Keplers Laws


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Keplers Laws

  1. 1. KEPLER: the laws of planetary motion Monica Lee A.P. Physics – Period 4 Mrs. Burns KEPLER’S FIRST LAW KEPLER’S SECOND LAW KEPLER’S THIRD LAW INTERESTING APPLETS
  2. 2. Johannes Kepler <ul><li>Born on December 27, 1571 in Germany </li></ul><ul><li>Studied the planetary motion of Mars </li></ul><ul><ul><li>Used observational data of Brahe </li></ul></ul>HOME
  3. 3. Tyco Brahe <ul><li>Danish astronomer who hired Kepler as his assistant </li></ul><ul><li>Came up with accurate observations of Mars with his naked eyes </li></ul><ul><li>Assigned Kepler to develop a theory of planetary motion using his observations </li></ul>HOME
  4. 4. Instruments <ul><li>Tyco Brahe </li></ul><ul><ul><li>only compass and sextant </li></ul></ul><ul><ul><li>No telescope – naked eye </li></ul></ul>HOME
  5. 5. Kepler’s FIRST Law <ul><li>“ The orbit of each planet is an ellipse and the Sun is at one focus” </li></ul><ul><li>Kepler proved Copernicus wrong – planets didn’t move in circles </li></ul>HOME
  6. 6. Ellipse <ul><li>Elongated & flattened circle </li></ul><ul><li>Characterized by eccentricity and length of major axis </li></ul><ul><li>Eccentricity – degree of flatness </li></ul><ul><li>Major axis – longer axis </li></ul>HOME KEPLER’S FIRST LAW
  7. 7. Focus <ul><li>Focus – one of two special points on the major axis of an ellipse </li></ul><ul><li>Foci – plural of focus </li></ul><ul><li>A+B is always the same on any point on the ellipse </li></ul>KEPLER’S FIRST LAW HOME
  8. 8. Eccentricity <ul><li>Eccentricity is the degree of flatness </li></ul><ul><li>Eccentricity (e) = 0 is circle </li></ul><ul><li>Earth e = 0.017 </li></ul><ul><li>e = c/a </li></ul><ul><ul><li>c = center to focus </li></ul></ul><ul><ul><li>a = half of major axis/ semi-major axis </li></ul></ul>KEPLER’S FIRST LAW HOME
  9. 9. Aphelion & Perihelion <ul><li>Aphelion is the point on the orbit farthest from the sun </li></ul><ul><li>Perihelion is the point on the orbit closest to the sun </li></ul>KEPLER’S FIRST LAW HOME
  10. 10. Kepler’s SECOND Law <ul><li>“ The line joining the planet to the sun sweeps out equal areas in equal intervals of time” </li></ul>HOME
  11. 11. In Another Words… <ul><li>The area from one time to another time is equal to another area with the same time interval </li></ul><ul><li>All of the areas (in yellow and peach) have equal intervals of time </li></ul>KEPLER’S SECOND LAW HOME
  12. 12. Acceleration of Planets <ul><li>Planet moves faster when closer to the sun </li></ul><ul><ul><li>Force acting on the planet increases as distance decreases and planet accelerates in its orbit </li></ul></ul><ul><li>Planet moves slower when farther from the sun </li></ul>HOME KEPLER’S SECOND LAW
  13. 13. Kepler’s THIRD Law <ul><li>“ The square of the period of any planet is proportional to the cube of the semi-major of its axis” </li></ul><ul><li>Also referred to as the Harmonic Law </li></ul>HOME
  14. 14. T ²  a ³ <ul><li>T = orbital period in years </li></ul><ul><li>a = semi-major axis in astronomical unit (AU) </li></ul><ul><li>Can calculate how long it takes (period) for planets to orbit if semi-major axis is known </li></ul>HOME KEPLER’S THIRD LAW
  15. 15. Astronomical Unit <ul><li>Astronomical unit – AU </li></ul><ul><li>AU is the mean distance between Earth and the Sun </li></ul><ul><li>1 AU ≈ 1.5 x 10 8 km ≈ 9.3 x 10 7 miles </li></ul>HOME KEPLER’S THIRD LAW
  16. 16. Examples of 3 rd Law <ul><li>Calculating the orbital period of 1AU </li></ul><ul><ul><li>T ² = a ³ </li></ul></ul><ul><ul><li>T ² = (1)³ = 1 </li></ul></ul><ul><ul><li>T = 1 year </li></ul></ul><ul><li>Calculating the orbital period of 4AU </li></ul><ul><ul><li>T ² = a ³ </li></ul></ul><ul><ul><li>T ² = (4)³ = 64 </li></ul></ul><ul><ul><li>T = 8 years </li></ul></ul>HOME KEPLER’S THIRD LAW
  17. 17. Orbital Data <ul><li>The orbital data of various planets </li></ul>HOME
  18. 18. Comets <ul><li>Although Kepler’s laws were intended to describe the motion of planets around the sun, the laws also apply to comets </li></ul><ul><li>Comets are good examples because they have very elliptical orbits </li></ul>HOME
  19. 19. Kepler’s Three Laws <ul><li>Orbit of each planet is an ellipse & Sun is at one focus </li></ul><ul><li>Equal areas in equal intervals of time </li></ul><ul><li>T ² = a ³ </li></ul>HOME
  20. 20. Contributions <ul><li>Kepler’s second law (equal area) helped Newton come up with his Law of Universal Gravitation </li></ul><ul><li>Motions of satellite and spacecraft in orbit near planets </li></ul>HOME
  21. 21. Interesting Applets <ul><li> </li></ul><ul><li>http://csep10.phys. utk . edu /astr162/ lect /binaries/visual/ kepleroldframe .html </li></ul><ul><li>http://www. ioncmaste .ca/homepage/resources/web_resources/CSA_Astro9/files/multimedia/unit4/ keplers _laws/ keplers _laws.html </li></ul>HOME
  22. 22. Works Cited <ul><li>Drennon, Bill. “Kepler’s laws.” Central Valley Christian High School. 14 March 1997. 23 May 2008. </li></ul><ul><li>Fendt, Walter. “Kepler’s First Law.” Java Applets on Physics. 18 January 2003. 23 May 2008. </li></ul><ul><li>Fendt, Walter. “Kepler’s Second Law.” Java Applets on Physics. 18 January 2003. 25 May 2008. </li></ul><ul><li>&quot;Johannes Kepler.&quot; World of Earth Science . Online. Thomson Gale, 2006. Reproduced in Biography Resource Center . Farmington Hills, Mich.: Gale, 2008. </li></ul><ul><li>“ Johannes Kepler: The Laws of Planetary Motion.” University of Tennessee. 25 May 2008. </li></ul>HOME
  23. 23. Works Cited II <ul><li>“ Kepler’s Laws.” Orbitessera. 26 May 2008 </li></ul><ul><li>&quot;Kepler's laws of planetary motion.&quot; Encyclopædia Britannica . 2008. Encyclopædia Britannica Online. 25  May  2008. </li></ul><ul><li>Nave, R. “Kepler’s Laws.” HyperPhysics. 25 May 2008. </li></ul><ul><li>Soper, Davison. “Kepler’s First Law.” University of Oregon. 2002. 23 May 2008. </li></ul><ul><li>Weisstein, Eric. “Kepler’s Third Law.” Eric Weisstein’s World of Physics. 2007. 26 May 2008. </li></ul>HOME