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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