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Historical Models of our Solar System and Kepler’s Laws of Planetary Motion

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##### Historical Models of our Solar System and Kepler’s Laws of Planetary Motion

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**Historical Models of our Solar Systemand Kepler’s Laws of**Planetary Motion**Geocentric Model**• Earth is center of our Solar System • Aristotle- Over 2000 years ago, • Unexplained on how planets appear to move backwards • Ptolemy- Planets move in small circles or epicycles**Heliocentric Model**• Sun is center of our Solar System • Copernicus- Over 450 years ago (1543 ad) • First to suggest heliocentric theory and vaguely mapped out the planets orbiting the sun in a circular orbit.**Galileo**• Supporter of Copernicus’s Heliocentric theory • House arrest • Observed moons orbiting Jupiter and theorized objects can revolve around other planets not just Earth**Solar System precisely measured**• Tycho Brahe- studied Solar System and made very accurate recordings of his observations • Tycho’s assistant, Kepler, used information for the details of orbits**Kepler’s Laws of Planetary Motion**1st Law - Law of Ellipses Each planet orbits the sun in a path called an ellipse or elongated circle An ellipse is a closed curve whose path is determined by 2 points or foci within the ellipse Focus 1 is the Sun and Focus 2 is a mathematical imaginary point Semi-major axis = ½ major axis or average distance from sun (AU)**Degree of elongation or shape of planet’s orbit**Ratio between the foci and length of major axis Circular = 0 Very elongated = 1 Eccentricity**2nd Law – Law of Equal Areas**• An imaginary line between the Sun and a planet sweeps out equal areas in equal times as the planet travels around the ellipse. • Perihelion (P) – a planet is closer to the sun • Aphelion (A) – a planet is further from the sun**3rd Law – Law of Periods**• Mathematical relationship P2 = a3 • a= semi-major axis (planets average distance from Sun measured in AU’s) • p= planet’s orbital period (time)**Newton**• Used Kepler’s Laws of planetary motion and published Principia for short. In this publication, considered to be the greatest piece of scientific literature ever written. • Contains Newton’s laws of motion including universal gravitation.**Einstein (1879-1955)**• Changed Newton’s gravitational theory based on findings of Mercury’s orbit. • Developed Theory of Relativity. It completely changed the way we study gravity and even changed our understanding of the universe.**Kepler’s Laws Simulations**Click http://www.physics.sjsu.edu/tomley/kepler.html Law of Ellipses– Change the size of the ellipse with the scrollbar Describe the eccentricity (number and shape) when you move scrollbar to the right. ____________________________________________________________________________ Describe the eccentricity (number and shape) when you move scrollbar to the left. ______________________________________________________________________________**Law of Equal Areas –What happens to the speed and distance**for the planet? Set eccentricity to be between .5 and .6 Describe the speed as the planet orbits the sun at eccentricity between .5 & .6. ____________________________________ Why does speed change when it approaches the sun? __________________________ __________________________________**Describe the distance a planet covers when it orbits the sun**at A) .0P to .1P and compare it to B) .4P to .5P. __________________________________ Why is the distance different? ___________________________________ Why is Kepler’s 2nd law called Equal Areas in Equal Time? _____________________________________________________________________**Law of Equal Periods –**Click on last option “different a, same e” (AU’s, eccentricity) Move the scrollbar to the right for two different a’s or AU’s Hint: 3.5 AU and 1 AU The larger a planet’s AU amount the ______________________ they are to the Sun and the __________________ their period of revolution (orbit) around the Sun.**Bibliography**• http://www.astro.umass.edu/~myun/teaching/a100/images/geocentric.jpg • http://www.physics.hku.hk/~nature/CD/regular_e/lectures/images/chap04/heliocentric.jpg • http://www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/galileo5.jpg • http://galileo.rice.edu/sci/brahe.html • http://www.asu.cas.cz/~had/tycho.jpg • http://cseligman.com/text/history/ellipse2.jpg • http://www.windows.ucar.edu/the_universe/uts/kepler3_small.gif • http://library.thinkquest.org/27585/frameset_intro.html • http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/imgrel/merc.gif • http://zebu.uoregon.edu/~soper/Orbits/eccentricity.gif • http://www.physics.hku.hk/~nature/CD/regular_e/lectures/images/chap04/geocentric.jpg • http://outreach.atnf.csiro.au/education/senior/cosmicengine/images/cosmoimg/keplerellipse.gif