU AU is the mean distance between Earth and the Sun 1 AU ≈ 1.5 x 108 km ≈ 9.3 x 107 miles KEPLER’S THIRD LAW Examples of 3rd Law HOME 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 KEPLER’S THIRD LAW HOME Orbital Data The orbital data of various planets Planet eccentricity (e) T (yr) a (AU) T2 a3 Mercury 0.206 0.24 0.39 0.06 0.06 Venus 0.007 0.62 0.72 0.39 0.37 Earth 0.017 1 1 1 1 Mars 0.093 1.88 1.52 3.53 3.51 Jupiter 0.048 11.9 5.2 142 141 Saturn 0.056 29.5 9.54 870 868 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 Kepler’s Three Laws HOME Orbit of each planet is an ellipse & Sun is at one focus Equal areas in equal intervals of time T² = a³ 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 Interesting Applets HOME 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://www.ioncmaste.ca/homepage/reso urces/web_resources/CSA_Astro9/files/ multimedia/unit4/keplers_laws/keplers_la ws.html Works Cited HOME 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 Works Cited II “Kepler’s Laws.” Orbitessera. 26 May 2008 HOME 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