KEPLER the laws of planetary motion Physics Chapter

KEPLER: the laws of planetary motion Physics Chapter 7—Circular Motion KEPLER’S FIRST LAW KEPLER’S SECOND LAW KEPLER’S THIRD LAW INTERESTINGAPPLE TS

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

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

Instruments l Tyco Brahe u only compass and sextant u No telescope – naked eye HOME

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

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

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

HOME Eccentricity l Eccentricity is the degree of flatness l Eccentricity (e) = 0 is circle l Earth e = 0. 017 l e = c/a u c = center to focus u a = half of major axis/ semi-major axis KEPLER’S FIRST LAW

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

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

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

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

HOME Kepler’s THIRD Law l “The square of the period of any planet is proportional to the cube of the semimajor of its axis” l Also referred to as the Harmonic Law

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

HOME Astronomical Unit l Astronomical unit – AU l AU is the mean distance between Earth and the Sun l 1 AU ≈ 1. 5 x 108 km ≈ 9. 3 x 107 miles KEPLER’S THIRD LAW

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

HOME Orbital Data l The orbital data of various planets

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

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

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

HOME Interesting Applets l http: //www. fed. cuhk. edu. hk/sci_lab/ntnujava/Kepl er/Kepler. html l http: //csep 10. phys. utk. edu/astr 162/lect/binaries/ visual/kepleroldframe. html l http: //www. ioncmaste. ca/homepage/resources/w eb_resources/CSA_Astro 9/files/multimedia/unit 4/ keplers_laws/keplers_laws. html

HOME Works Cited l Drennon, Bill. “Kepler’s laws. ” Central Valley Christian High School. 14 March l l 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/ph 14 e/keplerlaw 1. htm Fendt, Walter. “Kepler’s Second Law. ” Java Applets on Physics. 18 January 2003. 25 May 2008. http: //www. walter-fendt. de/ph 14 e/keplerlaw 2. 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/Bio. RC “Johannes Kepler: The Laws of Planetary Motion. ” University of Tennessee. 25 May 2008. http: //csep 10. phys. utk. edu/astr 161/lect/history/kepler. html

HOME Works Cited II l “Kepler’s Laws. ” Orbitessera. 26 May 2008 l l http: //www. mindspring. com/~n 2 wwd/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. ” Hyper. Physics. 25 May 2008. http: //hyperphysics. phyastr. gsu. edu/hbase/kepler. html Soper, Davison. “Kepler’s First Law. ” University of Oregon. 2002. 23 May 2008. http: //zebu. uoregon. edu/~soper/Orbits/kepler 1. html Weisstein, Eric. “Kepler’s Third Law. ” Eric Weisstein’s World of Physics. 2007. 26 May 2008. http: //scienceworld. wolfram. com/physics/Keplers. Third. Law. html